Paper 4 · statistics - mean and standard deviation

Using the same pocket money data (20 girls, values in cents: 50,50,50,75,100,100,100,150,175,200,200,200,250,250,300,325,330,375,450,550, mean \$2.14), what is the standard deviation, to the nearest cent?

A$2.54

B$1.37

C$1.41

D$1.52

Explanation:

\sum x^2 = 1{,}291{,}400

(cents

^2

), so the variance is

1{,}291{,}400/20 - 214^2 = 64{,}570 - 45{,}796 = 18{,}774

, giving

\sigma = \sqrt{18774} \approx 137.0

cents

\approx \$1.37

Derived from ZIMSEC Maths Paper 1, November 2008, Q1 (Statistics)

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