Chapter 16.5, Problem 10RE

a.

To determine

Calculate the average.

Answer to Problem 10RE

 The average is 0.15.

Explanation of Solution

Calculation:

Here, 200 draws are made randomly with replacement from the box containing the numbers         –3, –2, –1, 0, 1, 2, 3.

The sum of 200 draws is 30 and their average is calculated as follows:

$\begin{array}{c}Average=\frac{sumofthedraws}{numberofdraws}\\ \overline{x}=\frac{{\displaystyle \sum x}}{n}\\ \overline{x}\text{ = }\frac{30}{200}\\ \overline{x}=0.15\end{array}$

Thus, the average is 0.15.

b.

To determine

Find the average.

Answer to Problem 10RE

 The average is –0.10.

Explanation of Solution

Calculation:

Here, 200 draws are made randomly with replacement from the box containing the numbers         –3, –2, –1, 0, 1, 2, 3.

The sum of 200 draws is –20 and their average is calculated as follows:

$\begin{array}{c}Average=\frac{sumofthedraws}{numberofdraws}\\ \overline{x}=\frac{{\displaystyle \sum x_i}}{n}\\ \overline{x}\text{ = }\frac{-20}{200}\\ \overline{x}=-0.10\end{array}$

Thus, the average is –0.10.

c.

To determine

Find the general term of average.

Answer to Problem 10RE

The general term of average is sum of the draws divided by 200.

Explanation of Solution

Calculation:

The average is the sum of the draws divided by number of draws.

$\begin{array}{c}Average=\frac{sumofthedraws}{numberofdraws}\\ \overline{x}=\frac{{\displaystyle \sum x_i}}{n}\\ \end{array}$

The general term of average is sum of the draws divided by 200.

d.

To determine

Check whether the options are same.

If not same, identify the better one.

Answer to Problem 10RE

Same.

Explanation of Solution

In option (i), the sum of 200 draws is –5 and 5 and their average is calculated as:

$\begin{array}{c}Average=\frac{sumofthedraws}{numberofdraws}Average=\frac{sumofthedraws}{numberofdraws}\\ \overline{x}=\frac{{\displaystyle \sum x_i}}{n}\overline{x}=\frac{{\displaystyle \sum x_i}}{n}\\ \overline{x}\text{ = }\frac{-5}{200}\overline{x}\text{ = }\frac{5}{200}\\ \overline{x}=-0.025\overline{x}=0.025\end{array}$

Hence, the average is –0.025 and 0.025 which is same as the average in option (ii).

Thus, the average is same in both the options.

Same.