Question

ervin bowled 7 games last weekend. his scores are: 155, 165, 138, 172, 127, 193, 142. what is the sample standard deviation of ervin’s scores?

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{155 + 165+138+172+127+193+142}{7}=\frac{1092}{7}=156$

Step2: Calculate the squared - differences

$(155 - 156)^2=(-1)^2 = 1$
$(165 - 156)^2=9^2 = 81$
$(138 - 156)^2=(-18)^2 = 324$
$(172 - 156)^2=16^2 = 256$
$(127 - 156)^2=(-29)^2 = 841$
$(193 - 156)^2=37^2 = 1369$
$(142 - 156)^2=(-14)^2 = 196$

Step3: Calculate the sum of squared - differences

$S=\sum_{i = 1}^{n}(x_i-\bar{x})^2=1+81 + 324+256+841+1369+196=3068$

Step4: Calculate the sample variance

$s^2=\frac{S}{n - 1}=\frac{3068}{7 - 1}=\frac{3068}{6}\approx511.33$

Step5: Calculate the sample standard deviation

$s=\sqrt{s^2}=\sqrt{511.33}\approx22.61$

Answer:

22.61