Question

27 POINTS

Identify the outlier in the data set 6, 9, 3, 2, 10, 138, 13. Then find the mean and median with and without the outlier. If necessary, round your answers to the nearest tenth.

Answer 1

The outlier would be 138, as an outlier is nowhere near the rest of the numbers.

With Outlier: 
Mean: 25.86 or 25.9
Median: 9

Without Outlier:  
Mean: 7.16 or 7.2 
Median: 7.5 (doesn't need to be rounded to the nearest tenth)

Hope I helped you! 

Answer 2

An outlier is a value that is much smaller or larger than the other values in the set. So, in this case, 138 is the outlier.

Now the question wants us to calculate the mean average and the median average of the set. But with and without the outlier.

To find the median of a set of numbers, line them up by size and pick the middle one.

2, 3, 6, 9, 10, 13, 138

In this case, the median is 9.

Now without the outlier.

2, 3, 6, 9, 10, 13

In this set of numbers, there is no "middle" number.
So, we will take the two middle numbers and take their mean average.

6 + 9 = 15 / 2
15 / 2 = 7.5

In this case, the median is 7.5

Now for the mean average. To calculate the mean average, add up all the numbers then divide the sum by the number of elements in the set.

With the outlier.

6 + 9 + 3 + 2 + 10 + 138 + 13 = 181
181 / 7 ≈ 25.857

Round to the nearest tenth.

25.857 ≈ 28.9

So, the mean average with the outlier is 28.9

Now without the outlier.

6 + 9 + 3 + 2 + 10 + 13  = 43
43 / 6 ≈ 7.166

Round to the nearest tenth.

7.166 ≈ 7.2

So, without the outlier, the mean average is 7.2.