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

Original data points: \(1,2,2,3,4,4\). Number of data points \(n = 6\).

Step2: Calculate the original mean

Original mean \(\bar{x}_{1}=\frac{1 + 2+2 + 3+4+4}{6}=\frac{16}{6}=\frac{8}{3}\approx2.67\).

Step3: Calculate the original median

For \(n = 6\) (even), median \(M_{1}=\frac{2 + 3}{2}=2.5\).

Step4: Add the new data point

New data points: \(1,2,2,3,4,4,12\). Number of data points \(n = 7\).

Step5: Calculate the new mean

New mean \(\bar{x}_{2}=\frac{1+2 + 2+3+4+4+12}{7}=\frac{28}{7} = 4\).

Step6: Calculate the new median

For \(n=7\) (odd), median \(M_{2}=3\).

Answer:

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