Chapter 3.1, Problem 14P

Critical Thinking Consider two data sets.

Set $\text{A}:n=5;\bar{x}=10$

Set $\text{B}:n=50;\bar{x}=10$

(a) Suppose the number 20 is included as an additional data value in Set A. Compute $\bar{x}$ for the new data set. Hint: $\sum x=n\bar{x}$. To compute $\bar{x}$ for the new data set. add 20 to $\sum x$ of the original data set and divide by 6.

(b) Suppose the number 20 is included as an additional data value in Set B. Compute $\bar{x}$ for the new data set.

(c) Why does the addition of the number 20 to each data set change the mean for Set A more than it does for Set B?