Median, Quartiles And Percentiles (Grouped Data)

For grouped data, we can obtain the quartiles from the cumulative frequency graph of the distribution.

Example :

The following cumulative frequency graph shows the distribution of marks scored by a class of 40 students in a test.

Use the graph to estimate

a) the median mark b) the upper quartile

c) the lower quartile d) the interquartile range

Solution:

a) Median corresponds to the 50th percentile i.e. 50% of the total frequency.

50% of the total frequency =

From the graph, 20 on the vertical axis corresponds to 44 on the horizontal axis. The median mark is 44.

b) The upper quartile corresponds to the 75th percentile i.e. 75% of the total frequency.

75% of the total frequency =

From the graph, 30 on the vertical axis corresponds to 52 on the horizontal axis. The upper quartile is 52.

c) The lower quartile corresponds to the 25th percentile i.e. 25% of the total frequency.

25% of the total frequency =

From the graph, 10 on the vertical axis corresponds to 36 on the horizontal axis. The lower quartile is 36.

d) The interquartile range = upper quartile – lower quartile

= 52 – 36 = 16

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