A-LevelMathematicsProbability and statistics9709/53 · May/June 2022 · Q13 Marks
The time taken, t minutes, to complete a puzzle was recorded for each of 150 students. These times are summarised in the table. Time taken (t minutes): t≤ 25, t≤50, t≤75, t≤100, t≤150, t≤200 Cumulative frequency: 16, 44, 86, 104, 132, 150
- (a)Draw a cumulative frequency graph to illustrate the data.[2]
- (b)Use your graph to estimate the 20th percentile of the data.[1]
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Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [M1] At least 3 points plotted accurately at class upper end points (25,16) (50,44) (75,86) (100,104) (150, 132) (200, 150). Linear cf scale 0 < cf < 150 and linear time scale 0 time(mins) < 200 with at least 3 values identified on each axis.
- [A1] All points plotted correctly, curve drawn (within tolerance) and joined to (0,0). Axes labelled cumulative frequency (cf), time (t) and minutes (min), or a suitable title.
- [B1 FT] Line from cumulative frequency = 30 to meet graph at t is between 37.5 and 42. Not from wrong working. Must be an increasing cumulative frequency graph.
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