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|---|---|---|---|---|---|
stat895
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/895.png
|
An opaque bag contains 5 red balls and m blue balls. These balls are identical in all respects except for their color. A student conducted the following experiment: randomly draw one ball from the bag, note its color, then return it and mix thoroughly before repeating the trial. Based on the recorded data from the ball-drawing experiment shown in the table, the estimated value of m is ________.
|
20
|
NULL
|
free_form
|
stat896
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/896.png
|
In order to implement the 'double reduction' policy, a school in Dongying City conducted a questionnaire survey on the after-school homework duration of junior high school students. The homework durations of 15 students are summarized in the table below. What is the mode of this dataset?
|
70
|
NULL
|
free_form
|
stat897
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/897.png
|
A company decided to recruit one advertising planner. The scores (in points) of an applicant's three skill tests are as follows: Test Items: Creativity, Comprehensive Knowledge, Language Expression Test Scores: 88, 80, 75. If the final score of the applicant is determined based on the scores of Creativity, Comprehensive Knowledge, and Language Expression in a ratio of 5:3:2, what is the applicant's final score?
|
83
|
NULL
|
free_form
|
stat898
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/898.png
|
The germination test results of a certain type of rapeseed under the same conditions are shown in the table below:
Batch size 50 100 300 400 600 1000
Germination frequency 45 96 283 380 571 948
The germination probability of this type of rapeseed is approximately __________. (Result accurate to 0.01)
|
0.95
|
NULL
|
free_form
|
stat899
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/899.png
|
A certain shooter has their shooting performance recorded under the same conditions as follows:
Shooting Attempts: 20, 40, 100, 200, 300, 400, 1000
Number of shots hitting above 9 rings: 15, 30, 75, 150, 240, 310, 801
Frequency of shots hitting above 9 rings: 0.75, 0.85, 0.75, 0.75, 0.8, 0.78, 0.801
What is the probability of hitting above 9 rings (round the result to 0.1) ______?
|
0.8
|
NULL
|
free_form
|
stat9
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/9.png
|
As shown in the figure, the areas of the 8 sectors on the spinner are all equal. If the spinner is spun once randomly, what is the probability that the pointer will point to a number greater than 6 when it stops?
|
1/4
|
NULL
|
free_form
|
stat90
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/90.png
|
To promote the implementation of the 'Double Reduction' policy, effectively address the issue of student burden, and strictly control homework time, the policy plans to investigate the daily homework duration of all 560 students at the school. Investigators randomly selected a portion of students for a survey and created a statistical chart based on the results. According to the chart, estimate the number of students at the school who spend at least 1 hour on homework each day after the implementation of the 'Double Reduction' policy: _______.
|
160 students
|
NULL
|
free_form
|
stat900
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/900.png
|
In order to enhance environmental education, a middle school organized students to participate in a volunteer activity to collect used batteries. The following statistics are based on a random sample of 40 students and the number of used batteries they collected:
Number of used batteries/pieces: 4 5 6 7 8
Number of students/people: 9 11 11 5 4
If the data is represented using a pie chart, the central angle of the sector representing 'collecting 8 used batteries' is equal to __________°.
|
36
|
NULL
|
free_form
|
stat901
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/901.png
|
A community launched a 'Save Every Drop of Water' campaign. To promote water-saving activities, the water-saving situation of one month was surveyed by selecting 20 households out of 1000 households in the community. The data is shown in the following table:
Water saved/m³ 0.2 0.25 0.3 0.4 0.5
Number of households 2 4 6 7 1
Estimate the total amount of water saved by the 1000 households in the community in one month. The answer is approximately ________m³.
|
325
|
NULL
|
free_form
|
stat902
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/902.png
|
Grandma Li opened a convenience store in a residential area, supplying three types of food: A, B, and C. Due to the different shelf lives of these foods, Grandma Li pays close attention when restocking to avoid spoilage from unsold items. To help Grandma Li solve this problem, Xiao Ming randomly recorded the sales of A, B, and C over a week as shown in the table below:
Food Type | A | B | C
Sales Quantity (pieces) | 15 | 45 | 30
According to the statistical data, the reasonable ratio of quantities for restocking food types A, B, and C is __________.
|
1:3:2
|
NULL
|
free_form
|
stat903
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/903.png
|
The students of a certain class are divided into three groups based on different interests in extracurricular reading, as shown in the table below. Fill in the values of a and b in the table, and determine the value of a, which should be ____________.
|
7
|
NULL
|
free_form
|
stat904
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/904.png
|
A company recruits employees using a combination of written exams and interviews, with both scores having a maximum of 100 points. The scores of three candidates with IDs ①, ②, and ③ are as follows:
Written exam scores: 85, 89, 90
Interview scores: 85, 92, 90
According to the company's regulations, the written score and interview score are weighted at 80% and 20%, respectively, to calculate an overall score. What is the highest score among these three candidates?
|
90.6
|
NULL
|
free_form
|
stat905
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/905.png
|
"Scientific use of eyes, protecting vision" is a specific expression of teenagers cherishing life. The vision check data of 48 students in a class is as follows:
Vision 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0
Number 2 3 6 9 12 8 5 3
The mode of the vision of these 48 students is ________.
