Median, Quartiles And Percentiles (Ungrouped Data)

We have learnt that the median is the middle value when a set of data is arranged in order of increasing magnitude. We will now consider lower quartiles and upper quartiles.

The median divides the data into a lower half and an upper half.

The lower quartile is the middle value of the lower half.

The upper quartile is the middle value of the upper half.

Example :

Find the median, lower quartile and upper quartile of the following numbers.

12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25

Solution:

First, arrange the data in ascending order:

Median (middle value) = 22

Lower quartile (middle value of the lower half) = 12

Upper quartile (middle value of the upper half) = 36

If there is an even number of data items, then we need to get the average of the middle numbers:

Example:

Find the median, lower quartile, upper quartile, interquartile range and range of the following numbers.

12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25, 65

Solution:

First, arrange the data in ascending order:

Lower quartile or first quartile =

Median or second quartile =

Upper quartile or third quartile =

Interquartile range = Upper quartile – lower quartile

= 39 – 13 = 26

Range = largest value – smallest value

= 65 – 5 = 60

When evaluating the quartiles, always remember to first arrange the data in increasing order.

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