1. Histogram Edexcel S1 Mathematics 2003

2. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.

3. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. (b) Estimate the number of students under 158 cm in height Answer (a): find class boundaries label horizontal axis using continuous scale find class widths find class frequency densities label vertical axis for frequency densities draw bars using class boundaries and frequency densities

4. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class boundaries

5. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class boundaries Eg boundary between 154 and 155 is 154.5

6. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class boundaries Eg boundary between 154 and 155 is 154.5

7. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class boundaries Height cm heights of 325 students

8. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): label horizontal axis using continuous scale heights of 325 students Height cm

9. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): label horizontal axis using continuous scale 120130140150160170180190200 Height cm heights of 325 students

10. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 120130140150160170180190200 Height cm heights of 325 students Answer (a): find class widths

11. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 120130140150160170180190200 Height cm heights of 325 students Answer (a): find class widths Eg 164.5 – 154.5 = 10

12. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class widths 120130140150160170180190200 Height cm heights of 325 students Eg 164.5 – 154.5 = 10

13. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class widths 120130140150160170180190200 Height cm heights of 325 students

14. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 120130140150160170180190200 Height cm heights of 325 students Answer (a): find class frequency densities Frequency density =

15. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 120130140150160170180190200 Height cm heights of 325 students Answer (a): find class frequency densities Frequency density = Eg=

16. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class frequency densities 0 Frequency density (No of students per cm) 120130140150160170180190200 Height cm heights of 325 students Frequency density = Eg= 5

17. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class frequency densities 0 Frequency density (No of students per cm) 120130140150160170180190200 Height cm heights of 325 students

18. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): label vertical axis for frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

19. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

20. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

21. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

22. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

23. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

24. Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 Answer (a): draw bars using class boundaries and frequency densities heights of 325 students

25. Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): find class containing 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

26. Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 5055 50 55 heights of 325 students

27. Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 5055 heights of 325 students

28. Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 158 – 154.5 = 3.5 3.5 50

29. Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 158 – 154.5 = 3.5 50. 10 3.5 50

30. Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 17.532.5 158 – 154.5 = 3.5 50.= 17.5 10 3.5

31. Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 17.532.5 158 – 154.5 = 3.5 50.= 17.5 55 + 17.5 = 72.5

32. Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 158 – 154.5 = 3.5 50.= 12.5 55 + 17.5 = 72.573 students 72.5 Approx 73 students under 158 cm 158 17.532.5

33. Histogram - example Question: The heights of 325 students were measured to the nearest cm Answer: 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 158 heights of 325 students (a)Draw a histogram to illustrate the above data. (b) Estimate the number of students under 158 cm in height Approx 73 students under 158 cm 72.5