|
4.7
|
NULL
|
free_form
|
stat906
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/906.png
|
On March 12, 2023, which marks the 45th Arbor Day in China, a forestry department conducted a study to estimate the survival rate of a certain type of sapling under specific conditions. A large number of these saplings were transplanted under the same conditions, and their survival statistics are as follows:
| Number of Saplings Transplanted (units) | 100 | 1000 | 5000 | 10000 | 70000 |
| --------------------------------------- | ------| -------| -------| --------| ------- |
| Number of Saplings Surviving (units) | 87 | 883 | 4455 | 7029 | 63022 |
| Survival Rate of Transplanted Saplings | 0.8700| 0.8820 | 0.8910 | 0.8930 | 0.9002 |
Estimate the survival rate of this type of sapling under normal conditions. (Result accurate to 0.01)
|
0.90
|
NULL
|
free_form
|
stat907
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/907.png
|
Reading Fireworks, Appreciating the Beauty of Truth and Goodness. On March 6, 2023, the 11th reading event of Yangcheng County was held at the Thai Group Champagne Academy. The event, themed 'Opening a Book to Explore the World and Knocking on Radiant Splendor,' aimed to cultivate participants' most genuine infectiousness and oral power through situational recitation and reading sharing, and also held a recitation competition as part of the event to better implement the educational policy of 'five education strategies.' Below is the score situation of three contestants, A, B, and C, each graded by audience ratings and judge ratings:
Evaluator Score Weight A B C
Audience (Students) 40% 95 points 90 points 93 points
Judges (Teachers) 60% 90 points 95 points 92 points
After the final aggregation, the contestant with the highest total score is ____ (A, B, or C).
|
B
|
NULL
|
free_form
|
stat908
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/908.png
|
A company intends to hire a creative director and conducted three quality tests on two candidates. The test scores for each candidate are shown in the table below:
Candidate | Innovation Ability | Computer Skills | Public Relations Skills
A | 72 | 50 | 88
B | 85 | 45 | 82
If the scores for Innovation Ability, Computer Skills, and Public Relations Skills are weighted in a ratio of 3:2:3 to determine the final score for each candidate, then ________ (fill in 'A' or 'B') will be hired.
|
B
|
NULL
|
free_form
|
stat909
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/909.png
|
The germination ability of coffee tree seeds weakens as the storage time increases. When stored for up to three months, the germination rate is about 95%; from three months to five months, the germination rate gradually decreases to 75%; and from five months to nine months, the germination rate gradually decreases to 25%. The Academy of Agricultural Sciences recorded the germination of a batch of coffee tree seeds, and the results are shown as follows: Based on this, deduce the storage time of this batch of coffee tree seeds among the following three periods (fill in 'within three months', 'three to five months', or 'five to nine months').
|
Three to five months
|
NULL
|
free_form
|
stat91
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/91.png
|
As shown in the figure, in a small square grid with a side length of 1, the three vertices of △ABC are all on the grid points. If a needle is thrown into the square grid, the probability of it landing inside △ABC is ________________.
|
5/16
|
NULL
|
free_form
|
stat910
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/910.png
|
In a shooting team selection training for a shooting competition, the performance of two athletes, A and B, stood out. It was decided to select one of them to participate in the competition. Their shooting results over 10 tests are analyzed as shown: Athlete | Average Score (rings) | Variance A | 9.1 | 0.69 B | 9.1 | 0.03 Past competitions have shown that an average score above 9.0 rings is highly likely to win a medal. If a participant is to be selected to ensure the medal win, who is most likely to be chosen (write 'A' or 'B')?
|
B
|
NULL
|
free_form
|
stat911
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/911.png
|
Enjoy the good times, read at the right time. On the occasion of the 28th World Book Day, on April 20, the 2023 Henan Provincial Youth Student Reading Action Launch Ceremony and the Henan Province Primary and Secondary School Book-Fragrant Campus Construction On-Site Meeting were held in Puyang City, hosted jointly by eight departments including the Provincial Department of Education. A certain middle school in Henan actively responded to the call by updating and implementing the education policy of cultivating students in five aspects comprehensively (moral, intellectual, physical, aesthetic, and labor education). The following are the frequencies of competition scores for contestants A, B, and C as shown in the table. Each contestant's score is composed of audience ratings and judge scores: After the final tally, the contestant with the highest total score is _____ (fill in A, B, or C).
|
B
|
NULL
|
free_form
|
stat912
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/912.png
|
Eyes are the windows to the soul. To protect students' eyesight, Qihang Middle School conducts vision tests for students every semester. The table below shows the right eye vision test results of 39 students in a certain class. For this set of vision data, the median is:
|
4.6
|
NULL
|
free_form
|
stat913
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/913.png
|
The following table shows Xiaohong's scores in a 'Sunshine Sports' competition:
| Project | Running | Fancy Rope Skipping | Rope Skipping |
| Score | 90 | 80 | 70 |
When evaluating the total score, running accounts for 50%, fancy rope skipping accounts for 30%, and rope skipping accounts for 20%. What is Xiaohong's final score?
|
83 points
|
NULL
|
free_form
|
stat914
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/914.png
|
A company wants to hire an employee. Three candidates, A, B, and C, underwent tests in three aspects: comprehensive knowledge, work experience, and language skills. Their scores in each test are shown in the table below:
| Category | Comprehensive Knowledge | Work Experience | Language Skills |
|----------|--------------------------|-----------------|-----------------|
| A | 85 | 70 | 80 |
| B | 90 | 80 | 70 |
| C | 70 | 85 | 75 |
If the total score of each candidate is calculated using a weight ratio of 5:2:3 for comprehensive knowledge, work experience, and language skills respectively, and the candidate with the highest total score is hired, who will be selected?
