The median is the middlemost observation, when the data is arranged in ascending or descending order. It divides the total frequency into two equal parts. Median is a position average. For a given set of observations, the sum of deviations is minimum when the deviation is taken from the median.

To find the median for individual observations:

First arrange the numbers in ascending order or descending order.

If the number of observations is odd, the median is in the position in the arrangement.

If the number of observations is even, the median is the arithmetic mean of the values in the and positions in the arrangement.

Example 1: The heights of the members of a basketball team are as follows: 69", 78", 75", 73", 72", 71", 75", 70", and 74". Find the median height of the players.

Solution: Arrange the heights in ascending order:

69"

70"

71"

72"

73"

74"

75"

75"

78"

Since there are 9 numbers, the median will be in the = 5th position.

Therefore, the median is 73". This tells us that half of the players (50%) have a height less than 73" and 50% have a height greater than 73".

Example 2: The 10 members of a babysitters club charged the following rates per hour for babysitting: $4.50, $5.50, $4.75, $5.75, $10.00, $6.50, $6.00, $8.25, $9.00 and $6.50. Find the median rate per hour charged by the babysitters club members.

Solution: Arrange the rates in ascending order:

$4.50

$4.75

$5.50

$5.75

$6.00

$6.50

$6.50

$8.25

$9.00

$10.00

Since there are an even number of terms (10), the median will be the average of the 5th and 6th terms.

Next, average these amounts:

Therefore, the median rate charged by the babysitters is $6.25. Half of the members charge less than $6.25 per hour and 50% charge more than $6.25 per hour.

Advantages and disadvantages

It is useful in case of open-end distribution.

It is not influenced by the presence of extreme values.

The absolute sum of the deviation of observations from the median is minimum.

It can be located by inspection and the graphical method gives curves.

Median is not capable of algebraic treatment.

It is affected by sampling fluctuations.