Question

study the data - set {4, 6, 7, 8, 10, 10}. if one of the 10s is removed, how will it affect the mean of the set? a the mean will increase. b the mean will decrease. c the mean remains unchanged. d the mean will become zero.

Explanation:

Step1: Calculate the original mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The original data - set is $\{4,6,7,8,10,10\}$, $n = 6$, and $\sum_{i=1}^{6}x_{i}=4 + 6+7 + 8+10+10=45$. So the original mean $\bar{x}_{1}=\frac{45}{6}=7.5$.

Step2: Calculate the new mean

After removing one of the 10s, the new data - set is $\{4,6,7,8,10\}$, $n = 5$, and $\sum_{i = 1}^{5}x_{i}=4 + 6+7 + 8+10=35$. So the new mean $\bar{x}_{2}=\frac{35}{5}=7$.

Step3: Compare the means

Since $7<7.5$, the mean decreases.

Answer:

B. The mean will decrease