Draw a cumulative frequency table. The table shows the times taken to complete 20 telephone calls. Time Cumulative Frequency t  3 t  6 t  9 t  15 Time Frequency 0  t  3 5 3  t  6 8 6  t  9 4 9  t  15 3 5 + 8 13 + 4 17 + 3 20 Draw a cumulative frequency table.

Drawing a cumulative frequency curve. Time CF t  3 5 t  6 13 t  9 17 t  15 20 21 18 15 Cumulative frequency 12 9 6 3 2 4 6 8 10 12 14 16 Time (mins)

Drawing a cumulative frequency curve. Time CF t  3 5 t  6 13 t  9 17 t  15 20 2 4 6 8 12 14 16 10 3 9 15 18 21 Time (mins) Cumulative frequency

Finding the median, lower and upper quartile. 2 4 6 8 12 14 16 10 3 9 15 18 21 Time (mins) Cumulative frequency The upper quartile is at the 75% mark. The lower quartile is at the 25% mark. The median is at the 50% mark. Upper Q = 7 75% of 20 = 15 Median = 5 10 is 50% of 20 5 is 25% of 20 Lower Q = 3

7 – 3 = 4 Finding the inter-quartile range 2 4 6 8 12 14 16 10 3 9 15 3 9 15 18 21 Time (mins) Cumulative frequency 7 – 3 = 4 Upper Q = 7 Median = 5 The inter-quartile range is the difference between the upper and lower quartiles. Lower Q = 3