Question

Which statement is true if a tenth data point of 45 is added to the data set?

Answer 1

First, let us find the actual mean and median:

Mean:

`\begin{gathered} Mean=(8+11+12+10+9+7+5+3+9)/(9) \\ Mean=8.22 \end{gathered}`

Median:

8 11 12 10 9 7 5 3 9

Organize the data set from smallest to greatest:

3 5 7 8 9 9 10 11 12

Take the data in the middle:

3 5 7 8 9 9 10 11 12

Hence, the median is 9.

Now, if we add 45 to the data set:

Mean

`\begin{gathered} Mean=(3+5+7+8+9+9+10+11+12+45)/(10) \\ Mean=11.9 \end{gathered}`

Median:

3 5 7 8 9 9 10 11 12 45

Take the two values on the middle

3 5 7 8 9 9 10 11 12 45

Find the average of change between 9 and 9:

Median = (9 + 9)/2

Median = 9

Hence, with the new value of 45, the mean will increase but the median will remain the same.

The correct answer is option C.