Imagine a class
of 23 children standing in line in order of their height with the
shortest to the left and the tallest to the right. Then the height
of the 6th child, the child of a quarter of the way along, is called
the lower quartile. Similarly height of the 18th child, three-quarters
of the way along, is called upper-quartile.

In general, if there
are N numbers, then the lower quartile is the value of the 1/4
(N + 1)th Number and the upper quartile is the value of the 3/4
(N + 1)th Number. For large population these can be taken as the values
of the 1/4 Nth and 3/4 Nth and 3/4 Nth numbers.

The values of the
quartiles can be found from a cumulative frequency diagram of the
data. The example shows the cumulative frequency diagram of the
weights of the 200 children on entry to a large secondary school.
The lower quartile approximates to the weight of the 50th child
in order, and the upper quartile approximates to the weight of the
150th child. Statistics which divide the observations in a numeric
sample into 4 intervals, each containing 25% of the data. The lower,
middle, and upper quartiles are computed by ordering the data from
smallest to largest and then finding the values below which fall
25%, 50%, and 75% of the data. The middle quartile is usually called
the Median. The point one quarter or three quarters of the way through
a set of data.