Question

Thenges in yours) of a random sample of shoppers at a gaming store are shown. Determine the range, mesin, variance, and standard deviation of the sample data set. 12, 21, 23, 15, 21, 17, 20, 17, 13, 16 The range is (Simplify your answer.) The mean is (Simplify your answer. Round to the nearest tenth as needed) The variance is (Simplify your answer. Round to the nearest hundredth as needed.) The standard deviation is (Simplify your answer. Round to the nearest tenth as needed)

Answer 1

We have x_i as follows {12,21,23,15,21,17,20,17,13,16}

The range is defined as max (x_i)-min(x_i) = 23-12 = 11

mean = _$\sum(xi)$ ^{/ n}

^{here n = 10}

_$\sum(xi)$= 12+21+23+15+21+17+20+17+13+16=175

mean = 175/10 =17.5

Variance = (_{$\sum(x^{^{2}})$} - n*(mean)^2)/(n-1)

_{$\sum(x^{^{2}})$ =} 12²+21²+23²+15²+21²+17²+20²+17²+13²+16² =3183

Variance =(3183-10*(17.5)²)/(10-1) =13.38889

Variance= 13.4 (rounding)

Standard deviation = $\sqrt(Variance)$

Standard deviation = $\sqrt(13.38889)$ = 3.659083

Standard deviation = 3.7 (rounding)