Task 4 – Extension Cumulative Frequency 1. An operator took 100 calls at a call centre. The table gives information about the time (t seconds) it took the operator to answer each call. (a) Time (t seconds) Frequency 0 < t ≤ 10 16 10 < t ≤ 20 34 20 < t ≤ 30 32 30 < t ≤ 40 14 40 < t ≤ 50 4 Complete the cumulative frequency table. Time (t seconds) Cumulative Frequency 0 < t ≤ 10 16 0 < t ≤ 20 0 < t ≤ 30 0 < t ≤ 40 0 < t ≤ 50 (b) On the grid, draw a cumulative frequency graph for your table. (c) Use your graph to find an estimate for the number of calls the operator took more than 18 seconds to answer...................................... (2) (Total 5 marks) 2. A company tested 100 batteries. The table shows information about the time in hours that the batteries lasted. (a) Time(t hours) Frequency 50 ≤ t < 55 12 55 ≤ t < 60 21 60 ≤ t < 65 36 65 ≤ t < 70 23 70 ≤ t < 75 8 Complete the cumulative frequency table. (1) (b) Time (t hours) Cumulative frequency 50 ≤ t < 55 12 50 ≤ t < 60 50 ≤ t <65 50 < t < 70 50 ≤ t < 75 On the grid, draw a cumulative frequency graph for your completed table. (2) (c) Use your completed graph to find an estimate for the median time. 100
Cumulative
frequency
80
60
40
20
0
50
55
60
65
Time (t hours)
70
75
………………………hours (1) (Total 4 marks) 4. 60 people went on a boat. The grouped frequency table shows information about their ages. (a) Age (A years) Frequency 0 < A ≤ 10 4 10 < A ≤ 20 8 20 < A ≤ 30 11 30 < A ≤ 40 16 40 < A ≤ 50 9 50 < A ≤ 60 7 60 < A ≤ 70 5 Complete the cumulative frequency table. Age (A years) Cumulative frequency 0 < A ≤ 10 4 0 < A ≤ 20 0 < A ≤ 30 0 < A ≤ 40 0 < A ≤ 50 0 < A ≤ 60 0 < A ≤ 70 (1) (b) On the grid on the right, draw a cumulative frequency graph for your table. 60
Cumulative frequency
50
40
30
20
10
0
0
10
20
30
40
50
60
70
Age ( A years)
(2) (c) Use your graph to find an estimate for the median age of these 60 people. ........................... years (1) (Total 4 marks)