Higher November 2020 Paper 5 Q16

OCRHigherCurrent spec8 marksGrouped DataHistograms

16

(a) The masses, \(m\) kg, of some parcels are shown below.

4   15   14   11   12   3   1   18   13   2   16   10

Jack constructs this grouped frequency table to record the masses.

Mass (m kg)TallyFrequency
\(0 \leqslant m \leqslant 5\)
\(5 \leqslant m \leqslant 10\)
\(10 \leqslant m \leqslant 15\)
\(15 \leqslant m \leqslant 20\)

Explain why Jack’s table is unsuitable to record the masses. [1]

(b) The histogram summarises the times taken, in minutes, by some students to complete a race.
Histogram of frequency density against time (minutes) from 30 to 70: 30–40 height 1, 40–45 height 4, 45–50 height 6, 50–70 height 2
(i) Show that 70 students took between 45 and 70 minutes to complete the race. [2]
(ii) Calculate an estimate of the mean time taken to complete the race.
Show your working. [5]
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