GCSE Mathematics (9-1)

25.3 Histograms — Practise

  1. H A class of width 88 has frequency 2424. Find the frequency density.
  2. H The class 10<x≤3010<x\leq30 has frequency 4040. Find its width and frequency density.
  3. H A histogram bar has width 66 and frequency density 44. Find the frequency.
  4. H Class A has width 55 and frequency 1515. Class B has width 1010 and frequency 2020. Find both densities and state which bar is taller.
  5. H A class from 2020 to 3535 has frequency density 1.61.6. Find its frequency.
  6. H A class 0≤x<40\leq x<4 has frequency 1212. Find its frequency density.
  7. H A histogram bar has width 1212 and density 2.52.5. Find the frequency.
  8. H A class has frequency 1818 and density 33. Find its class width.
  9. H Classes 0<x≤50<x\leq5, 5<x≤155<x\leq15, 15<x≤2015<x\leq20 have frequencies 10,20,1510, 20, 15. Find the density for each class.
Answers and concise solutions

1. Frequency density

Answer: 33.

2. Width and density

Answer: Width 2020; density 40/20=240/20=2.

3. Frequency from bar area

Answer: Frequency =6×4=24=6\times4=24.

4. Compare histogram heights

Answer: A density 33; B density 22. Class A has the taller bar.

5. Class frequency

Answer: Width 1515; frequency 15×1.6=2415\times1.6=24.

6. Frequency density

Answer: 33.

7. Frequency

Answer: 3030.

8. Class width

Answer: Width =18/3=6=18/3=6.

9. Three frequency densities

Answer: Densities 2,2,32,2,3.

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