|
B
|
NULL
|
free_form
|
stat915
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/915.png
|
To prepare for the 12th Sports Games of the city, a county conducted a shooting test for four athletes: A, B, C, and D. The average score x̄ (unit: points) and variance s² (unit: points) of their shooting test results are shown in the table below. Based on the data in the table, to select an athlete with good performance and stable results to participate in the competition, the choice should be _______________.
|
D
|
NULL
|
free_form
|
stat916
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/916.png
|
A study group conducted an experiment by tossing a bottle cap, and the experimental data is organized as follows: Cumulative tosses: 50, 100, 200, 300, 500, 1000; Times the cap landed face up: 24, 54, 108, 159, 264, 550; Frequency of cap landing face up: 0.480, 0.540, 0.540, 0.530, 0.528, 0.550. Below are three inferences: ① Based on the experimental results, it can be inferred that it is highly likely the bottle cap is not uniformly made; ② The result of the 2000th experiment is definitely: 'Face up'; ③ As the number of experiments increases, the probability of 'face up' will approach 0.53. Which of these is correct? ( )
|
①③
|
NULL
|
free_form
|
stat917
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/917.png
|
The table below records the results of four athletes in several 100-meter sprint selection trials. Now it is necessary to select an athlete with good performance and stable results to participate in the city sports meeting 100-meter sprint project. The choice should be __________.
|
B
|
NULL
|
free_form
|
stat918
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/918.png
|
A factory produced 1000 light bulbs. To determine the lifespan of these 1000 light bulbs, 50 light bulbs were randomly sampled and their lifespans (in hours) were recorded as follows:
| Lifespan (hours) | <1000 | ≥1000 and <1600 | ≥1600 and <2200 | ≥2200 |
| Number of Bulbs | 5 | 10 | 17 | 18 |
Based on the given data, estimate the number of light bulbs out of the 1000 whose lifespan is at least 2200 hours. Answer: ______ bulbs.
|
460
|
NULL
|
free_form
|
stat919
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/919.png
|
March 14th is International Mathematics Day. A school conducted a fun mathematics knowledge competition (scored out of 100) and randomly selected the competition scores of 50 students (the competition did not have a full score). After organizing the data, the following information table was obtained. Information 1: Frequency distribution table of the competition scores of 50 students. Information 2: The scores in the interval 70 <= x < 80 are: 74, 71, 73, 74, 79, 76, 74, 73, 72, 75. Based on the information, answer the following questions: The mode of the scores in the range 70 <= x < 80 is ___________, and the median score of the 50 students is ___________.
|
74 78
|
NULL
|
free_form
|
stat92
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/92.png
|
The frequency distribution histogram (incomplete) of the weights of 40 students in a certain class is shown in the figure. The class width is _______ kg.
|
5
|
NULL
|
free_form
|
stat920
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/920.png
|
The statement 'Thoroughly implementing the action for seed industry revitalization' in the 20th National Congress report will give a strong boost to research, selection, and promotion of 'China's seeds.' The corn research institute of Shanxi Agricultural University (Provincial Academy of Agricultural Sciences) has bred 'Jinnu No. 20,' which has been promoted and planted in 26 provinces across the country, yielding great harvests. Below are part of the data obtained by the research team under the same experimental conditions, studying the germination rate of this grain seed: Germinated: 28, 72, 125, 200, 457, 814, 1187, 1258 Number of seeds: 30, 75, 130, 210, 480, 856, 1250, 2300 Based on the data above, estimate the probability of germination for this grain seed under these experimental conditions. (Round your result to 0.01.)
|
0.95
|
NULL
|
free_form
|
stat923
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/923.png
|
1. The study monitor conducted a survey on the extracurricular reading habits of the students in the class over a week. The statistical results based on the reading time are shown in the table below. What is the value of α? ________.
|
20
|
NULL
|
free_form
|
stat924
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/924.png
|
The results of a germination experiment of a certain kind of rice seeds under the same conditions are as follows:
Number of seeds per batch: 1000 1200 1000 1500 500 500
Number of germinated seeds: 904 942 728 922 390 485
Germination frequency: 0.904 0.785 0.728 0.615 0.78 0.97
What is the estimated germination frequency of this rice seed (rounded to 0.1)?
|
0.9
|
NULL
|
free_form
|
stat925
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/925.png
|
The table records the scores of two athletes, A and B, in the first 5 rounds of the 40-shot women's air rifle competition. Which athlete performed more consistently in the first 5 rounds?
|
A
|
NULL
|
free_form
|
stat926
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/926.png
|
A batch of sports shoes was inspected, and the number of qualified sports shoes was recorded to obtain the frequency table of qualified sports shoes as follows:
Number of pairs sampled (pairs) | 20 | 40 | 60 | 80 | 100 | 300 | 1500
Number of qualified pairs | 17 | 38 | 57 | 76 | 95 | 285 | -
Qualification rate | 0.85 | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 | 0.95
Approximately how many defective pairs are there out of the estimated 1500 pairs of sports shoes?
