The distances, $$\(x \mathrm{~m}\)$$, travelled to school by 140 children were recorded. The results are summarised in the table below. Calculate estimates of the mean and standard deviation of the distances. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w21_qp_52 Year：2021 Question No：7(c)
Answer:
[Mean =]
\(\frac{16 \times 100+30 \times 250+42 \times 400+34 \times 700+12 \times 1050+6 \times 1400}{140}\)
505
Variance \(=\)
\(\frac{16 \times 100^{2}+30 \times 250^{2}+42 \times 400^{2}+34 \times 700^{2}+12 \times 1050^{2}+6 \times 1400^{2}}{140}\)
\(-505^{2}\)
S.d. \(=[\sqrt{105010.7}=] 324\)
\(\frac{16 \times 100+30 \times 250+42 \times 400+34 \times 700+12 \times 1050+6 \times 1400}{140}\)
505
Variance \(=\)
\(\frac{16 \times 100^{2}+30 \times 250^{2}+42 \times 400^{2}+34 \times 700^{2}+12 \times 1050^{2}+6 \times 1400^{2}}{140}\)
\(-505^{2}\)
S.d. \(=[\sqrt{105010.7}=] 324\)
Knowledge points:
5.1.5 calculate and use the mean and standard deviation of a set of data (including grouped data) either from the data itself or from given totals , and use such totals in solving problems which may involve up to two data sets.
Solution:
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