O-LevelMathematicsStatistics4024/21 · Oct/Nov 2017 · Q28 Marks

Sunil recorded the lengths, in minutes, of the 150 phone calls he made one month. His results are summarised in the table. Length of call (t minutes) | 0<t≤5 | 5<t≤10 | 10<t≤20 | 20<t≤30 | 30<t≤50 ---|---|---|---|---|--- Frequency | 35 | 42 | 30 | 28 | 15

(a)Calculate an estimate of the mean length of a call.[3]
(b)On the grid below, draw a histogram to represent this data.[3]
(c)Find an estimate for the percentage of Sunil's calls that were longer than 25 minutes.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[3] B1 for use of correct midpoints soi
[3] M1 for (2.5 x 35 +7.5×42 + 15×30 + 25×28 + 40 × 15) ÷ 150
[3] 14.35 or 14.4
[3] B2 for all 5 bar heights correct with frequency density axis scaled OR B1 for at least 3 correct heights drawn or 3 correct frequency densities calculated B1 for 5 bars correct width and position
[3] Correct histogram with linear scale on frequency density axis
[2] M1 for (15+14) ÷ 150
[2] 18 to 20

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