These data are the number of on-campus burglaries reported in a given year for ten western Pennsylvania universities.
$\begin{array}{llllllllll}37 & 27 & 18 & 21 & 18 & 14 & 19 & 18 & 19 & 23\end{array}$
For the above data set,
I
(b) Find the median.
(c) Find the midrange.
(d) Find the mode.
Round to one decimal place, if necessary.
Answer
Final Answer: The median of the data set is \(\boxed{19.0}\), the midrange is \(\boxed{25.5}\), and the mode is \(\boxed{18}\).
Step 1 ：First, we need to sort the data in ascending order. The sorted data is \([14, 18, 18, 18, 19, 19, 21, 23, 27, 37]\).
Step 2 ：To find the median, we need to find the middle value. Since there are 10 data points, the median is the average of the 5th and 6th values. So, the median is \(\frac{19+19}{2} = 19.0\).
Step 3 ：To find the midrange, we need to find the average of the smallest and largest values in the data set. So, the midrange is \(\frac{14+37}{2} = 25.5\).
Step 4 ：To find the mode, we need to find the value that appears most frequently in the data set. The value 18 appears three times, which is more than any other value. So, the mode is 18.
Step 5 ：Final Answer: The median of the data set is \(\boxed{19.0}\), the midrange is \(\boxed{25.5}\), and the mode is \(\boxed{18}\).
