Step 1. The first step is to identify the outlier in the data set.
An outlier is a number or an element of the set that is very different from the other numbers, it is an atypical value in the set.
In the following image, we have a graph of all of the given values:
As you can see, there is a point that doesn't look like a part of the data set because it is far apart. That point is:
The outlier is 369.
Step 2. We are also asked to find the mean, median, and mode when the outlier is included and when it is not.
Let's start with the mode.
The mode of a data set is the element that is repeated most. In this case, there are no repeated numbers in the data set, thus:
Mode including the outlier: No mode
Mode not including the outlier: No mode
Step 3. Not let's find the median.
For the median, we need to arrange the numbers in order and find the value in the middle.
Median including the outlier:
Arranging the numbers in order:
The median is:
158.
Median not including the outlier:
The number arranged in order:
The median is:
142.
Step 4. The final step will be to find the mean of the data set.
The mean of a set of numbers is the sum of all of the numbers divided by the number elements in the data set.
![\operatorname{mean}=\frac{\text{Sum of the elements}}{\text{Number of elements}}]()
Mean including the outlier:
The sum of the numbers including the outlier is:
And there are 14 numbers. The mean is:
![\begin{gathered} \operatorname{mean}=(2,247)/(14) \\ \operatorname{mean}=160.5 \end{gathered}]()
160.5
Mean not including the outlier:
The sum of the numbers is:
And there are 13 numbers. Thus, the mean is:
![\begin{gathered} \operatorname{mean}=(1878)/(13) \\ \operatorname{mean}=144.4615385 \end{gathered}]()
Rounding this result to the nearest tenth (1 decimal place):
![\operatorname{mean}=144.5]()
144.5
Answer:
• Outlier -- 369
,
• Mode: No mode with or without outlier
,
• Median: 158 including the outlier and 142 not including the outlier.
,
• Mean: 160.5 including the outlier and 144.5 not including the outlier