WJEC MATHEMATICS - MrGoreMaths

[Pages:11]WJEC MATHEMATICS INTERMEDIATE

STATISTICS AND PROBABILITY

CUMULATIVE FREQUENCY

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Contents Cumulative Cumulative Frequency Graph Quartiles Interquartile Range Box Plot Credits WJEC Question bank

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Cumulative

'Cumulative' means to add up as you go along. Often you are asked

to turn a frequency table into a cumulative frequency table. Consider

this example showing the length of different pieces of string

Length

Frequency

21-24

3

25-28

7

29-32

12

33-36

6

37-40

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To turn this into a cumulative frequency table, we need a new

column, one that adds up the frequency column as it goes down.

Length Frequency Cumulative Frequency

21-24 3

3

25-28 7

10 (3+7)

29-32 12

22 (3+7+12)

33-36 6

28 (3+7+12+6)

37-40 4

32 (3+7+12+6+4)

Cumulative Frequency Graph

Plot the cumulative frequency against the upper value in

each range.

JOIN THEM UP WITH A CURVE LOOK FOR THE S

SHAPE

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Quartiles Consider the axis (the cumulative frequency axis).

To find the lower quartile go one quarter of the way to the max value

To find the median go halfway to the max value To find the upper quartile go three quarters of the way up to the

max value

For the example on the previous page, the maximum value (the biggest value in the cumulative frequency column) is 32. So,

One quarter of the way up will be at 8 Half way up will be up at 16 Three quarters of the way up will be at 24

Follow the arrows across to the curve, then drop down to

the x axis LQ = 28 Median = 30 UQ = 33

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IMPORTANT INTERQUARTILE RANGE = UQ - LQ

So, for our example, Box Plots Box and Whisker plots are used to display information about the range, median, and quartiles. This is how you construct the box and whisker plot

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Example The oldest person in Mathsminster is 90. The youngest person is 15. The median age of the residents is 44, the lower quartile is 25, and the upper quartile is 67. Represent this information with a box and whisker plot

Very often you will need to extract this information from a cumulative frequency graph.

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Exam Questions S12 1.

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2.

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