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Definition: Cumulative frequency is found by adding each frequency to the sum of the previous ones down the frequency table. Cumulative frequency can be used to estimate the median and the quartiles. It is important to note that the last cumulative frequency in a table must be equal to the sum of the frequencies of the given data.

The Cumulative Frequency Curve or The Ogive:

A cumulative frequency curve or ogive can be drawn by plotting the cumulative frequencies against the corresponding upper class boundaries.

The curve that is formed by joining the points is the ogive. An ogive has a distinctive S-shape curve. The cumulative frequency curve is used to estimate the median and quartiles of both discrete and continuous data.

Median

In order to estimate the median using the cumulative frequency curve or ogive mark the middle point on the cumulative frequency axis and trace it horizontally to the point of intersection on the curve then trace it vertically to the item axis and then take the reading.

Thus the median divides the distribution into two equal parts. If “n” is large as the total frequency, then the median value = \( \frac{n}{2} \scriptsize th \; value \! \!\), however if the total frequency “n” is not large ( ≤ 50) then, median value = \( \frac{1}{2} \scriptsize (n + 1)th \; value. \)

Note that the median is denoted by Q2.

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