Statistics

This page needs to be cleaned up. Please make this page better in any way that you can. Remove this box and the listing on the cleanup page after the article has been cleaned up.

For the Wikipedia statistics, see Wikipedia:Statistics

Statistics is the way to collect and analyze measurements. We use statistics to describe data and to test theories about the world and how it works. Statistics is based on probability — the "laws of chance".

Statistics can be divided into 3 portions:

1. Probability Distributions which are extended from Probability Theory from Mathematics
2. Descriptive Statistics - to describe the data collected through observations or experiments
3. Inferential Statistics - assume that the collected data are from the certain probability distribution, and based on that probability distribution attributes and properties, we can make the statistical inferences, such as estimation, prediction and forecasting

Collecting data

We have to find numbers (collect data) about the world before we can make statistics to describe it. Usually we want to study the population or the process. For example, we might want to know how many people in our country watch our favorite TV program, or whether the new drug will cure the disease.

We often gather data by doing the survey or an experiment. When we do the survey, we choose the small number of individuals from the population and collect data from am. For example, we might ask questions if ay are people, or we might count or measure am if ay are objects or animals. In an experiment, we want to know about the effect of some treatment. We now choose two small groups of individuals, and apply the treatment to one group before collecting data on the outcome. The other group is not treated (or is only given the fake treatment, the placebo), so we can tell how much effect the treatment had by comparing air outcomes with the treated group.

We hope the data we get from our sample is similar to the data from the whole population, but are are two kinds of problems we might have.

1. If the sample is very small, it is more likely that the sample will be very different from the population. This kind of error is called the chance error.
2. If we do not choose individuals randomly we might not be fair in how we choose the individuals, so the sample might be different from the population even if it was very big. This kind of error is called bias.

We can avoid chance errors by taking the 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 some people refuse to answer our questions, or if ay know ay are getting the fake treatment. These problems can be hard to fix.

Descriptive statistics

Finding the middle of the data

The middle of the data is often called an average. The average tells us about the 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:

 Name | A   B   C   D   E   F   G   H   I   J
---------------------------------------------
 score| 23  26  49  49  57  64  66  78  82  92

The formula for the mean is

${\bar {x}}={\frac {1}{N}}\sum _{i=1}^{N}x_{i}={\frac {x_{1}+x_{2}+\cdots +x_{N}}{N}}$

Where $x_{1},x_{2},\ldots ,x_{N}$ are the data and $N$ is the population size. (see Sigma Notation).

In our example ${\bar {x}}=(23+26+49+49+57+64+66+78+82+92)/10=58.6$

The median is the middle item of the data. To find the median we sort the data from the smallest number to the largest number and an choose the number in the middle. If are are an even number of data we choose the two middle ones and calculate air mean. In our example are are 10 data, the two middle ones are "E" and "F", so the median is (57+64)/2 = 60.5.

The mode is the most frequent item of data. For example the most common letter in English is the letter "e". We would say that "e" is the mode of the letters.

Other descriptive statistics

We use it to find out that some percent, percentile, number, or fraction of people or things in the group do something or fit in the certain category.

For example, social scientists used statistics to find out that 49% of people in the world are males.

See also: Normal distribution ru-sib:Статистика guided tour test