Cumulative frequency graphs

The Maths Habit Handout to print

A tap is filling a bath. Every minute you check how much water is in it.

Can the amount ever go down? Why?

No: water is only ever added

Cumulative frequency
A running total of the frequencies.

Time (seconds)FrequencyCumulative
frequency
0 < t ≤ 105
10 < t ≤ 208
20 < t ≤ 307

The cumulative frequencies are 5, 14 and 26.
What is the frequency of the last class?

12

The ages of the people at a party. Work out the cumulative frequency for

Age (years)Frequency
0 < a ≤ 108
10 < a ≤ 2015
20 < a ≤ 3020
30 < a ≤ 4012
40 < a ≤ 505

  1. 0 < a ≤ 10

    8

  2. 10 < a ≤ 20

    23

  3. 20 < a ≤ 30

    43

  4. 30 < a ≤ 40

    55

  5. 40 < a ≤ 50

    60
Mass (kg)FrequencyCumulative
frequency
0 < m ≤ 2055
20 < m ≤ 401217
40 < m ≤ 601532
60 < m ≤ 80840
Height (cm)FrequencyCumulative
frequency
140 < h ≤ 1506
150 < h ≤ 16014
160 < h ≤ 17016
170 < h ≤ 1804
Mass (kg)FrequencyCumulative
frequency
0 < m ≤ 205
20 < m ≤ 4012
40 < m ≤ 6015
60 < m ≤ 808
MarkFrequencyCumulative
frequency
0 < m ≤ 1033
10 < m ≤ 20912
20 < m ≤ 301325
30 < m ≤ 40530

Cumulative frequency worksheet, page 1

Answer sheet

  1. The cumulative frequencies for five classes are 7, 19, 34, 46 and 50. Work out the five frequencies.

    7, 12, 15, 12, 4

  2. Leo plots each point at the middle of its class. Why is this wrong?

    The total is only reached at the top of the class

  1. Complete the cumulative frequency column of the table.

    3, 12, 26, 32
    Time (t s)FrequencyCumulativefrequency0 < t ≤ 10310 < t ≤ 20920 < t ≤ 301430 < t ≤ 406

  2. Which point is plotted for the class 20 < t ≤ 30 in question 1?

    (30, 26)

  3. The cumulative frequencies of four classes are 5, 13, 29 and 36. Find the frequency of the third class.

    16
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