Question

Identify the outlier in the data set. Then find the mean, median, and mode of the data set when the outlier is included and when it is not. 117 211 186 17637275122922283129142197102

Answer 1

Case: Outliers in a data set

Given: A set of numbers:

117, 211, 186, 176, 372, 7, 51, 229, 222, 83, 129, 142, 197, 102.

Required:

A) Identify the outliers

B) Mean with outliers

C) Median with outliers

D) Mode with outliers

E) Mean without outliers

F) Median without outliers

G) Mode without outliers

Final Answers

A) The outliers

First we arrange the data:

7, 51, 83, 102, 117, 129, 142, 176, 186, 197, 211, 222, 229, 372

Now we select the outliers

Because of the space in the data, the suspected outliers are:

7

because it is far from the central values

B)

The mean with outliers

`\begin{gathered} mean=(7+51+83+102+117+129+142+176+186+197+211+222+229+372)/(14) \\ Mean=\text{ 158.9} \end{gathered}`

C)

Median with outlier

Median = (142+176)/2

Median= 159

D) Mode with outlier

This data has no mode

E) Mean without outlier

51, 83,102, 117, 129, 142, 176, 186, 197, 211, 222, 229, 372

`\begin{gathered} Mean=\text{ }(51+83+102+117+129,+142+176+186+197+211+222+229+372)/(10) \\ Mean=\text{ 170.5} \end{gathered}`

F) Median without outlier

Median = 176

G) Mode without outlier

The data has no mode