Mathematics, what is the median,

Median refers to the symbol value of each unit in the distribution sequence, arranged in order of size and located in the middle position. In other words, the median is the symbol value located at the center of the symbol value sequence. There are 50% units above and below the median, indicating that the median represents the approximate level of the phenomenon of the symbol value being in the middle, so it is a position average.

There are different methods to calculate the median according to two different situations: ungrouped and grouped series.

(A) the median calculation method of ungrouped series

First of all, we must determine the position number of the median in the series. No matter whether the series is odd or even, the number of positions of the median is certain. Then the mark value of the intermediate position number is taken as the intermediate value.

For example, if there is a series: 2 1, 23, 45, 46, 67, 72, 83. This series is odd, in which the number of digits is: (bits), and the flag value 46 corresponding to the fourth digit is the median.

There is another series: 23, 24, 25, 25, 26, 27, 27, 28, 29, 55. The series is even, in which the number of bits is: (bit), that is, between the fifth and sixth bits, so its corresponding flag value is the average of the flag values of the fifth and sixth bits, that is, the average of 26 and 27:, which is the median of the series.

(B) the calculation method of median of grouping series

Grouping series has single grouping and group spacing grouping, so its calculation method is as follows:

① Calculation method of single grouping order.

Firstly, a formula is used to determine the number of digits of the median, and this formula is used to determine the group to which the median belongs. The flag value of this group is the median. For example, students in a class are grouped by age, as shown in Table 5-9.

Table 5-9 Students in a class are grouped by age

Group by age

Number of people (persons)

Cumulative times

2 1

eight

2 1

seven

three

eight

Combination plan

First calculate the number of digits (bits) of the median, and then determine the group to which the median belongs. The number of intermediate positions is 29.5 bits. Judging from the cumulative number of times, it should be in the age of 19, so the age of 19 is the median. However, some people think that the median calculated by single grouping does not meet the definition of median, because the units on both sides of the median are not equal. As shown in this example, the number of cells below the median 19 is 27, and the number of cells above the median is 10.

(2) Calculation method of interval sequence.

For example, the weight data of a class of boys are shown in Table 5- 10.

Table 5- 10 Weight Data of Boys in a Class

By weight

group

number of people

(person)

Upward accumulation

Downward accumulation

49~5 1

5 1~53

53~55

55~57

57~59

59~6 1

6 1~63

four

2 1

six

four

Forty nine

108

120

126

122

102

six

First calculate the number of digits in the median: (bits). From the upward accumulation or downward accumulation, it can be determined that the median belongs to 55 ~ 57 groups, and then the median is calculated according to the lower limit formula or the upper limit formula.

Lower bound formula:

Upper limit formula:

Symbols in the formula:-median;

-the lower limit of the median;

-Upper limit of median;

-the median number of times;

—— Cumulative times below the median group;

-Cumulative times higher than the median group;

-is the total number of times;

-Interval between median groups.

According to the lower bound formula:

According to the upper limit formula: