At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were Find the interquartile range.
$$\begin{array} { l l l l l l l l l l }
27 & 3 & 7 & 20 & 28 & 38 & 31 & 45 & 19 & 11 \
9 & 19 & 35 & 30 & 33 & 16 & 25 & 37 & 13 & 38
\end{array}$$
A)46.5
B)19.5
C)22.5
D)48.5
E)21.5

Question

At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were Find the interquartile range.
$$\begin{array} { l l l l l l l l l l } 
27 & 3 & 7 & 20 & 28 & 38 & 31 & 45 & 19 & 11 \
9 & 19 & 35 & 30 & 33 & 16 & 25 & 37 & 13 & 38
\end{array}$$
A)46.5
B)19.5
C)22.5
D)48.5
E)21.5

Quizplus · Accepted Answer

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) in a data set, representing the middle 50% of the data. To find the IQR, first, we need to arrange the data in ascending order and then find Q1 and Q3.Arranged data: 3, 7, 9, 11, 13, 16, 19, 19, 20, 25, 27, 28, 30, 31, 33, 35, 37, 38, 38, 45With 20 data points, Q1 is the average of the 5th and 6th values (since Q1 is at the 25th percentile, or 1/4th of 20, which is 5), and Q3 is the average of the 15th and 16th values (since Q3 is at the 75th percentile, or 3/4ths of 20, which is 15).Q1 = (13 + 16) / 2 = 14.5Q3 = (33 + 35) / 2 = 34IQR = Q3 - Q1 = 34 - 14.5 = 19.5