Question

if a new data point at 12 is added to the graph, which will be true? the mean will increase, and the median will stay the same. the median will increase, and the mean will stay the same. the mean will increase more than the median, but both will increase. the median will increase more than the mean, but both will increase.

Explanation:

Step1: Recall mean and median concepts

Mean is sum of data divided by count. Median is middle - value.

Step2: Analyze original data (assume data points are 1, 2, 2, 2, 4, 4, 4, 5)

Original count \(n = 8\). Mean \(\bar{x}=\frac{1 + 2+2+2+4+4+4+5}{8}=\frac{24}{8}=3\). Median of 8 - data set (even count) is average of 4th and 5th ordered values, \(\frac{2 + 4}{2}=3\).

Step3: Add new data point 12

New count \(n = 9\). New mean \(\bar{x}=\frac{24 + 12}{9}=\frac{36}{9}=4\). New median (9 - data set, odd count) is 5th ordered value. In ordered set \(1,2,2,2,4,4,4,5,12\), median is 4.

Answer:

The mean will increase more than the median, but both will increase.