the Median of a data record is the centervalue after the record has been sorted in either ascending or descending order. The symbol used for the median is x̃. We pronounce x̃ as “x-tilde”.

Since the median is the mean, it divides an ordered data set into two equal parts.

There are two ways to find the median. The first way to find it is to follow the diagram below.

Find the median of a data set with the help of a useful chart

Find the median of a data set

example 1

Find the median of this data set.

15 7 12 3 6 10

Sort the data

3 6 7 10 12 15

How many values? There are 6 values, so the number of values ​​is even.

The median is the average of the two middle numbers.

The middle two numbers are 7 and 10.

Average = (7 + 10) / 2 = 8.5

The median is 8.5

3 6 7 8.5 10 12 15

There are 3 values ​​on the right and 3 values ​​on the left, so the median actually divides the amount into two equal parts.

Example # 2

Find the median of this data set.

11 7 11 4 12 2 6

Sort the data

2 4 6 7 11 11 12

How many values? There are 7 values, so the number of values ​​is odd.

The median is the value in the middle

The value in the middle is 7, so the median is 7

The second way to find the median is to use the following formula.

Find the median of a data set with a useful formula

Median = value of the [(n+1)/2] term in an ordered data set with n equal to the number of values.

Example # 3

Find the median of this data set.

5 6 4 9 2 4 7

Sort the data

2 4 4 5 6 7 9

The number of values ​​is 7

(7 + 1) / 2 = 4

The median of this amount is the 4th term.

Starting from 2, the fourth term is 5, so the median is 5.

Example # 4

Find the median of this data set.

50 60 40 90 20 40 70 30

Sort the data

20 30 40 40 50 60 70 90

The number of values ​​is 8

(8 + 1) / 2 = 4.5

The median of this amount is 4.5. Term.

The 4.5. Term is between 40 and 50.

Which number is between 40 and 50?

Since the number is between 40 and 50 45, the median is 45.

Median versus average

The main difference between the median and the average is that, unlike the average, the median is not affected by outliers.

Therefore, for data sets with outliers, the median is the preferred measure for the central tendency.

In addition, the median always indicates the center point of the histogram or data set. The average does not always indicate the midpoint of the data set.



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