|
75
|
NULL
|
free_form
|
stat927
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/927.png
|
A certain school evaluates outstanding class collectives, scoring comprehensively from four aspects: 'study,' 'hygiene,' 'discipline,' and 'participation in activities,' with full scores of 100 for each aspect. The corresponding proportions are shown in the table below:
| Item | Study | Hygiene | Discipline | Activity Participation |
| ------------ | ----- | ------- | ---------- | ----------------------- |
| Proportion | 40% | 30% | 20% | 10% |
The scores of a certain class for these four aspects are 83, 82, 73, and 80, respectively. What is the comprehensive score of the class for these four aspects?
|
80.4
|
NULL
|
free_form
|
stat928
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/928.png
|
To understand the vision condition of middle school students in a certain region, a random sample of 500 middle school students from the region was surveyed. The sample data was organized into the table below: Vision 4.7 and below 4.7 ~ 4.9 4.9 ~ 5.0 5.0 ~ 5.2 Above 5.2 Number of Students 98 96 85 98 123 Based on the survey results, estimate the number of middle school students in the region with vision no less than 4.9 among 20,000 students: ______.
|
8800
|
NULL
|
free_form
|
stat929
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/929.png
|
As shown in the table, Xiaoming conducted the 'throwing thumbtacks experiment' and obtained data. The estimated probability of 'the point of the tack not touching the ground' is ________.
|
0.61
|
NULL
|
free_form
|
stat93
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/93.png
|
As shown in the figure, assuming that a point can be freely taken in the figure, what is the probability that this point falls in the shaded area?
|
4/9
|
NULL
|
free_form
|
stat930
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/930.png
|
In a physical education class, the results of 'one-minute rope skipping' for 7 students are shown in the table (units: skips per minute):
Name: Li Ming, Wang Hong, Liu Li, Wang Jia, Zhang Qiang, Zhao Tong, Zhou Xin
Results: 178, 183, 180, 181, 183, 183, 178
What is the median of this data set?
|
181
|
NULL
|
free_form
|
stat931
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/931.png
|
The average and variance of the jump rope test scores of four students (Jia, Yi, Bing, Ding) over five attempts are shown in the table. Considering both these statistical measures comprehensively, which student do you think performed the best?
|
Yi
|
NULL
|
free_form
|
stat932
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/932.png
|
A school is selecting a work to recommend for the 'Science and Technology Innovation' competition. Four works, A, B, C, and D, were quantitatively scored, with specific scores (percentage system) as shown in the table. If the total score is calculated with a weight of 60% for innovation and 40% for practicality, which of A, B, C, and D should be recommended?
|
B
|
NULL
|
free_form
|
stat933
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/933.png
|
A youth volleyball team consists of 12 players, and their ages are shown in the table below:
Age (years) | 18 | 19 | 20 | 21 | 22
Number | 3 | 5 | 2 | 1 | 1
What is the median age of these 12 players? Fill in the blank: ________ years.
|
19
|
NULL
|
free_form
|
stat934
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/934.png
|
A certain agricultural research station conducted a germination test for a crop's seeds under the same conditions. The results (partial data) are shown in the table below:
Seed count n 100 200 300 400 500
Germinated seeds count m 94 180 269 360 451
Germination frequency m/n (accurate to 0.001) 0.940 0.895 0.893 0.900 0.902
Estimate the probability that a randomly selected seed will germinate under the same conditions ( ).
|
0.90
|
NULL
|
free_form
|
stat935
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/935.png
|
Based on the above data, estimate the probability of this player making a free throw shot. (Accurate to 0.1)
|
0.5
|
NULL
|
free_form
|
stat936
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/936.png
|
A city broadcasting and television bureau intends to recruit a broadcaster. Two candidates, A and B, went through two quality tests, and their scores for the two tests are shown in the table below. Based on practical needs, the bureau calculates the total scores of the two candidates by weighting their interview and general knowledge test scores in a 3:2 ratio. _____ (fill in 'A' or 'B') will be hired.
|
B
|
NULL
|
free_form
|
stat937
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/937.png
|
Perform a repeated experiment of randomly tossing a paper cup and obtain the following data:
Total tosses | 100 | 200 | 400 | 800 |
Frequency of cup mouth up | 20 | 40 | 88 | 172 |
Estimate the probability of the cup mouth facing up when randomly tossing the paper cup.
|
0.22
|
NULL
|
free_form
|
stat938
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/938.png
|
A youth volleyball team has 12 players, with their ages shown in the following table: What is the median age of these 12 players? ______ years.
|
19
|
NULL
|
free_form
|
stat939
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/939.png
|
During the Mid-Autumn Festival, it is traditional in China to admire the moon and eat mooncakes. A certain department conducted a sampling inspection on a batch of mooncakes produced by a food company, with results as follows:
Number of mooncakes sampled: 50, 100, 200, 500, 1000, 2000
Number of first-grade products: 45, 92, 194, 474, 951, 1900
What is the approximate probability of randomly selecting a first-grade mooncake from this batch? (Accurate to 0.01)
|
0.95
|
NULL
|
free_form
|
stat94
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/94.png
|
A school has 300 students participating in a tree-planting activity, requiring each student to plant ≥1 tree. After the activity, 20 students were randomly selected to investigate the number of trees each of them planted, and a line chart was drawn accordingly. The average number of trees planted per student among these 20 students is ________ trees.
