Question

1. the list shown gives the heights, in inches, for the 6 ten - year - old children in a group: 52, 53, 54, 54, 55, 56. a seventh child with a height of 60 inches will be added to the group. which of the following correctly describes how the mean and the median of the group will change when the seventh child is added?

a) the mean and the median will increase.
b) the mean and the median will decrease.
c) the mean will increase, and the median will remain the same.
d) the mean will decrease, and the median will remain the same.

Explanation:

Step1: Calculate the original mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For \(n = 6\) and \(x=\{52,53,54,54,55,56\}\), \(\sum_{i=1}^{6}x_{i}=52 + 53+54+54+55+56=324\). The original mean \(\bar{x}_{1}=\frac{324}{6}=54\).

Step2: Calculate the new mean

After adding a child with height \(x = 60\), \(n = 7\) and \(\sum_{i = 1}^{7}x_{i}=324 + 60=384\). The new mean \(\bar{x}_{2}=\frac{384}{7}\approx54.86\).

Step3: Calculate the original median

For \(n = 6\) (even - numbered data set), the median \(M_{1}=\frac{54 + 54}{2}=54\).

Step4: Calculate the new median

For \(n = 7\) (odd - numbered data set) with data set \(\{52,53,54,54,55,56,60\}\), the median \(M_{2}=54\).

Answer:

C. The mean will increase, and the median will remain the same.