Chapter 11.6, Problem 1LC

Solution

Toidentify:The outlier in the data set, mean, median and mode of the data set when the outlier is included and when it is not.

The outlier is 54. The mean is 22.8, mode is 18 and median is 19.5. If outlier is removed then the mean is 19.33, mode is 18 and median is 19.

Given information:

The given data set is 16, 19, 21, 18, 18, 54, 20, 22, 23, 17.

Explanation:

Consider the given information.

The outlier of the given data set is 54 as the difference between adjacent values substantially different from 54.

Mean:

  $\begin{array}{c}Mean=\frac{16+19+21+18+18+54+20+22+23+17}{10}\\ =22.8\end{array}$

Arrange the data in increasing order. 16, 17, 18, 18, 19, 20, 21, 22, 23, 54.

Since the total number of data set is 10 which is even number so median is the average of 5^th and 6^th term.

  $\begin{array}{c}Median=\frac{19+20}{2}\\ =19.5\end{array}$

Mode is the highest frequency value of the given data set which is 18.

Now remove the outlier:

  $\begin{array}{c}Mean=\frac{16+19+21+18+18+20+22+23+17}{10}\\ \approx 19.33\end{array}$

Arrange the data in increasing order. 16, 17, 18, 18, 19, 20, 21, 22, 23.

Since the total number of data set is 9 which is odd number so median is the exactly middle value. Which is 19.

Mode is the highest frequency value of the given data set which is 18.