O-LevelMathematicsStatistics4024/21 · Oct/Nov 2022 · Q210 Marks

The table shows the ages and heights of 10 boys. Age (years) | 10 | 16 | 11 | 18 | 10 | 11 | 13 | 17 | 13 | 16 Height (cm) | 138 | 168 | 135 | 174 | 145 | 148 | 158 | 175 | 150 | 160 [Figure 2.1]

(a)(i)Complete the scatter diagram. The first six points have been plotted for you.[2]
(a)(ii)Draw a line of best fit.[1]
(a)(iii)Use your line of best fit to estimate the height of a 14-year-old boy.[1]
(a)(iv)Simon is 22 years old. Explain why your line of best fit should not be used to estimate his height.[1]
(b)(i)The table summarises the heights of 180 girls in Year 7 of a school. Height (h cm) | 125 < h < 135 | 135 < h ≤ 140 | 140 < h < 145 | 145 < h ≤ 150 | 150 < h ≤ 160 Frequency | 8 | 31 | 55 | 62 | 24 Work out the percentage of girls who are taller than 145cm.[2]
(b)(ii)Calculate an estimate of the mean height.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[2] (a)(i) Four points plotted correctly; B1 for 2 or 3 correct plots
[1] (a)(ii) Ruled line of best fit
[1] (a)(iii) Reading at age 14; FT their ruled straight line of best fit with positive gradient
[1] (a)(iv) Age outside range of given data oe; Do not allow contradictory statements
[2] (b)(i) 47.8 or 47.77 to 47.78; M1 for (62+24)/180 [x100] oe
[3] (b)(ii) 144 or 144.4 to 144.5 nfww; B1 for correct midpoints soi M1 for (130×8+137.5×31+142.5×55+147.5×62+155×24)/180

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