Question

6. Here is a data set:
5
10
10
10
15
100
a. After studying the data, the reasearcher realized that the value 100 was meant
to be recorded as 15. What happens to the mean and standard deviation of the
data set when the 100 is changed to a 15?
b. For the original data set, with the 100, would the median or the mean be a
better choice of measure for the center? Explain your reasoning.

Answer 1

The mean and standard deviation will change. Because it will not change in this case, the median is a better measure of the center. Given that the value 100 was changed to 15, the value of the mean will decrease because there is now a lower total value. As a result, the standard deviation will be reduced as well. Yes, the median is the better option. This is due to the fact that changing the value of 100 to 15 does not change the value of the median, and thus the previous information would not be changed if the median we used was.