Chapter 11.6, Problem 17PPSE

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 381. The mean is 161.21, mode is None and median is 158. If outlier is removed then the mean is 144.3, mode is None and median is 142.

Given information:

The given data set is 87, 104, 381, 215, 174, 199, 233, 186, 142, 228, 9, 53, 117, 129.

Explanation:

Consider the given information.

The outlier of the given data set is 381 as the difference between adjacent values substantially different from 381.

Mean:

  $\begin{array}{c}Mean=\frac{87+104+381+215+174+199+233+186+142+228+9+53+117+129}{14}\\ =161.21\end{array}$

Arrange the data in increasing order. 9, 53, 87, 104, 117, 129, 142, 174, 186, 199, 215, 228, 233, 381.

Since the total number of data set is 14 which is even number so median is the average of 7^th and 8^th term.

  $\begin{array}{c}Median=\frac{142+174}{2}\\ =158\end{array}$

Mode is the highest frequency value of the given data set. It can be observed that no value is repeated. So, mode is none.

Now remove the outlier:

  $\begin{array}{c}Mean=\frac{87+104+215+174+199+233+186+142+228+9+53+117+129}{13}\\ =144.3\end{array}$

After removing the outlier, the total number of data set is 13 which is odd number so median is the exactly middle value. Which is 142.

Mode is the highest frequency value of the given data set. It can be observed that no value is repeated. So, mode is none.