Question

Determine which measure(s) of center would best reflect the data and explain how you know

Answer 1

If we rearrage the data in ascending order,we get:

`\begin{gathered} 9,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,13,13, \\ 13,13,14,14,14,14,15,15,15,15,15,15,15,16,17,17,17,17,17 \end{gathered}`

notice that the median in this case is m = 13, while for the mean, we have:

`\begin{gathered} \mu=(9+7(10++6(11)+5(12)+4(13)+7(15)+16+5(17))/(40) \\ =(9+70+66+60+52+56+105+16+85)/(40)=(519)/(40)=12.98 \\ \mu=12.98 \end{gathered}`

as we can see, the mean is nearly the same value as the median. This is evident since there are no outliers on the data. Thus, the median or the mean can be used to describe the dataset