Exercise 7 Page 759

Consider the given data set for the scores in six basketball games. We are asked to find the standard deviation of these points scored.

Standard Deviation

The standard deviation of a data set is the average amount by which each individual value deviates or differs from the mean. $$\begin{array}{c}\sigma =\sqrt{\frac{(x_1-\mu {)}^2+(x_2-\mu {)}^2+\cdots +(x_n-\mu {)}^2}{n}}\end{array}$$ In the above formula, $x_1,\dots ,x_n$ are the values of the set of data, $\mu$ is the mean, and $n$ is the number of values.

The mean $\mu$ of a data set is the sum of the values divided by the total number of values in the set. Let's start by calculating the sum of the given values. There are $6$ values in our data set, so we have to divide the sum by $6.$ We will now use the formula for standard deviation. We have to subtract the mean from every given value and square the result.

$x_n$	$x_n-\mu$	$(x_n-\mu {)}^2$
$8$	$8-11.67=\text{-}3.67$	$(\text{-}3.67{)}^2=13.4689$
$11$	$11-11.67=\text{-}0.67$	$(\text{-}0.67{)}^2=0.4489$
$14$	$14-11.67=2.33$	$2.33^2=5.4289$
$7$	$7-11.67=\text{-}4.67$	$(\text{-}4.67{)}^2=21.8089$
$12$	$12-11.67=0.33$	$0.33^2=0.1089$
$18$	$18-11.67=6.33$	$6.33^2=40.0689$
Sum of Values		$81.3334$

Finally, we need to divide by $6$ and then calculate the square root. We can use our calculator to find this rounded to the nearest integer. Therefore, the answer is C.