Median of a set of data

The median of a set of data is the middle value after the data set has been ranked either in increasing or decreasing order. The symbol used for the median is x̃. We pronounce x̃ as "x-tilde."

Since the median is the middle value, it divides a ranked data set into two equal parts.

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

Finding the median of a set of data using a useful diagram

Find the median of a set of data

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 two middle 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 does indeed divide the set 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 very 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.

Finding the median of a set of data using a useful formula

Median = value of the [(n+1)/2]th term in a ranked 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 set 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 set is the 4.5th term.

The 4.5th term is between 40 and 50.

What number is between 40 and 50?

Since the number between 40 and 50 is 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, when data sets have outliers, the median is the preferred measure of central tendency.

Furthermore, the median always gives the center of the histogram or data set. The average does not always give the center of the data set.

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