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Revision:Cumulative Frequency

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Cumulative Frequency

Contents

Cumulative Frequency

This is the running total of the frequencies. On a graph, it can be represented by a cumulative frequency polygon, where straight lines join up the points, or a cumulative frequency curve.


Example

Frequency: Cumulative frequency:
4 4
6 10 (= 4 + 6)
3 13 (= 4 + 6 + 3)
2 15 (= 4 + 6 + 3 + 2)
6 21 (= 4 + 6 + 3 + 2 + 6)
4 25 (= 4 + 6 + 3 + 2 + 6 + 4)

When dealing with a cumulative frequency curve, n is the cumulative frequency (25 in the above example). Therefore the median would be (25+1)/2th value = the 13th value. To find this, on the cumulative frequency curve, find 13 on the y-axis (which should be labelled cumulative frequency). The corresponding 'x' value is an estimation of the median.


The Median Value

The median of a group of numbers is the number in the middle, when the numbers are in order of magnitude. For example, if the set of numbers is 4, 1, 6, 2, 6, 7, 8, the median is 6:

1, 2, 4, 6, 6, 7, 8      (6 is the middle value when the numbers are in order).

If you have n numbers in a group, the median is the (n + 1)/2 th value. For example, there are 7 numbers in the example above, so the median is the (7 + 1)/2 th value = 4th value. The 4th value is 6.


Quartiles

If we divide a cumulative frequency curve into quarters, the boundary for the lower quarter is referred to as the lower quartile, the value in the middle gives the median and the boundary at the upper quarter is the upper quartile.

A set of numbers may be as follows: 8, 14, 15, 16, 17, 18, 19, 50. The mean of these numbers is 19.625 . However, the extremes in this set (8 and 50) distort this value. The interquartile range is a method of measuring the spread of the middle 50% of the values and is useful since it ignores the extreme values.

The lower quartile is (n+1)/4 th value (n is the number of pieces of data, i.e. 8 in this case) and the upper quartile is the 3(n+1)/4 the value. The difference between these two is the interquartile range (IQR).


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