Helen measures the lengths of 150 fish of a certain species in a large pond. These lengths, correct to the nearest centimetre, are summarised in the following table. The mean length of these 150 fish is $$\(15.295 \mathrm{~cm}\)$$. Calculate an estimate for the variance of the lengths of the fish. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_52 Year：2020 Question No：7(c)
Answer:
Midpoints: 4.75, 12, 17, 25
\[
\operatorname{Var}=\frac{4.75^{2} \times 15+12^{2} \times 48+17^{2} \times 66+25^{2} \times 21}{150}-15.295^{2}
\]
\(=29.1\)
\[
\operatorname{Var}=\frac{4.75^{2} \times 15+12^{2} \times 48+17^{2} \times 66+25^{2} \times 21}{150}-15.295^{2}
\]
\(=29.1\)
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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