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: List original data points

From the dot plot, the data set is: $1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6$ (counting each dot as a value)

Step2: Calculate original mean

Sum of data: $1+2+2+2+3+4+4+5+5+5+5+6 = 44$
Mean: $\frac{44}{12} \approx 3.67$

Step3: Calculate original median

12 data points, median is average of 6th and 7th values: $\frac{4+4}{2} = 4$

Step4: Add new data point (12)

New data set: $1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 12$

Step5: Calculate new mean

New sum: $44 + 12 = 56$
New mean: $\frac{56}{13} \approx 4.31$

Step6: Calculate new median

13 data points, median is 7th value: $4$

Step7: Compare changes

Mean increases from ~3.67 to ~4.31; median stays at 4.

Answer:

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