Question

By how much does the outlier in the following data set increase the mean of the data set? Round your answer to the nearest hundredth if necessary.

{10, 12, 17, 18, 22, 30, 101}

I NEED THIS ANSWERED BEFORE 10 PM PST

Answer 1

Answer: 11.83

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Step-by-step explanation:

With the outlier, the mean is

m = (10+12+17+18+22+30+101)/7 = 30

I added up the values and divided by 7 since there are 7 values being added up.

Without the outlier 101, the mean is now

n = (10+12+17+18+22+30)/6 = 18.1667 approximately

We're dividing by one less item this time.

Subtract the values of m and n

m-n = 30-18.1667 = 11.8333

This rounds to 11.83

The large outlier 101 increases the mean by roughly 11.83

Any time the outlier is larger than the main cluster of values, the mean is pulled to be larger than it should be if we ignored the outlier. The further the outlier, the stronger the pull and the more skewed the mean will get.

Note how the median of {10,12,17,18,22,30} is 17.5 which is a better measure of center compared to m = 30 found earlier.