Question

The data to represent average test scores for a class of 16 students includes an outlier value of 78. If the mean, including the outlier of 78, equals 84, which statement is always true about the new data when the outlier is removed?

The mean would increase.
The mean would decrease.
The median would increase.
The median would decrease.

Answer 1

Given that The data to represent average test scores for a class of 16 students includes an outlier value of 78.

We can find sum of all 16 test scores = 84(16) = 1344

Outlier found = 78

If outlier is removed new sum = 1344-78 = 1266

Number of entries without outlier = 15

New average = 1266/12 =84.4

We find that average of new data increases.

Also whenever we remove outlier std deviation also would be reduced.

Explanation:

Answer 2

The mean would decrease.

Explanation:

Without the outlier, the mean decreases. The median stays the same with or without the outlier.