Question

The data set lists the number of tickets purchased for a school dance each day for 9 days. {13, 6, 13, 8, 2, 19, 11, 16, 17}If 32 is added to the data set, which statement will be TRUE?

Answer 1

D

1) The median is by nature more consistent and resistant to changes when some value is added to the data set. Let's visualize how that happens:

2) Mean

$\begin{gathered} \left\{13,6,13,8,2,19,11,16,17\right\} \\ \bar{x}=\frac{13+6+13+8+2+19+11+16+17}{9}=11.67 \\ 2)\operatorname{\{}13,\:6,\:13,\:8,\:2,\:19,\:11,\:16,\:17,32\operatorname{\}} \\ \bar{x}=\frac{\sum_{i=1}^na_i=137}{10}=13.7 \end{gathered}$

As we can see, the addition of 32 to the data set changes the mean.

3) Now, let's check the Median. Rewriting that into the ascending order:

$\begin{gathered} 2,\:6,\:8,\:11,\:13,\:13,\:16,\:17,\:19 \\ Median:13 \end{gathered}$

Note that 13 divides the distribution into two halves.

Now, let's add 32 to that dataset and check it:

$\begin{gathered} 2,\:6,\:8,\:11,\:13,\:13,\:16,\:17,\:19,\:32 \\ Md=\frac{13+13}{2}=13 \end{gathered}$

Thus, we can tell that the answer is: