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Mr. Schwartz gives his class a challenge problem. Five students take 2, 12, 10, 11, and 15 minutes to solve it. How does the outlier affect the mean of the data?

A) It makes the mean less than it would be otherwise
B) It makes the mean greater than it would be otherwise
C) It makes the mean equal to the median
D) It has no effect on the mean

User Paul Suart
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1 Answer

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Final answer:

The outlier, which is significantly different from the other values, lowers the mean of the data set from 12 minutes to 10 minutes when included. Therefore, the outlier makes the mean less than it would be without it, option A being the correct answer.

Step-by-step explanation:

The student is asking how an outlier in a data set affects the mean. To answer this, let’s calculate the mean with and without the outlier. The times taken by the five students to solve the problem are 2, 12, 10, 11, and 15 minutes. Adding these up gives us a total of 50 minutes. Dividing by the number of students (5), we get a mean time of 10 minutes. Now let’s consider the outlier, which in this case appears to be the 2 minutes, being much lower than the other times. If we remove this outlier, the remaining times (12, 10, 11, 15) add up to 48 minutes. Dividing this by 4 gives us a mean of 12 minutes. Comparing the two means, we can see that the inclusion of the outlier (2 minutes) has lowered the mean. Therefore, the correct answer is that the outlier makes the mean less than it would be otherwise, which corresponds to option A.

User Terence Chow
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