2a.04 Calculate and use frequency density to draw histograms (unequal class width), and... Quiz: Pearson Edexcel Statistics, Unit 2

The 20 questions

1. What is the formula for frequency density?

   • Frequency ÷ class width
   • Class width ÷ frequency
   • Frequency × class width
   • Frequency + class width

2. What is plotted on the vertical axis of a histogram with unequal class widths?

   • Cumulative frequency
   • Frequency
   • Class midpoint
   • Frequency density

3. Why must histograms with unequal class widths use frequency density on the vertical axis?

   • Area shows frequency
   • Width shows frequency
   • Mean shows frequency
   • Height shows frequency

4. A class runs from 20 up to 30 with frequency 15. What is its class width?

   • 15
   • 30
   • 20
   • 10

5. What is the frequency density for a class with frequency 24 and class width 6?

   • 4
   • 0.25
   • 6
   • 24

6. Which label is correct for the vertical axis of an unequal-width histogram?

   • Frequency density
   • Frequency
   • Cumulative frequency
   • Class width

7. What does the area of a histogram bar represent when class widths are unequal?

   • Class frequency
   • Cumulative total
   • Frequency density
   • Class width

8. What graphical feature is required when drawing histograms with unequal class widths?

   • Cumulative frequency
   • Equal bar heights
   • Frequency density
   • Standard class width

9. A class 0–10 has frequency 30 and a class 10–30 has frequency 60. What are the frequency densities?

   • 30 and 60
   • 1 and 3
   • 3 and 6
   • 3 and 3

10. Class 40-50 has frequency 18 and class 50-70 has frequency 36. Which histogram bar is taller?

    • The first bar
    • Cannot be determined
    • The second bar
    • They are equal

11. A class 25–35 has frequency 45. What is its frequency density?

    • 0.22
    • 9
    • 45
    • 4.5

12. A class 20–25 has frequency density 6. What is its frequency?

    • 30
    • 4
    • 6
    • 150

13. Two groups' 0-20 bars have frequency densities 2 and 3 with equal widths. Which group has a higher frequency?

    • Group X
    • Group Y
    • Both equal
    • Neither

14. What must be used correctly to calculate widths when drawing an unequal-width histogram?

    • Class frequencies
    • Raw data limits
    • Class boundaries
    • Midpoints

15. A class with boundaries 1.5 and 2.5 holds 8 values. What is its frequency density?

    • 16
    • 8
    • 4
    • 0.125

16. Classes are 0–5 with frequency 10, 5–15 with frequency 40, and 15–35 with frequency 60. Which class has the greatest frequency density?

    • 15–35, with density 3
    • 5–15, with density 4
    • All are equal
    • 0–5, with density 2

17. What graphical error occurs if unequal class width histograms plot frequency instead of density?

    • Exaggerates narrow classes
    • Exaggerates wide classes
    • Zeros all frequencies
    • Inverts the axes

18. Why must true class boundaries be used when calculating frequency density?

    • Wrong width changes density
    • It changes the median
    • It alters total frequency
    • It removes outliers

19. Class 100-120 has frequency 50 and 120-150 has frequency 45. Which histogram bar is taller?

    • The 100-120 bar
    • They are equal height
    • The 120-150 bar
    • Cannot be determined

20. A histogram has classes 0–10, 10–40 and 40–100 with frequencies 20, 45 and 60. Which class has the greatest frequency density?

    • 10–40, with density 1.5
    • All are equal
    • 0–10, with density 2
    • 40–100, with density 1

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