The numbers of chocolate bars sold per day in a cinema over a period of 100 days are summarised in the following table. Calculate estimates of the mean and standard deviation of the number of chocolate bars sold. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_51 Year：2020 Question No：7(c)
Answer:
Mean \(=\frac{18 \times 5.5+24 \times 13+30 \times 23+20 \times 40.5+8 \times 55.5}{100}=\frac{2355}{100}=23.6\)
\(\operatorname{Var}=\frac{18 \times 5.5^{2}+24 \times 13^{2}+30 \times 23^{2}+20 \times 40.5^{2}+8 \times 55.5^{2}}{100}-\) mean \(^{2}\)
\(\frac{77917.5}{100}-\) mean \(^{2}=224.57\)
Standard deviation \(=15.0\)
(FT their variance)
\(\operatorname{Var}=\frac{18 \times 5.5^{2}+24 \times 13^{2}+30 \times 23^{2}+20 \times 40.5^{2}+8 \times 55.5^{2}}{100}-\) mean \(^{2}\)
\(\frac{77917.5}{100}-\) mean \(^{2}=224.57\)
Standard deviation \(=15.0\)
(FT their variance)
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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