Chapter 11, Problem 22GR

Solution

To find:The measure of central tendencythat best represents the following data set.

  $\left\{1,3,3,3,4,10,20,30,40\right\}$

When you give a value to represent the typical data value in a data set, you are giving a measure of central tendency of the data set.

The mode 3, best represents the data set $\left\{1,3,3,3,4,10,20,30,40\right\}$ .

Given information:Data set $\left\{1,3,3,3,4,10,20,30,40\right\}$

Explanation:

A measure of central tendency indicates the “middle” of the data set. The mean , median and mode are the most common measures of central tendency.

Let’s calculate each one of them:

• $\text{Mean}=\frac{\text{sum of the data values}}{\text{number of data values}}$

$\begin{array}{c}=\frac{1+3+3+3+4+10+20+30+40}{9}\\ =\frac{114}{9}\\ =12.6\overline{7}\end{array}$

• Median: $\left\{1,3,3,3,4,10,20,30,40\right\}$ . The middle value in the data set is 4.

  Thus, the median is 4.

• Mode: It is the most frequently occurring value. Here, 3 occurs 3 times.

Thus, the mode is 3.

Here, the extreme values in the data set are either very small or large from the mean and median.

Therefore, the mode 3, best represents the data set $\left\{1,3,3,3,4,10,20,30,40\right\}$ .