Frequency distribution

In statistics, a frequency distribution is a list of the values that a variable takes in a sample. It shows the number of times each value appears. 

For example, imagine that 100 people are asked whether they agree with a statement, and have to give an answer on a scale from 1 to 5, where 1 means they strongly agree and 5 means they strongly disagree. The frequency distribution of their responses might look like this:

AnswerDegree of agreementNumber1Strongly agree252Agree somewhat353Not sure204Disagree somewhat155Strongly disagree5

A simple table like this might not work well in some cases. For example, if a variable can take any value within a range (for example, a measurement like height), or if the number of possible values is too large, making a simple table would be difficult or even impossible. In this case, we could instead use ranges of values. For example, the frequency table for the heights of the students in a class might look like the table below.

Height rangeNumber of students 4.5–5.0 feet255.0–5.5 feet355.5–6 feet206.0–6.5 feet20

 Applications 
It can be simpler to work with a frequency distribution of data instead of the raw data. There are simple algorithms that can calculate median, mean (statistics) and standard deviation using these tables.

Statistical hypothesis testing is based on the assessment of differences and similarities between frequency distributions. This assessment involves measures of central tendency or averages, such as the mean and median, and measures of variability or statistical dispersion, such as the standard deviation or variance.

A frequency distribution is said to be skewed when its mean and median are different. The kurtosis of a frequency distribution is the concentration of scores at the mean, or how peaked the distribution appears if depicted graphically—for example, in a histogram. If the distribution is more peaked than the normal distribution it is said to be leptokurtic; if less peaked it is said to be platykurtic.

Frequency distributions are also used in frequency analysis to crack codes and refer to the relative frequency of letters in different languages.

Category:Statistics