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1 ) June 2022 1H# 13 The table gives information about the ages, in years, of 80 people in a train carriage. Age ( a years) Frequency 0 < a 20 7 20 < a 30 25 30 < a 40 20 40 < a 50 14 50 < a 60 8 60 < a 70 6 (a) Complete the cumulative frequency table. Age ( a years) Cumulative frequency 0 < a 20 0 < a 30 0 < a 40 0 < a 50 0 < a 60 0 < a 70 (1) (b) On the grid opposite, draw a cumulative frequency graph for your table. (2) (c) Use your graph to find an estimate for the median age of the 80 people.
...................................................... years (1)
Age (years)
Cumulative frequency
Of the people in the train carriage, 60% of those who are aged between 18 and 65 are going to work. None of the other people in the train carriage are going to work. (d) Use your graph to find an estimate for the number of people in the train carriage who are going to work.
...................................................... (3) (Total for Question 13 is 7 marks)
Question 11 continued (b) Use your graph to find an estimate for the median of the ages of these people.
....................................................... years (1) (c) Use your graph to find an estimate for the interquartile range of the ages of these people.
....................................................... years (2) (d) Use your graph to find an estimate for the number of these people who are older than 55 years.
....................................................... (2) (Total for Question 11 is 7 marks)
3 ) January 2022 1H 12 The table gives information about the times, in minutes, taken by 80 customers to do their shopping in a supermarket. Time taken ( t minutes) Frequency 0 < t 10 7 10 < t 20 26 20 < t 30 24 30 < t 40 14 40 < t 50 7 50 < t (^60 ) (a) Complete the cumulative frequency table. Time taken ( t minutes) Cumulativefrequency 0 < t 10 0 < t 20 0 < t 30 0 < t 40 0 < t 50 0 < t 60 (1) (b) On the grid opposite, draw a cumulative frequency graph for your table.
11 The manager of a call centre asked the 120 people, who rang the call centre last week, how long they each waited before their call was answered. The table gives information about their replies. Time waited ( t minutes) Frequency 0 t - 5 8 5 t - 10 15 10 t - 15 17 15 t - 20 28 20 t - 25 33 25 t - 30 19 (a) Complete the cumulative frequency table. Time waited ( t minutes) Cumulative frequency 0 t - 5 0 t - 10 0 t - 15 0 t - 20 0 t - 25 0 t - 30 (1)
4 ) January 2021 1HR # 11
(b) On the grid below, draw a cumulative frequency graph for your table.
Time waited (minutes)
Cumulative frequency
(c) Use your graph to find an estimate for the median of the times waited. ...................................................... minutes (1) (d) Using your graph, find an estimate for the percentage of the 120 people who said that they waited longer than 23 minutes before their call was answered. Show your working clearly.
(Total for Question 11 is 6 marks)
Distance (km)
Cumulative frequency
(c) Use your graph to find an estimate for the interquartile range of the distances.
...................................................... km (2) (d) Use your graph to find an estimate for the number of teachers who travel more than 46 km.
...................................................... (2) (Total for Question 13 is 7 marks)
6 ) November 2021 1H # 11 11 The table gives information about the times taken by 90 runners to complete a 10 km race. Time ( t minutes) Frequency 25 < t 35 12 35 < t 45 24 45 < t 55 28 55 < t 65 12 65 < t 75 10 75 < t 85 4 (a) Complete the cumulative frequency table. Time ( t minutes) Cumulative frequency 25 < t 35 12 25 < t 45 25 < t 55 25 < t 65 25 < t 75 25 < t 85 (1)
7 ) June 2021 2H # 12 12 The cumulative frequency table gives information about the distance, in kilometres, that each of 80 workers travel from home to work at Office A. Distance travelled ( d km) Cumulative frequency 0 < d 5 17 0 < d 10 32 0 < d 15 57 0 < d 20 70 0 < d 25 76 0 < d 30 80 (a) On the grid below, draw a cumulative frequency graph for the information in the table. 80
70
Distance travelled (km)
Cumulative frequency
(b) Use your graph to find an estimate for the median distance travelled.
....................................................... km (1) (c) Use your graph to find an estimate for the interquartile range of the distances travelled.
....................................................... km (2) For Office B , the median distance workers travel from home to work is 15 km and the interquartile range is 5 km. (d) Use the information above to compare the distances that workers at Office A and workers at Office B travel from home to work. Write down two comparisons. 1 ............................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 2 ............................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (2) (Total for Question 12 is 7 marks)
Time (minutes)
Cumulative frequency
(c) Use your graph to find an estimate for the median. ...................................................... minutes (1) (d) Use your graph to find an estimate for the interquartile range.
...................................................... minutes (2) (Total for Question 11 is 6 marks)
14 The table gives information about the times taken by 80 people to run a race. Time taken ( t minutes) Frequency 50 < t 60 15 60 < t 70 16 70 < t 80 21 80 < t 90 14 90 < t 100 8 100 < t 110 6 (a) Complete the cumulative frequency table. Time taken ( t minutes) Cumulative frequency 50 < t 60 50 < t 70 50 < t 80 50 < t 90 50 < t 100 50 < t 110 (1)
9 ) June 2023 1HR
11 The cumulative frequency table gives information about the time, in hours, that each of 60 workers spent working from home in one week. Time ( t hours) 0 < t 0 < t 10 0 < t 15 0 < t 20 0 < t 25
Cumulative frequency 6 17 27 42 53 0 < t 30 60
(a) On the grid below, draw a cumulative frequency graph for the information in the table.
Time (hours)
Cumulative frequency
10 ) June 2024 2HR # 11
(b) Use your graph to find an estimate for the interquartile range of the times.
.............................................................. hours (2) 25 workers spent more than W hours working from home. (c) Use your graph to find an estimate for the value of W
W = ..............................................................
One of the 60 workers is chosen at random. This worker spent H hours working from home. (d) Find the probability that 5 < H 10
.............................................................. (1) (Total for Question 11 is 7 marks)
