Chapter 3, Problem 3.1.1RE

To determine

To find: The mean, median, mode and midrange of the data.

Answer to Problem 3.1.1RE

The mean for the data is 27.2.

The median for data is 19.

The mode for the data is 17.

The midrange for the data is 38.

Explanation of Solution

Given info:

The data represents the net worth (in billions of dollars) of a sample of the richest people in the United States.

59, 52, 28, 26, 19, 19, 18, 17, 17, 17

Calculation:

Mean:

The sum of all the entries divided by the total number of entries is known as mean.

The mean is,

$\overline{X}=\frac{{\displaystyle \sum X}}{n}$

$\begin{array}{c}\overline{X}=\frac{\left(59+52+28+26+19+19+18+17+17+17\right)}{10}\\ =\frac{272}{10}\\ =27.2\end{array}$

Thus, the mean for the data is 27.2.

Median:

• If the data set consists of odd number of entries then the median is the middle value of the data.
• If the data set consists of even number of entries then the median is the mean of the middle vales in the data set.

Arrange the data entries in ascending order.

17, 17, 17, 18, 19, 19, 26, 28, 52, 59

The sample has 10 entries which is an even number. Hence, the median is the mean of the middle value of the data.

Here, the middle values are 19 and 19.

$\begin{array}{c}\text{Median}=\frac{19+19}{2}\\ =\frac{38}{2}\\ =19\end{array}$

Thus, the median is 19.

Mode:

If the data value in the data set which has high frequency then the value is termed as mode.

Here, the value 17 repeated more than once that is, 3 times.

Thus, the mode value is 17.

Midrange:

If the sum of highest and lowest values in the data set is divided by 2 then the value is termed as midrange. It is denoted as MR.

$\text{MR}=\frac{\left(\text{Lowest value}\right)+\left(\text{Highest value}\right)}{2}$

Here the lowest and highest values in the data are 17 and 59.

$\begin{array}{c}\text{MR}=\frac{17+59}{2}\\ =\frac{76}{2}\\ =38\end{array}$

Thus, the midrange for the data is 38.