Question

Identify the outlier in the data set. Then find the man, median, and mode of the data set when the outlier is included and when it is not. 117, 211, 186, 176, 372, 7,51, 229, 222, 83, 129, 142, 197, 102Please answer the first and second part

Answer 1

Given

We have the data set:

$117,\text{ 211, 186, 176, 372, 7, 51, 229, 222, 83, 129, 142, 197, 102}$

(a) Identify the outlier

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

Answer: 7

(b) The mean of the dataset when the outlier is included

The mean of a dataset can be found using the formula:

$\begin{gathered} mean\text{ = }\frac{\sum_^x}{n} \\ Where\text{ }\sum_^x\text{ is the sum of the items in the dataset} \\ and\text{ n is the number of items in the dataset} \end{gathered}$

Hence:

$\begin{gathered} mean\text{ = }\frac{117\text{ + 211+186 + 176 + 372 + 7 + 51 + 229 + 222+ 83 + 129 + 142 + 197 + 102}}{14} \\ =\text{ }\frac{2224}{14} \\ =\text{ 158.857} \\ \approx\text{ 158.9} \end{gathered}$

Answer: 158.9