Question

question 11 of 18
which of the following best describes the change in the mean when 1213 is
included in the data set below?
34, 75, 26, 81, 65, 38, 49
a. it decreases.
b. it stays the same.
c. it increases.

Explanation:

Step1: Calculate the original mean

The original data set is \(34,75,26,81,65,38,49\).
The sum of the original data is \(34 + 75+26 + 81+65+38+49=\sum_{i = 1}^{7}x_{i}=368\).
The number of data points \(n = 7\).
The original mean \(\bar{x}_{1}=\frac{\sum_{i = 1}^{7}x_{i}}{n}=\frac{368}{7}\approx52.57\).

Step2: Calculate the new mean

The new data set is \(34,75,26,81,65,38,49,1213\).
The sum of the new data is \(\sum_{i = 1}^{8}x_{i}=368 + 1213=1581\).
The number of data points \(n = 8\).
The new mean \(\bar{x}_{2}=\frac{\sum_{i = 1}^{8}x_{i}}{n}=\frac{1581}{8}=197.625\).

Answer:

C. It increases.