Calculate the mean, median and mode of the following groups respectively. 10, 20, 80, 40, 30, 90, 50, 40, 50, 40

Calculate the mean, median and mode of the following groups respectively. 10, 20, 80, 40, 30, 90, 50, 40, 50, 40

Average: 45
Median: 40
Mode: 40

Why is the median larger than the mode

The mean, median and mode are all statistics to describe the average level of data, and they have their own characteristics. We are familiar with the mean. The median describes the medium level of a group of data, and the mode describes the most frequent occurrence of a group of data
One of the obvious advantages of the average is that it can make use of the characteristics of all data, and is relatively easy to calculate. In addition, in mathematics, the average is the statistic to minimize the sum of squares of errors, that is to say, using the average to represent the data can minimize the quadratic loss. Therefore, the average is a commonly used statistic in mathematics. But the average also has some shortcomings, For example, in a company, if the salary of the manager and the deputy manager is particularly high, the average salary of all members of the company will also be very high. But in fact, except the manager and the deputy manager, the average salary of the rest is not very high, Median and mode may be more reasonable statistics to describe the average wage level of all employees in this unit. The characteristics of median and mode are that they can avoid extreme data, but the disadvantage is that they do not fully use the information reflected by the data. Because each statistic has its own characteristics, we need to choose the appropriate statistic according to the actual problems
Of course, it's not necessary to use the median when extreme data appear. Generally, there is a statistical method to think that the data does not come from the population, so we should remove the data. For example, why do we need to remove the highest score and the lowest score from the familiar diving competition scores? We think that the two scores do not come from the population, It can't represent the judge's taste. So remove it and then average the rest of the data
It should be pointed out that most of the data we are dealing with now are symmetrical data, and the data conform to or approximately conform to the normal distribution. At this time, the mean (mean), median and mode are the same (as shown in the figure below)

Class 81 average 85, median 80, mode 85, class 82 average 85, median 80, mode 85

The data of the two classes are exactly the same. Of course, the two classes are as good as each other