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Higher November 2022 Paper 1 Q14

EduqasHigherCurrent spec9 marksCumulative FrequencyHistograms

14. The histogram below represents the greatest speed, \(v\) mph, of a car when driven by 50 drivers on a section of racetrack on Monday.

Histogram labelled Monday. Frequency density against greatest speed v (mph): 50 to 60 height 0.3, 60 to 65 height 1.0, 65 to 70 height 2.0, 70 to 80 height 2.2, 80 to 90 height 1.0
(a) Calculate an estimate of the percentage of the 50 drivers who drove at a greatest speed of 75 mph or more on this section of racetrack. [3]
(b) Use the histogram to complete this cumulative frequency table. [2]
Greatest speed,
\(v\) (mph)		\(v \leqslant 50\)\(v \leqslant 60\)\(v \leqslant 65\)\(v \leqslant 70\)\(v \leqslant 80\)\(v \leqslant 90\)
Cumulative frequency050
(c) The cumulative frequency diagram below represents the greatest speed, \(v\) mph, of the same car when driven by 50 different drivers on the same section of racetrack on Tuesday.
Cumulative frequency diagram labelled Tuesday, greatest speed v (mph) from 50 to 90, cumulative frequency 0 to 50; points plotted at (60, 0), (65, 2), (70, 5), (80, 15), (90, 50) and joined with straight lines
(i) On the grid above, draw the cumulative frequency diagram to represent the results of Monday’s drivers. [2]
(ii) On one of the days, many of the drivers were racing drivers.

On which day was this likely to be?
Give numerical evidence and explain your decision. [2]
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