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: Count the original data points

There are \(1 + 3+1 + 3+1=9\) data points. The data set (in order) is \(1,2,2,2,4,4,4,5,5\).

Step2: Calculate the original mean and median

• Mean: \(\frac{1 + 2+2+2+4+4+4+5+5}{9}=\frac{29}{9}\approx3.22\)
• Median: The 5 - th value of the ordered data set. So the median is \(4\)

Step3: Add the new data point

The new data set (in order) is \(1,2,2,2,4,4,4,5,5,12\). There are \(n = 10\) data points.

• New Mean: \(\frac{1+2 + 2+2+4+4+4+5+5+12}{10}=\frac{41}{10}=4.1\)
• New Median: The average of the 5 - th and 6 - th values. \(\frac{4 + 4}{10}=4\)

Answer:

The mean will increase, and the median will stay the same.