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# Another survey was done at Center Hospital to determine how long (in months) clerical staff had been in their current positions. The responses (in months) of 20 clerical staff members were$\begin{array}{llllllllll} 25 & 22 & 7 & 24 & 26 & 31 & 18 & 14 & 17 & 20 \\ 31 & 42 & 6 & 25 & 22 & 3 & 29 & 32 & 15 & 72 \end{array}$(a) Make a box-and-whisker plot. Find the interquartile range.

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Order the number from smallest to largest:

3, 6, 7, 14, 15, 17, 18, 20, 22, 22, 24, 25, 25, 26, 29, 31, 31, 32, 42, 72

Since the number of scores is even, the median is the average of the middle scores:

$M=Q_2=\dfrac{22+24}{2}=23$

The first quartile is the median of the data values below the median (or at 25% of the data):

$Q_1=\dfrac{15+17}{2}=16$

The third quartile is the median of the data values above the median (or at 75% of the data):

$Q_3=\dfrac{29+31}{2}=30$

The interquartile range IQR is the difference of the third and first quartile:

$IQR=30-16=14$

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