Histograms with unequal widths

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Calculator · 2 marks
(a) A histogram class covers 15 < t $\le$ 25 minutes and contains 18 journeys, where t is the journey time. Work out the frequency density for this class. (2)
Question 2Non-calculator · 4 marks
A histogram has class widths 10, 15 and 5. Its corresponding drawn bar heights are 2, 4 and 6 cm. The total frequency is 330.
(a) Find the frequency in the second class. (3)
(b) Explain why the frequencies cannot be read directly from the bar heights. (1)
Question 3Non-calculator · 5 marks
A table of waiting times for 65 patients has some gaps. $0 < t \le 10$ : frequency 8. $10 < t \le 20$ : frequency density 1.4. $20 < t \le 30$ : frequency 18. $30 < t \le 50$ : frequency density 0.8. $50 < t \le 80$ : frequency 9.
(a) Show that the frequencies are consistent with a total of 65. (2)
(b) Work out an estimate for the median waiting time. Give your answer to 1 decimal place. (3)

Answers and marks

(a) $1.8$

(a) $180$

(b) The widths differ, so frequency is proportional to bar area. Height alone represents frequency density up to the vertical scale.

C1 Correct conclusion with supporting reasoning: The widths differ, so frequency is proportional to bar area. Height alone represents frequency density up to the vertical scale.

(a) $8 + 14 + 18 + 16 + 9 = 65$

(b) 25.8 minutes

Histograms with unequal widths

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