The Seventh-day Adventists and other churches disagree with some of these views. They argue that the custom of meeting for worship on Sunday originated in paganism, specifically Sol Invictus and Mithraism (in which sun god worship took place on Sunday). This is therefore an explicit rejection of the commandment to keep the "seventh" day holy. Instead, they keep Saturday as the Sabbath as a memorial to God's work of creation believing that none of the Ten Commandments can ever be destroyed. Seventh-day Sabbatarians claim that the seventh day Sabbath was kept by the majority of Christian groups until the 2nd and 3rd century, by most until the 4th and 5th century, and a few thereafter, but because of opposition to Judaism after the Jewish-Roman wars, the original custom was gradually replaced by Sunday as the day of worship. The history of these changes is certainly not altogether lost regardless of any belief in a suppression of the facts by a conspiracy of the pagans of the Roman Empire and the clergy of the Catholic Church.
Jews had come to be hated in the Roman Empire after the Jewish-Roman wars. This led to the criminalization of the Jewish Sabbath. Hatred of Jews is apparent in the Council of Laodicea (4th Century AD) where Canon 37–38 states: "It is not lawful to receive portions sent from the feasts of Jews or heretics, nor to feast together with them." and "It is not lawful to receive unleavened bread from the Jews, nor to be partakers of their impiety." In keeping with this rejection of the Jews, this Roman council also criminalized the Jewish Sabbath as can be seen in Canon 29 of the Council Laodicea: "Christians must not Judaize by resting on the Sabbath, but must work on that day, rather honoring the Lord's Day; and, if they can, resting then as Christians. But if any shall be found to be judaizers, let them be excommunicated from Christ."
In the Gospel of Mark 2:28 Jesus says 'the Son of Man is lord even of the sabbath'.
Statistics
Statistics is a branch of applied mathematics that deals with collecting, organising, analysing, reading and presenting data. Descriptive statistics make summaries of data. Inferential statistics makes predictions. Statistics helps in the study of many other fields, such as science, medicine, economics, psychology, politics and marketing. Someone who works in statistics is called a statistician. In addition to being the name of a field of study, the word "statistics" can also mean numbers that are used to describe data or relationships.
The first known statistics are census data. The Babylonians did a census around 3500 BC, the Egyptians around 2500 BC, and the Ancient Chinese around 1000 BC.
Starting in the 16th century mathematicians such as Gerolamo Cardano developed probability theory, which made statistics a science. Since then, people have collected and studied statistics on many things. Trees, starfish, stars, rocks, words, almost anything that can be counted has been a subject of statistics.
Before we can describe the world with statistics, we must collect data. The data that we collect in statistics are called measurements. After we collect data, we use one or more numbers to describe each observation or measurement. For example, suppose that we want to find out how popular a certain TV show is. We can pick a group of people (called a "sample") out of the total population of viewers. Then we ask each viewer in the sample how often they watch the show. The sample is data that one can see, and the population is data that one cannot see (assuming that not every viewer in the population are asked). For another example, if we want to know whether a certain drug can help lower blood pressure, we could give the drug to people for some time and measure their blood pressure before and after.
Numbers that describe the data one can see are called descriptive statistics. Numbers that make predictions about the data one cannot see are called inferential statistics.
Descriptive statistics involves using numbers to describe features of data. For example, the average height of women in the United States is a descriptive statistic: it describes a feature (average height) of a population (women in the United States).
Once the results have been summarized and described, they can be used for prediction. This is called inferential statistics. As an example, the size of an animal is dependent on many factors. Some of these factors are controlled by the environment, but others are by inheritance. A biologist might therefore make a model that says that there is a high probability that the offspring will be small in size—if the parents were small in size. This model probably allows to predict the size in better ways than by just guessing at random. Testing whether a certain drug can be used to cure a certain condition or disease is usually done by comparing the results of people who are given the drug against those who are given a placebo.
Most often, we collect statistical data by doing surveys or experiments. For example, an opinion poll is one kind of survey. We pick a small number of people and ask them questions. Then, we use their answers as the data.
The choice of which individuals to take for a survey or data collection is important, as it directly influences the statistics. When the statistics are done, it can no longer be determined which individuals are taken. Suppose we want to measure the water quality of a big lake. If we take samples next to the waste drain, we will get different results than if the samples are taken in a far-away and hard-to-reach spot of the lake.
There are two kinds of problems which are commonly found when taking samples:
We can reduce chance errors by taking a larger sample, and we can avoid some bias by choosing randomly. However, sometimes large random samples are hard to take. And bias can happen if different people are not asked, or refuse to answer our questions, or if they know they are getting a fake treatment. These problems can be hard to fix. See standard error for more.
The middle of the data is called an average. The average tells us about a typical individual in the population. There are three kinds of average that are often used: the mean, the median and the mode.
The examples below use this sample data:
The formula for the mean is
formula_1
Where formula_2 are the data and formula_3 is the population size (see also Sigma Notation).
This means that one calculates the mean by adding up all the values, and then divide by the number of values. For the example above, the mean is:
formula_4
The problem with the mean is that it does not tell anything about how the values are distributed. Values that are very large or very small change the mean a lot. In statistics, these extreme values might be errors of measurement, but sometimes the population really does contain these values. For example, if there are 10 people in a room who make $10 per day and 1 who makes $1,000,000 per day. The mean of the data is $90,918 per day. Even though it is the average amount, the mean in this case is not the amount any single person makes, and thus is not very useful for some purposes.
The mean described above is the "arithmetic mean". Other kinds are useful for some purposes.
The median is the middle item of the data. For a given data formula_5, this is sometimes written as formula_6. To find the median, we sort the data from the smallest number to the largest number, and then choose the number in the middle. If there is an even number of data, there will not be a number right in the middle, so we choose the two middle ones and calculate their mean. In our example above, there are 10 items of data, the two middle ones are "57" and "64", so the median is (57+64)/2 = 60.5.