Chapter 14.2, Problem 16E

(a)

To determine

To find: The mean of the weights of the crates.

Answer to Problem 16E

The mean of the weights of the cratesis $145$ .

Explanation of Solution

Given:

The given data is as:

  $142,160,151,139,145,117,172,155,\text{and}124$ .

Calculation:

The mean is calculated as:

  $\begin{array}{c}\overline{x}=\frac{{\displaystyle \sum x_i}}{N}\\ \overline{x}=\frac{142+160+151+139+145+117+172+155+124}{9}\\ =\frac{1305}{9}\\ =145\end{array}$

The mean of the weights of the crates is $145$ .

(b)

To determine

To find: The median of the weight of the crates.

Answer to Problem 16E

The median is $145$ .

Explanation of Solution

Arrange the data in ascending order.

  $\left\{117,124,139,142,145,151,155,160,172\right\}$

The median is calculated as:

  $\begin{array}{c}\text{Median}=\left(\frac{N+1}{2}\right)\text{th term}\\ =5\text{th term}\\ =145\end{array}$

The median is $145$ .

(c)

To determine

To find: The affected mean and median.

Answer to Problem 16E

The explanation is given below.

Explanation of Solution

Given:

If $5$ pounds is added to each crate.

If $5$ pounds is added to each crate, both the mean and median would be $5$ pounds greater than the mean and median of the original data.

The explanation is given above.