question 1 of 10 which of the following choices is the variance of the sample shown here? 30, 32, 47, 57…

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{30 + 32+47+57+66+79}{6}=\frac{311}{6}\approx51.83$.

Step2: Calculate squared - differences

$(30 - 51.83)^2=(-21.83)^2 = 476.55$, $(32 - 51.83)^2=(-19.83)^2=393.23$, $(47 - 51.83)^2=(-4.83)^2 = 23.33$, $(57 - 51.83)^2=(5.17)^2=26.73$, $(66 - 51.83)^2=(14.17)^2 = 200.79$, $(79 - 51.83)^2=(27.17)^2=738.21$.

Step3: Calculate the sum of squared - differences

$476.55+393.23 + 23.33+26.73+200.79+738.21 = 1858.84$.

Step4: Calculate the variance

The sample variance $s^2=\frac{1858.84}{6 - 1}=\frac{1858.84}{5}=371.768\approx371.8$.

Answer:

E. 371.8