Cumulative-Frequency-Charts gcse Edexcel

Cumulative Frequency

What is cumulative frequency?

• Cumulative refers to a “running total” or “adding up as you go along”

• So in a table of grouped data

  • cumulative frequency means all of the frequencies for the different groups totalled up to the end of the group in a given row

• When working out cumulative frequencies you may see tables presented in two ways

  • A regular grouped data table with an extra column for cumulative frequencies

    • e.g. rows labelled 0 ≤ x < 20, 20 ≤ x < 40, 40 ≤ x < 60, etc

      	frequency	cumulative frequency
      0 ≤ x < 20	14	14
      20 ≤ x < 40	25	39 (because 14+25=39)
      40 ≤ x < 60	29	68 (because 14+25+29=68)
      60 ≤ x < 80	12	80 (because 14+25+29+12=80)

  • or a separate table where every group is relabelled as starting at the beginning (often zero)

    • e.g. rows labelled 0 ≤ x < 20, 0 ≤ x < 40, 0 ≤ x < 60, etc.

    • or x < 20, x < 40, x < 60, etc.

      	cumulative frequency
      0 ≤ x < 20 (or x < 20)	14
      0 ≤ x < 40 (or x < 40)	39
      0 ≤ x < 60 (or x < 60)	68
      0 ≤ x < 80 (or x < 80)	80

  • In the second type of table, you can subtract to find the individual frequencies

    • e.g. the frequency of the 20 ≤ x < 40 class interval is 39-14=25

    • the frequency of the 40 ≤ x < 60 class interval is 68-39=29

    • etc.

Cumulative Frequency Step Polygons

What is a cumulative frequency step polygon?

• A cumulative frequency step polygon is a way of representing discrete data

  • For grouped continuous data a cumulative frequency diagram would be used instead

How do I draw a cumulative frequency step polygon?

• This is best explained with an example

  • The numbers of eggs found in each nest in a survey of 50 American alligator nests are shown in the table below:

    Number of eggs	Frequency
    29	5
    30	6
    31	11
    32	15
    33	7
    34	6
    Total	50

  • Then the cumulative frequency is the running total of the frequencies

    Number of eggs	Frequency	Cumulative Frequency
    29	5	5
    30	6	5 + 6 = 11
    31	11	11 + 11 = 22
    32	15	22 + 15 = 37
    33	7	37 + 7 = 44
    34	6	44 + 6 = 50
    Total	50

• We can now draw the cumulative frequency step polygon

  • The cumulative frequency will always go on the vertical axis

    • The values in the data set will appear along the horizontal axis

  • The cumulative frequency is zero until we get to 29 eggs

    • So start at the point (29, 0)

  • Then the cumulative frequency jumps up to 5

    • Draw a vertical line from (29, 0) to (29, 5) to show this jump

  • Nothing changes until we get to 30 eggs

    • Draw a horizontal line from (29, 5) to (30, 5) to show this

  • At 30 eggs the cumulative frequency jumps up to 11

    • Draw a vertical line from (30, 5) to (30, 11) to show this jump

  • Continue the same way through the rest of the values in the table

    • The graph will end at the point (34, 50)

• Here is the final cumulative frequency diagram for the numbers of eggs

Cumulative Frequency Diagrams

What is a cumulative frequency diagram?

• A cumulative frequency diagram is a way of representing grouped continuous data

  • For discrete data a cumulative frequency step polygon would be used instead

• A cumulative frequency diagram can be used to estimate other statistical values

  • For example the median, quartiles or percentiles

How do I draw a cumulative frequency diagram?

• This is best explained with an example

  • The times taken to complete a short general knowledge quiz taken by 50 students are shown in the table below:

    Time taken ( seconds)	Frequency
    	3
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