What is a Median? Definition and Examples


What is a median? A median is the number in the middle for a set of data when the data are arranged in order form least to greatest or from greatest to least. 

For example, the median of the data set below is 56 because 56 is the value right in the middle.

45    48    56    60    63  

What is the median though if you remove 63 from the data set?

45    48    56    60

The value in the middle is not there this time because the number of values is even.

Just find the value between 48 and 56 mathematically by taking the average of 48 and 56.

(48 + 56) / 2 = 104 / 2 = 52

The median is 52

How to find the median:

If the number of values in the set is odd, just locate the number in the middle.

If the number of values in the set is even, just take the average of the two numbers in the middle of the data set. 

Median

Real life examples showing what the median is and how to find it


Example #1

The price for 1 scoop of ice cream on a cone at 10 different ice cream shops is shown below. What is the median price?

2.50   3.75   2.25   4   1.75   3   1   3.25   2.75   1.50

Order the data set from greatest to least

4   3.75   3.25   3   2.75   2.50   2.25   1.75   1.50  1

Since the number of values in the set is even, the median is between 2.75 and 2.50.

(2.75 + 2.50) / 2 = 5.25 / 2 = 2.625

The median is 2.625

Example #2

The yearly salary for 5 people are shown below in USD . What is the median salary?

70,000   55,000  30,000  73,000  60,000

Order the set from greatest to least

73,000  70,000  60,000   55,000  30,000  

Since the number of values in the set is odd, just locate the number in the middle.

The number in the middle is 60,000, so the median salary is 60,000

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