|
3.3
|
NULL
|
free_form
|
stat940
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/940.png
|
The germination test results of a certain type of mung bean under the same conditions are as follows:
Each batch grain count n: 100 500 1000 5000 8000 10000
Germination frequency m: 94 466 928 4628 7424 9281
Germination rate (m/n) (accurate to 0.001): 0.94 0.932 0.928 0.926 0.928 0.928
Based on the table, estimate the probability of germination of this type of mung bean ________ (accurate to 0.01).
|
0.93
|
NULL
|
free_form
|
stat941
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/941.png
|
A school implemented an activity called 'Save Electricity, Protect the Environment.' To assess the electricity savings in one month, a random sample of 40 students was selected from the 300 eighth-grade students. The monthly electricity savings for each of their households were recorded and tabulated as shown below. Estimate the total electricity savings of the households of all 300 eighth-grade students in one month, approximately _______ kW·h.
|
1140
|
NULL
|
free_form
|
stat942
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/942.png
|
Historically, some individuals have conducted thousands or even tens of thousands of coin-tossing experiments. The results of some of these experiments are shown in the table below:
Tosses 2048 4040 12000 20000
Frequency of 'Heads' 0.5181 0.5069 0.5006 0.5001
From this, calculate the probability of getting 'Heads' when repeatedly tossing a coin ________ (Round the result to one decimal place).
|
0.5
|
NULL
|
free_form
|
stat943
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/943.png
|
Every March 12th is Arbor Day in China. A local forestry department wants to investigate the survival rate of a certain type of seedling under specific conditions. The following statistical data was collected during the transplanting process of the seedlings:
Number of transplanted seedlings (units) | 400 | 1500 | 3500 | 7000 | 9000 |
Number of surviving seedlings after transplantation (units) | 325 | 1336 | 3263 | 6520 | 8120 |
Survival frequency of transplanted seedlings | 0.81 | 0.89 | 0.93 | 0.93 | 0.90 |
Based on this, estimate the probability of survival for this type of seedling under these conditions (rounded to 0.01).
|
0.90
|
NULL
|
free_form
|
stat944
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/944.png
|
The school conducted a survey of 20 male students on how many times they played basketball in a given week, with the results shown in the table below. The average number of times these 20 students played basketball that week is ______.
|
4
|
NULL
|
free_form
|
stat945
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/945.png
|
A certain middle school conducted a survey to understand the extracurricular reading habits of students by randomly investigating the average daily reading time of some students. The statistical results are shown in the table below. In this survey, the median of the students' reading time data is ______.
|
1
|
NULL
|
free_form
|
stat946
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/946.png
|
A study group conducted an experiment on 'estimating probability using frequency,' calculated the frequency of a certain outcome, and created the following table. The approximate probability of this outcome occurring is ______ (accurate to 0.1).
|
0.3
|
NULL
|
free_form
|
stat947
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/947.png
|
A certain shooter has recorded their shooting records under the same conditions as follows:
Number of shots: 20 80 100 200 400
Number of times hitting 'above 8 rings': 18 68 82 163 328
Frequency of hitting 'above 8 rings' (results rounded to two decimals): 0.90 0.85 0.82 0.82 0.82
Based on the stability of the frequency, estimate the probability that the shooter hits 'above 8 rings' in a single shot: ______.
|
0.82
|
NULL
|
free_form
|
stat948
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/948.png
|
In order to further promote quality education, enrich campus cultural life, cultivate artistic sentiment, and showcase the achievements of middle school students in art education, a school conducted an instrumental music competition in October with the theme 'Play the Main Melody of the Era, Showcase Campus Style.' After several rounds of selection, the school finally decided to choose one student from four candidates (A, B, C, and D) to represent the school in the district-level instrumental competition. The average scores (in points) and variance (in points) of the performances of the four students are shown in the table. If a student with good performance and stable status is to be selected, then ______ should be chosen.
|
A
|
NULL
|
free_form
|
stat949
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/949.png
|
The Chinese shooting team is among the best in the world. A shooting team plans to select one athlete from four candidates: Jia, Yi, Bing, and Ding, to participate in an international shooting competition. During the selection process, each person shoots 10 times, and their average scores and variances are calculated as shown in the table below: Based on the provided data as well as their average performance and stability, who will be selected as the athlete? ______.
|
Yi
|
NULL
|
free_form
|
stat95
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/95.png
|
As shown in the figure, a geometric body is composed of 8 identical small cubes. Now, one of the four small cubes marked ①, ②, ③, ④ is randomly removed. What is the probability that the new geometric body has the same front view as the original geometric body? ________.
|
1/4
|
NULL
|
free_form
|
stat950
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/950.png
|
There are a total of 40 balls in an opaque box, among which there are α red balls. These balls have no other differences besides color. To estimate the value of α, Xiaoying conducts a ball-drawing experiment. She mixes the balls in the box thoroughly, randomly draws one ball, records its color, and then puts it back in the box, repeating the process continuously. The experimental data is recorded as follows:
Number of draws 10 20 30 40 50 60
Number of red balls drawn 6 11 18 23 31 36
Based on the above data, the estimated value of α is ______.
|
24
|
NULL
|
free_form
|
stat951
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/951.png
|
A class of 10 students participated in community volunteer service activities during the holidays. Their community service hours are as follows:
Service hours (hours): 2 4 6
Number of people: 2 5 3
The median of the community service hours for these 10 students is ________ hours.
