Question

HELP A.S.A.P!!!! The data to represent average test scores for a class of 16 students includes an outlier value of 78. If the outlier is included, then the mean is 84. Which statement is always true about the new data when the outlier is removed?
The mean would decrease.
The mean would increase.
The median would decrease.
The median would increase.

Answer 1

When the outlier is removed The mean would increase.

Step-by-step explanation:

Outliers are the value that lies outside the set of data. i.e. the data doesn't fit in the group.

Removing outliers can affect mean more than median. Because outlier removal sometimes affect the median but in a small percentage or sometimes it will remain the same.

Let us prove, consider 16 values one with 78 and other 15 with values nearly 85, 84 that will give the mean value as 84.

78, 84, 82, 86, 84, 85, 83, 86, 82, 85, 84, 83, 86, 85, 86, 85.

Mean =$\frac{Sum of the values}{Number of values}$.

Mean =$\frac{78+84+82+86+84+85+83+86+82+85+84+83+86+85+86+85}{16}$.

Mean =$\frac{1344}{16}$.

Mean = 84.

Remove 78 from the data set then the data set is 84, 82, 86, 84, 85, 83, 86, 82, 85, 84, 83, 86, 85, 86, 85 and number of data is reduced to 15.

Mean =$\frac{84+82+86+84+85+83+86+82+85+84+83+86+85+86+85}{15}$.

Mean =$\frac{1266}{15}$.

Mean = 84.4.

The mean is increased.