Cumulative Frequency (Cambridge (CIE) IGCSE Maths)

The cumulative frequency of an item is the total frequency of all items that are less than or equal to the given item.

Cumulative frequency is a running total of the frequencies.

To find the actual frequency for a particular group from a cumulative frequency table, subtract the previous cumulative frequency from the cumulative frequency for the the group that you want.

E.g. to find the cumulative frequency for the group 40 ≤ x < 60, subtract the cumulative frequency from the group 0 ≤ x < 40 from the cumulative frequency for the group 0 ≤ x < 60: .

To draw a cumulative frequency diagram:

• For each group, plot the cumulative frequency at the endpoint of the group

• Join the points together with a smooth curve that is always increasing

False.

To draw a cumulative frequency diagram, you do not plot the midpoint of a group against its frequency. This is a mistake that students often make on the exam.

You plot the endpoint of a group against its cumulative frequency.

A typical cumulative frequency diagram is an 's-shaped' curve, e.g.

False.

A cumulative frequency diagram will never get closer to the x-axis.

If the total frequency is 100, you can use a cumulative frequency diagram to estimate the median value.

1. Draw a horizontal line from 50 () on the vertical axis to the curve.

2. Draw a vertical line down from this point on the curve to the horizontal axis.

The value on the horizontal axis is an estimate of the median.

To estimate the lower quartile using a cumulative frequency diagram:

1. Divide the total frequency by 4.

2. Draw a horizontal line from that result on the vertical axis to the curve.

3. Draw a vertical line down from this point to the horizontal axis.

The number on the horizontal axis is an estimate for the lower quartile.

False.

If you follow those steps you have found the number of data items that are less than or equal to the specified value.

To find the number of data items that are greater than the value, you need to subtract the number of data items that are less than or equal to the specified value from the total number of data items.