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3. Histograms Histograms are different to bar charts. Bar charts are frequency diagrams that show categories along the horizontal axis, whereas histograms are frequency diagrams that show grouped data values along the horizontal axis. Histograms can be used to show both discrete and continuous data. Walk Bike Bus Car Frequenc y MTWT F S S Pupils travelling to school Meals sold during the week. Frequenc y 12 3 4 5 66+ Number of pets owned. Bar Charts Categories Number category directly underneath middle of bar. Intro

4. Histograms Histograms are different to bar charts. Bar charts are frequency diagrams that show categories along the horizontal axis, whereas histograms are frequency diagrams that show grouped data values along the horizontal axis. Histograms can be used to show both discrete and continuous data. Walk Bike Bus Car Frequenc y MTWT F S S Pupils travelling to school Meals sold during the week. Frequenc y 12 3 4 5 66+ Number of pets owned. Bar Charts Runs 0-9 10-19 Temperature ( o C) 10 14 18 22 26 28 32 Frequency Histograms Grouped Data Runs scored in matches by a batsman last season. Maximum daytime Temperature 20-2930-39 40-49 50-59 Discrete data. Continuous data

5. 1. Use the histogram to determine how many times the batsman scored 40 runs or more. Histograms for Discrete Data Frequency Runs Scored 0 - 19 5 10 15 20 Runs scored by an opening batsman in one-day cricket matches last season. 20 - 39 40 - 59 60 - 7980 - 100 16 8 2 26 Cricket

6. 2. Use the histogram to determine how many times the batsman scored less than 60 runs. Histograms for Discrete Data Frequency Runs Scored 0 - 19 5 10 15 20 Runs scored by an opening batsman in one-day cricket matches last season. 20 - 39 40 - 59 60 - 7980 - 100 16 9 5 30

7. 3. Use the histogram to determine how many times the batsman scored more than 19 but less than 80 runs. Histograms for Discrete Data Frequency Runs Scored 0 - 19 5 10 15 20 Runs scored by an opening batsman in one-day cricket matches last season. 20 - 39 40 - 59 60 - 7980 - 100 9 16 8 33

8. 4. Use the histogram to determine how many cricket matches the batsman played last season. Histograms for Discrete Data Frequency Runs Scored 0 - 19 5 10 15 20 Runs scored by an opening batsman in one-day cricket matches last season. 20 - 39 40 - 59 60 - 7980 - 100 5 9 16 40 8 2

9. 5. The histogram shows that the batsman scored between 40 and 59 runs in most of his matches. True or false? Discuss Histograms for Discrete Data Frequency Runs Scored 0 - 19 5 10 15 20 Runs scored by an opening batsman in one-day cricket matches last season. 20 - 39 40 - 59 60 - 7980 - 100 False: He scored that many runs in only 16 out of 40 matches.

10. 6. The histogram shows that the batsman scored 50 runs in some of the matches. True or false? Discuss Histograms for Discrete Data Frequency Runs Scored 0 - 19 5 10 15 20 Runs scored by an opening batsman in one-day cricket matches last season. 20 - 39 40 - 59 60 - 7980 - 100 False

11. 7. The histogram shows that the batsman scored some runs in every match. True or false? Discuss Histograms for Discrete Data Frequency Runs Scored 0 - 19 5 10 15 20 Runs scored by an opening batsman in one-day cricket matches last season. 20 - 39 40 - 59 60 - 7980 - 100 False

12. 8. The histogram shows that the batsman scored more than 39 runs in most of his matches. True or false? Discuss Histograms for Discrete Data Frequency Runs Scored 0 - 19 5 10 15 20 Runs scored by an opening batsman in one-day cricket matches last season. 20 - 39 40 - 59 60 - 7980 - 100 True: He scored more than 39 runs in 26 out of 40 matches.

13. The histogram below shows the number of marks scored in a maths test by some students. Frequency 5 10 15 20 25 Histograms for Discrete Data(2) 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 60 Marks Test Scores Test

14. 1. Use the histogram to determine how many students passed the test if the pass mark was 30 marks. Frequency 5 10 15 20 25 Histograms for Discrete Data(2) 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 60 Marks Test Scores 14 8 1 23

15. 2. Use the histogram to determine how many students got less than 20 marks. Frequency 5 10 15 20 25 Histograms for Discrete Data(2) 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 60 Marks Test Scores 15 4 19

16. 3. Use the histogram to determine how many students got more than 9 but less than 50 marks. Frequency 5 10 15 20 25 Histograms for Discrete Data(2) 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 60 Marks Test Scores 15 23 60 14 8

17. 4. Use the histogram to determine the total number of students that sat the test. Frequency 5 10 15 20 25 Histograms for Discrete Data(2) 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 60 Marks Test Scores 4 15 65 23 14 8 1

18. 5. The Histogram shows that some students scored 25 marks in the test. True or false? Discuss. Frequency 5 10 15 20 25 Histograms for Discrete Data(2) 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 60 Marks Test Scores False

19. 6. The Histogram shows that most students scored between 20 to 29 marks in the test. True or false? Discuss. Frequency 5 10 15 20 25 Histograms for Discrete Data(2) 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 60 Marks Test Scores False: Only 23 out of 65 out of scored within this range.

20. 7. Since the pass mark for this test was a score of 30, discuss whether you think the test was easy or hard. Frequency 5 10 15 20 25 Histograms for Discrete Data(2) 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 60 Marks Test Scores The test was hard since only 23/65 students passed the test. Most of them failed!

21. Drawing a Histogram from raw data. FrequencyTallyRuns Too many! Too few! Groups of between 6 and 9 look best. 100 - 119 80 - 99 60 - 79 40 - 59 20 - 39 0 - 19 1. Choose a suitable grouping and display in a frequency table. The following data shows the number of runs scored by an opening batsman during matches last season. 42 34 39 49 62 99 18 24 37 38 59 112 47 72 85 68 53 101 45 12 0 33 42 61 80 30 21 27 56 90 5 35 94 63 75 33 20 44 33 71 Drawing

22. Drawing a Histogram from raw data. The following data show the number of runs scored by an opening batsman during matches last season. 42 34 39 49 62 99 18 24 37 38 59 112 47 72 85 68 53 101 45 12 0 33 42 61 80 30 21 27 56 90 5 35 94 63 75 33 20 44 33 71 FrequencyTallyRuns 100 - 119 80 - 99 60 - 79 40 - 59 20 - 39 0 - 19 1. Choose a suitable grouping and display in a frequency table. 2. Complete the frequency table then draw the histogram. 0-1920-39 40-59 60-79 80-99 100-119 Runs Scored 2 5 7 9 13 4 f 5 10 15 0 Runs scored in matches

23. Comparing Histograms 0-9 10-19 20-29 30-39 40-4950-60 Marks Paper 1 Scores 0-9 10-19 20-29 40-4950-60 30-39 Marks Paper 2 Scores 5 10 15 20 25 f 5 10 15 20 25 f Sixty students sat two maths papers and their results are recorded in the histogram below. The pass mark for both was 30. Discuss the results for each paper. Compare

24. Drawing a Histogram from raw data. The following data show the number of runs scored by an opening batsman during matches last season. 42 34 39 49 62 99 18 24 37 38 59 112 47 72 85 68 53 101 45 12 0 33 42 61 80 30 21 27 56 90 5 35 94 63 75 33 20 44 33 71 FrequencyTallyRuns Worksheet