|
4
|
NULL
|
free_form
|
stat952
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/952.png
|
The 19th Asian Games were held in Hangzhou from September 23 to October 8, 2023. During the preparation period for the Asian Games, a basketball player conducted free throw training. The table records his data under certain conditions. Based on this, the probability of this basketball player successfully making a free throw can be estimated to be approximately ____.
|
0.8
|
NULL
|
free_form
|
stat953
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/953.png
|
A technology company conducts technical development, under the same conditions, to test the qualification rate of a batch of products produced using new technology. The following table represents a set of statistical data during the testing process:
| Number of Products Extracted | 500 | 1000 | 1500 | 2000 | 2500 | 3000 | 3500 |
| Number of Qualified Products | 476 | 967 | 1431 | 1926 | 2395 | 2873 | 3340 |
| Frequency of Qualified Products | 0.952 | 0.967 | 0.954 | 0.963 | 0.958 | 0.961 | 0.955 |
Estimate the probability that a product from this batch is qualified: ______.
|
0.959 (the answer is not unique)
|
NULL
|
free_form
|
stat954
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/954.png
|
The table below shows the experimental data of several mathematicians 'tossing a coin':
| Experimenter | Mori Osamu | Buffon | Feller | Pearson | Pearson |
| ------------ | ---------- | ------ | ------ | ------- | ------- |
| Number of tosses | 2048 | 4404 | 10000 | 12000 | 24000 |
| Times 'Heads' appeared | 1041 | 2207 | 5000 | 6000 | 12000 |
| Frequency | 0.508 | 0.501 | 0.500 | 0.500 | 0.500 |
Based on the above data, estimate the probability P of a coin landing 'heads up'. (Accurate to 0.1)
|
0.5
|
NULL
|
free_form
|
stat955
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/955.png
|
A landscaping company plans to purchase a batch of saplings with an approximate height of 1.8 meters for street greening. Four sapling production bases have submitted bids (the price per sapling is the same). The procurement team randomly inspected 100 saplings from each base, and the data obtained are as follows:
| Average Height of Saplings (unit: meters) | Variance |
|------------------------------------------|----------|
| Base A: 1.6 | 0.5 |
| Base B: 1.8 | 0.2 |
| Base C: 1.8 | 0.1 |
| Base D: 1.9 | 0.5 |
Please help the procurement team make a recommendation. They should purchase saplings from base _____.
|
C
|
NULL
|
free_form
|
stat956
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/956.png
|
A sportswear store of a certain brand analyzed last week's sales situation as shown in the table; the manager decided to stock more red sportswear this week. The manager made this decision based on the ________ of this dataset.
|
Mode
|
NULL
|
free_form
|
stat958
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/958.png
|
A shooting team is preparing to select athletes to participate in a shooting competition. The table below shows the scores (in rings) of one athlete during 10 shooting attempts:
Score 7.5 8.5 9 10
Frequency 2 2 3 3
What is the average score of this athlete's shooting performance (in rings)?
|
8.9
|
NULL
|
free_form
|
stat959
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/959.png
|
A store sold 20 pairs of a certain type of women's shoes in a week. The sales volume of women's shoes in various sizes is shown in the table below. What is the mode of the sold shoe sizes? _______ size.
|
36
|
NULL
|
free_form
|
stat96
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/96.png
|
In order to understand the height situation of 300 male students in a certain middle school, a certain number of male students were randomly selected for height measurement. The collected data (all in integer centimeters) were then sorted and used to plot the frequency distribution histogram shown in the figure. Based on this, it can be estimated that the number of male students in the school whose heights are between 169.5 and 179.5 is ______.
|
108
|
NULL
|
free_form
|
stat960
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/960.png
|
It is known that the probability of an electric current normally passing through each electronic component [______] within a certain time period is P. (In one trial, the state of each electronic component has two possibilities: on or off, and these two states are equally likely). As shown in the figure, the probability of the electric current normally passing between A and B within a certain time period is ________.
|
1/4
|
NULL
|
free_form
|
stat961
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/961.png
|
Seeds are the origin of all growth and the foundation of human food production. The results of germination tests for a certain type of corn seed under the same conditions are as follows:
| Total number of seeds | 500 | 1000 | 1500 | 2000 | 3000 | 4000 |
|-----------------------|-------|------|-------|-------|-------|-------|
| Number of seeds germinated | 464 | 930 | 1398 | 1866 | 2790 | 3712 |
| Germination frequency | 0.928 | 0.93 | 0.932 | 0.933 | 0.93 | 0.928 |
Estimate the germination probability of this type of corn seed as _________ (accurate to 0.01).
|
0.93
|
NULL
|
free_form
|
stat962
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/962.png
|
A school organized a series of activities titled 'The Chinese Dream · Aerospace Love.' Below are the scores (in points) for various events from Classes A and B of Grade Eight. If the final score is determined by the weights of 4:3:3 for the knowledge quiz, speech contest, and panel creation, the class with the higher final score is ____.
|
Class B
|
NULL
|
free_form
|
stat963
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/963.png
|
7. In an opaque bag, there are several balls that are identical except for their color. During the ball-drawing experiment, the balls are shuffled thoroughly, and one ball is randomly drawn, its color is recorded, and then it is returned to the bag. This process is repeated continuously. The table below represents a set of statistical data from the experiment:
Number of draws (n): | 54 | 99 | 111 | 150 | 200 |
Number of white balls drawn (m): | 34 | 59 | 66 | 90 | 123 |
What is the probability of drawing a white ball? (Result accurate to 0.1)
|
0.6
|
NULL
|
free_form
|
stat964
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/964.png
|
In a school's 'Save Every Drop of Water' campaign, 10 students from a group of 200 were selected to report their families' monthly water-saving data. The data was compiled into the table on the right. Estimate the total amount of water saved by the families of these 200 students in one month, approximately _______ t.
