The monthly telephone usage (in minutes) of 30 adults is listed below. Find the interquartile range for thetelephone usage of the 30 adults. $$\begin{array} { l l l l l l l l l l }
154 & 156 & 165 & 165 & 170 & 171 & 172 & 180 & 184 & 185 \
189 & 189 & 190 & 192 & 195 & 198 & 198 & 200 & 200 & 200 \
205 & 205 & 211 & 215 & 220 & 220 & 225 & 238 & 255 & 265
\end{array}$$
A) 31
B) 30
C) 32
D) 29

Question

The monthly telephone usage (in minutes) of 30 adults is listed below. Find the interquartile range for thetelephone usage of the 30 adults. $$\begin{array} { l l l l l l l l l l } 
154 & 156 & 165 & 165 & 170 & 171 & 172 & 180 & 184 & 185 \
189 & 189 & 190 & 192 & 195 & 198 & 198 & 200 & 200 & 200 \
205 & 205 & 211 & 215 & 220 & 220 & 225 & 238 & 255 & 265
\end{array}$$
A) 31
B) 30
C) 32
D) 29

Quizplus · Accepted Answer

The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1). Q3 is the median of the upper half of the data, and Q1 is the median of the lower half of the data.To find Q3, we first sort the data in ascending order:$$154, 156, 165, 165, 170, 171, 172, 180, 184, 185, 189, 189, 190, 192, 195, 198, 198, 200, 200, 200, 205, 205, 211, 215, 220, 220, 225, 238, 255, 265$$The median of the upper half of the data is 205, so Q3 = 205.To find Q1, we first sort the data in ascending order:$$154, 156, 165, 165, 170, 171, 172, 180, 184, 185, 189, 189, 190, 192, 195, 198, 198, 200, 200, 200, 205, 205, 211, 215, 220, 220, 225, 238, 255, 265$$The median of the lower half of the data is 185, so Q1 = 185.Therefore, the interquartile range is Q3 - Q1 = 205 - 185 = 31.

The Monthly Telephone Usage (In Minutes) of 30 Adults Is