Chapter B.2, Problem 35E

To determine

To explain:

Reason for set $\left\{4,4,20,20\right\}$ has standard deviation of $8$ .

Answer to Problem 35E

The standard deviation is $8$ .

Explanation of Solution

Given information:

Set: $\left\{4,4,20,20\right\}$

The given data set is $\left\{4,4,20,20\right\}$ .

The standard deviation of s set is a measure of how much a typical number in the set differs from the mean of set.

As the variation from the mean increases, the standard deviation also increases.

Now find out the mean of the given set,

  $\begin{array}{l}\overline{x}=\frac{4+4+20+20}{4}\\ =\frac{48}{4}\\ =12\end{array}$

So the mean is $12$ .

The standard deviation is given as $\sigma$ ,

  $\begin{array}{l}\sigma =\left|x_1-12\right|\\ =8\end{array}$

As each data set is $8$ units from $12$ .

Therefore, the standard deviation is $8$ .