O-LevelMathematicsStatistics4024/21 · May/June 2019 · Q812 Marks

The table summarises the distances, dm, that 80 women threw the javelin. Distance (dm) | Frequency 20 < d ≤ 25 | 6 25 < d ≤ 30 | 16 30 < d ≤ 35 | 25 35 < d ≤ 40 | 18 40 < d ≤ 45 | 13 45 < d ≤ 50 | 2

(a)One of these women is chosen at random. Find the probability that she threw the javelin 30 metres or less.[1]
(b)Calculate an estimate of the mean distance the javelin was thrown.[3]
(c)Draw the cumulative frequency diagram for this data on the grid on the next page.[3]
(d)Use your graph to find an estimate for
(d)(i)the median,[1]
(d)(ii)the interquartile range.[2]
(e)Women who threw the javelin more than 43 m qualified for a regional competition. Use your graph to estimate the number of women who qualified for this competition.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[1] 22/80 or 11/40 oe
[3] 33.875 or 33.9 nfww B1 for correct use of midpoints M1 for Σfx/80
[3] Correct cumulative frequency diagram B2 for at least 5 correct points plotted or B1 for 6, 22, 47, 65, 78, 80 soi
[1] 32.5 to 34 FT their cumulative frequency diagram
[2] 8 to 9.5 FT their cumulative frequency diagram M1 for [LQ] 29 to 30 nfww or [UQ] 38 to 39 nfww
[2] 6, 7 or 8 M1 for attempt to read at 43

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