How to draw a cumulative frequency graph

If the data is jumbled, sort it out by using a table 23, 24, 34, 45, 56, 23, 57, 41, 37, 65, 17, 26, 35, 44, 33, 48, 19, 61, 58, 55, 49, 44, 57, 43 Data Frequency 10 – 20 2 20 – 30 4 30 – 40 5 40 – 50 7 50 – 60 60 – 70 You must decide sensible intervals

Complete the third column by adding the second column like this: Data Frequency Cumulative Frequency 10 – 20 2 20 – 30 4 2 + 4 = 6 30 – 40 5 2 + 4 + 5 = 11 40 – 50 7 2 + 4 + 5 +7 = 18 50 – 60 2 + 4 + 5 +7 + 4 = 22 60 – 70 2 + 4 + 5 +7 + 4 + 2 = 24

You don’t have to show working Data Frequency Cumulative Frequency 10 – 20 2 20 – 30 4 6 30 – 40 5 11 40 – 50 7 18 50 – 60 22 60 – 70 24

Plot the second number in the data column against the number in the cumulative frequency column 10 – 20 2 20 – 30 4 6 30 – 40 5 11 40 – 50 7 18 50 – 60 22 60 – 70 24 Plot these numbers

Now, join up the points

You can use this to find the middle half ¾ (18) ½ (12) Upper Q (53) ¼ (6) Lower Q (30) Median (42)

The Lower Quartile is 30 Median is 42 The Upper Quartile is 53 This means that the middle half is between 30 and 53. Called the inter-quartile range. 53 – 30 = 23 The Lower Quartile is 30 Median is 42 The Upper Quartile is 53