|
240
|
NULL
|
free_form
|
stat965
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/965.png
|
A mathematics interest group conducts repeated experiments of 'randomly tossing a thumbtack' and obtains the following data after multiple trials:
Repeated Trials: 10 50 100 500 1000
Instances of the Tack Pointing Up: 5 15 35 200 400
Based on this, estimate the probability that the tack points up in a single random toss. (Result accurate to 0.1)
|
0.4
|
NULL
|
free_form
|
stat966
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/966.png
|
A student recorded the number of calls and the duration of each call in October of this year, and created a frequency distribution table:
Call duration x (minutes): 0≤x<5 5≤x<10 10≤x<15 15≤x<20 x≥20
Number of calls (frequency): 21 14 8 5 2
What is the frequency of call durations exceeding 10 minutes?
|
0.3
|
NULL
|
free_form
|
stat967
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/967.png
|
The table below shows the scores of Xiaoming participating in a 'Youth Style' talent display competition:
| Item | Calligraphy | Dance | Singing |
|-------|-------------|-------|---------|
| Score | 85 | 90 | 70 |
For the final score calculation, the weights are as follows: Calligraphy accounts for 40%, Dance accounts for 30%, and Singing accounts for 30%. What is Xiaoming's final score?
|
82 points
|
NULL
|
free_form
|
stat968
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/968.png
|
In 2023, China's space launch frequency once again reached 60+! In this year, Chinese space enthusiasts continuously made history and took firm steps forward on the road to building a strong space-faring nation. The school organized a space knowledge competition, and Class 8 (1) decided to hold a preliminary contest to select participants. Below is a table showing the average scores and variances for the top four students in the class before the competition. If we are to select a student with good performance and stable status, who should we choose? ______.
|
B
|
NULL
|
free_form
|
stat969
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/969.png
|
The table below records the results of a player shooting at the free-throw line:
Number of shots n 50 100 150 200 250 300
Number of hits m 30 50 80 101 130 160
Frequency of hits m/n 0.60 0.50 0.53 0.51 0.52 0.53
The probability of this player making a shot is approximately ________ (rounded to 0.1).
|
0.5
|
NULL
|
free_form
|
stat97
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/97.png
|
A dart is randomly thrown onto the regular hexagonal dartboard shown in the diagram. If the dart has an equal chance of landing on any point, what is the probability that it lands in the shaded area?
|
1/3
|
NULL
|
free_form
|
stat970
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/970.png
|
The testing center evaluates a newly launched smartphone in the market based on four aspects: operating system, hardware specifications, screen size, and battery life. The scores for each item are as follows:
Evaluation Items | Operating System | Hardware Specifications | Screen Size | Battery Life
Scores (out of 10) | 7 | 8 | 9 | 6
Finally, the comprehensive score is calculated based on the weights 3:3:2:2 for the four scores respectively. What is the comprehensive score of this smartphone in ________ points?
|
7.5
|
NULL
|
free_form
|
stat971
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/971.png
|
As shown in the table, 100 seeds germinate each day:
Days 1 2 3 4 5
Number of germinated seeds (seeds) 10 65 15 5 5
To illustrate the percentage of seeds germinating each day relative to the total number of seeds, you could use a ______ type of statistical chart; to reflect the germination trend of the seeds, you could use a ______ type of statistical chart.
|
Pie chart Line chart
|
NULL
|
free_form
|
stat972
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/972.png
|
In order to raise environmental protection awareness, on June 5th, 'World Environment Day,' a research group on the 'Controlling Noise Pollution' topic, composed of a number of 'Environmental Protection Little Guards,' under the guidance of environmental bureau staff, conducted a sample survey at 40 noise measurement points in the city regarding noise levels at a certain time (unit: dB). The survey data were processed (assuming the measured data are positive integers) and presented in the frequency distribution table below (incomplete): If there are a total of 20 measurement points in the city, then approximately how many measurement points at this moment have a noise level of 75-dB?
|
60
|
NULL
|
free_form
|
stat973
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/973.png
|
The scores of 10 shooting athletes in the first round of competition are shown as follows:
Score: 7 8 9 10
Number of athletes: 3 2 3 2
What is their average score for this round of competition?
|
8.4
|
NULL
|
free_form
|
stat974
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/974.png
|
The age distribution of 12 players in a middle school basketball team is as follows:
Age (years): 14 15 16 17 18
Number of players: 4 3 2 2 1
What is the average age of the players on this team?
|
16
|
NULL
|
free_form
|
stat975
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/975.png
|
The age distribution of 10 students in a math interest group in a certain class is as follows:
Age (years) | 12 | 13 | 14 | 15 |
Number | 1 | 4 | 4 | 1 |
What is the average age of these 10 students? ________.
|
13.5 years
|
NULL
|
free_form
|
stat976
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/976.png
|
In the Olympic selection trials of the Chinese diving team, the average scores and standard deviations (S) of four athletes, A, B, C, and D, are shown in the table. Since the overall level of the Chinese diving team is high, one athlete should be selected from them to compete. The choice should be ______.
