Theory question 106
StatisticsThe table shows the distribution of marks obtained by some candidates in a test
Marks: 10 − 14, 15 − 24, 25 − 29, 30 − 39, 40 − 44, 45 − 49
No. of candidates: 14, 30, 22, 18, 12, 4
Draw a histogram for the distribution.
Show the model answer
Model answer
Class boundaries: 9.5–14.5, 14.5–24.5, 24.5–29.5, 29.5–39.5, 39.5–44.5, 44.5–49.5
Class widths 5, 10, 5, 10, 5, 5 are unequal, so bar heights must be frequency densities
Heights per 5 marks: 14, 15, 22, 9, 12, 4 (frequency ÷ width × 5)
Bars drawn touching on the class boundaries, with a stated scale and labelled axes
Explanation
The classes have different widths, so the area (not the height) of each bar must show the frequency.