The times, $$\(t\)$$ minutes, taken by 150 students to complete a particular challenge are summarised in the following cumulative frequency table. Calculate estimates of the mean and the standard deviation of the time taken to complete the challenge. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_51 Year：2020 Question No：6(c)
Answer:
Frequencies: \(\begin{array}{lllll}12 & 36 & 58 & 28 & 16\end{array}\)
Mean \( =\frac{10 \times 12+25 \times 36+35 \times 58+50 \times 28+80 \times 16}{150} \)
\( \frac{120+900+2030+1400+1280}{150} \)
\( 38.2,38 \frac{1}{5} \)
Variance \( =\frac{12 \times 10^{2}+36 \times 25^{2}+58 \times 35^{2}+28 \times 50^{2}+16 \times 80^{2}}{150}- mean ^2 \)
\( =\frac{1200+22500+71050+70000+102400}{150}- mean ^{2} \)
\( (Standard deviation =\sqrt{321.76} ) =17.9 \)
Mean \( =\frac{10 \times 12+25 \times 36+35 \times 58+50 \times 28+80 \times 16}{150} \)
\( \frac{120+900+2030+1400+1280}{150} \)
\( 38.2,38 \frac{1}{5} \)
Variance \( =\frac{12 \times 10^{2}+36 \times 25^{2}+58 \times 35^{2}+28 \times 50^{2}+16 \times 80^{2}}{150}- mean ^2 \)
\( =\frac{1200+22500+71050+70000+102400}{150}- mean ^{2} \)
\( (Standard deviation =\sqrt{321.76} ) =17.9 \)
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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