O-LevelMathematicsStatistics4024/22 · May/June 2016 · Q310 Marks

Steven asked 25 women how many children they have. The results are summarised in the table below. Number of children | Frequency -------------------|----------- 0 | 7 1 | 5 2 | 6 3 | 4 4 | 3

(a)(i)Find the mean,[2]
(a)(ii)the median,[1]
(a)(iii)the mode.[1]
(b)Steven says that the mode is the average that best represents the data. Explain why Steven is wrong.[1]
(c)Steven chooses two women at random from the group. Calculate the probability that both of them have just one child. Give your answer as a fraction in its simplest form.[2]
(d)Draw a bar chart to represent this data. [Figure 3.1][2]
(e)Steven shows Frank the paper on which he recorded the data from his survey. Part of the paper has been torn. 1 4 2 2 3 0 1 0 3 2 2 0 4 1 3 1 0 0 2 2 Which five numbers are missing from the paper?[1]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

[2] (a)(i) 1.64 or 1 16/25
[2] (a)(i) M1 for (0×7+1×5+2×6+3×4+4×3) / (7+5+6+4+3)
[1] (a)(ii) 2
[1] (a)(iii) 0
[1] (b) appropriate reason
[2] (c) 1/30 cao
[2] (c) M1 for 5/25 × 4/24 oe
[2] (d) Correct bar chart with axes labelled
[2] (d) B1 if only one error (eg incorrect height, scales missing / incorrect, inconsistent bar widths, or 4 correct bars)
[1] (e) 00134

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