Why is the mean to the right of the mode and median?

The median means that when a set of data is arranged in order of size, the value in the middle position, that is, for a variable, 50% of the cases have a value below the median. In layman's terms, half of all observations in the sample are larger than the median, and half are smaller than the median. There are two scenarios when calculating the median:

When the number of samples (n) is an odd number, all the observations of the samples are arranged in order from small to large (or large to small), and the value in the middle position is the median. When the sample is even, the average of the values in the middle two positions is the median. The median is suitable for ordinal variables, and for fixed-distance variables, the simple way to group the observations first is to use the median of the middle group as the median of the variable. �

The mean, also known as the mean, is equal to the sum of all n observations of the sample divided by the sample size. Suppose n observations are ,...... by x1, x2x n denotes the mean value by x and the formula for the mean is:

Here equation (2) is for grouped data, where x represents the value of a variable, f represents the frequency of the variable falling in a certain group, and represents the sum of all values (or the sum of all groups).

The mean is the most typical and commonly used statistic, which is suitable for both distance and ratio variables. The average is also the most "meaningful" statistic, and it can be seen as the "equilibrium" or "center of gravity" of the data. Because the median is calculated using all the data, it contains the most information compared to the mode and median.

However, the mean is greatly affected by extreme values, and individual extreme values will directly affect the well-known change of the mean, which is not as stable as the median and mode. Therefore, when the distribution of the survey data is relatively regular, there are no extreme values, or the deviation of the data from the center is not very large, the mean is a good description statistic; If there are extreme values or large deviations in the distribution steps, the mode and median must also be used to supplement the description.

Mode, median, and mean are all descriptions of the center of distribution of variables, with the mean being the most commonly used.

The mode is the number that occurs the most times, while the median is the one in the middle after a series of numbers, two if it is even, one for the leaning number, and the mean is the average after all the numbers

Mode, median, and mean are the three main measures that describe trends in a dataset. When the data are normally distributed, the three measurements are exactly equal; When the distribution is skewed, the three show differences. If it is a right-skewed distribution, then; If it is a left-biased distribution, then.

Generally speaking, the distance between the mean and the median is about 1 2 of the distance between the median and the mode. This law can be roughly expressed as:

In fact, it doesn't matter, the mode is the number with the most, the median is the middle number, and the mean is the average, which has something to do with the number, and the three have little to do with it.

1. The average is calculated by calculation, so it will change with each change in the data.

2. The median is obtained by sorting, and it is not affected by the two extreme values of the maximum and minimum The median combines the advantages of the average and the median to a certain extent, and has a relatively good representativeness. Changes in some data have no effect on the median, and it is often used to describe the concentrated trend of a set of data when individual data changes significantly. In addition, because the median is in the middle of the numerical ranking of a set of data, 3. The mode is also a representative number of data, reflecting the concentration of a group of data In daily life, such as "best", "most popular", "most satisfied", etc., are related to the mode, which reflects the most common tendency

The mean, median, and mode all have their own advantages and disadvantages Mean: (1) All data from the whole group are required to calculate;

2) Susceptibility to extreme values in the data

Median: (1) It is only necessary to arrange the data in order;

2) It is not susceptible to extreme values in the data

Mode: (1) obtained by counting;

2) It is not susceptible to extreme values in the data