|
B
|
NULL
|
free_form
|
stat977
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/977.png
|
The table below shows Xiaoying's physical education scores for this semester. The average score of these three items is _________ points. If the school stipulates that the final score is calculated based on the ratio of 3:3:4 for these three items, then Xiaoying's final physical education score is _________ points.
|
84 84.5
|
NULL
|
free_form
|
stat978
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/978.png
|
In the Olympic selection trials for the Chinese diving team, the average scores and standard deviation S of four athletes, A, B, C, and D, are shown in the table below. Since the overall level of the Chinese diving team is high, which athlete should be selected for the competition?
|
B
|
NULL
|
free_form
|
stat980
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/980.png
|
In order to understand the water usage of residents in a certain community, a random survey was conducted on 10 households' monthly water consumption. The results are as follows:
Monthly water consumption (t): 10 13 13 14 18
Number of households: 2 3 2 2 1
What is the mode of the monthly water consumption for these 10 households? ______ What is the median? ______
|
13 13.5
|
NULL
|
free_form
|
stat981
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/981.png
|
A type of wheat grain was tested for germination under the same conditions, and the results are shown in the table below:
Number of test grains: 100 200 300 400 500
Number of germinated grains: 93 186 279 372 465
Germination frequency m: 0.93 0.93 0.93 0.93 0.93
Estimate the probability that a randomly selected grain will germinate ________. (Round the result to two decimal places)
|
0.95
|
NULL
|
free_form
|
stat982
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/982.png
|
A basketball player is standing at the free-throw line for fixed-point shooting training. He recorded the number of shots and corresponding successful shots during training, as shown in the table below:
Number of Shots | 10 | 100 | 200 | 300 | 500 | 1000
Successful Shots | 7 | 81 | 160 | 243 | 401 | 800
From the data in the table, it can be concluded that the probability of this player successfully making a shot is ________. (Round the result to two decimal places)
|
0.80
|
NULL
|
free_form
|
stat983
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/983.png
|
To prepare for the sports meet, four shooters (A, B, C, and D) were tested for their shooting performance. The average score and variance of their results are shown in the following table:
Table content:
----------------
A B C D
x 9.68 9.99 9.69 9.62
y 5.40 8.92 3.08 3.80
----------------
Based on the data in the table, to choose a shooter who performs well and is consistent for the competition, the choice should be ________.
|
D
|
NULL
|
free_form
|
stat984
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/984.png
|
The GDP of China in different years is as follows:
Year
1970 1980 1990 2000 2010 2020
GDP (billion yuan) 2279.7 4587.6 18872.9 100280.1 412119.3 1015986.2
Please choose an appropriate type of statistical chart to reflect the achievements of China's economic development. The ______ statistical chart is most suitable.
|
line chart
|
NULL
|
free_form
|
stat985
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/985.png
|
Farmer Xiao Ming randomly selected 20 loquat trees from each of the three varieties A, B, and C. The average yield x (in kilograms) and variance S^2 (in kilograms^2) for each tree are shown in the table below. He plans to choose one of the three varieties of loquat trees for planting, aiming for high and stable yield. Which variety should he choose?
|
A
|
NULL
|
free_form
|
stat987
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/987.png
|
In the 2023 physical education exam, a certain middle school in Pan County conducted a statistical analysis of the physical education scores of eight students in a particular class and created the following table. Based on the table, the median score of this data set is ___ points.
|
45.5
|
NULL
|
free_form
|
stat988
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/988.png
|
In an opaque bag, there are 5 balls of two different colors, red and white. A study group conducts an experiment in which a ball is randomly drawn from the bag, the color is recorded, and then the ball is returned to the bag. This process is repeated multiple times. Below is a set of statistical data from the ongoing activity:
| Number of Draws (m) | 100 | 200 | 500 | 1000 | 2000 | 5000 |
| --------------------- |-----|-----|-----|------|------|------|
| Times White Ball is Drawn (n) | 59 | 116 | 301 | 601 | 1205 | 3008 |
| Frequency of Drawing White Ball \( n/m \) | 0.59 | 0.58 | 0.602 | 0.601 | 0.603 | 0.601 |
Estimate: When m is very large, the frequency of drawing a white ball will approach _____ (accurate to 0.1).
|
0.6
|
NULL
|
free_form
|
stat989
|
/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/989.png
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A technology company conducts research and development. Under the same conditions, the qualified rate of a batch of products produced using new technology is tested. Below is a set of statistical data from the testing process:
The number of products sampled (n) is 500, 1000, 1500, and 2000 respectively;
The number of qualified products (m) is 476, 943, 1419, and 1891 respectively;
The frequency of qualified products (m/n) is 0.95, 0.943, 0.946, and 0.945 respectively.
Estimate the probability of qualified products in this batch of products to ________ (accurate to 0.01).
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0.96
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NULL
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free_form
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stat99
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/home/yz979/scratch/chengye/math/data/original_set/statset/images/images/99.png
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As shown in the figure, in a 5×6 rectangular dartboard grid, every small square is identical except for its color, and the vertices of the small squares are called grid points. The center of the circular sector OAB and the endpoints of the arc are all grid points. Assuming that hitting each small square is equally likely (if the dart hits the boundary of the sector or misses the dartboard, it is thrown again), the probability of hitting the circular sector OAB (shaded area) in a single throw of the dart is:
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π/12
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NULL
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free_form
|
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