Questions: A 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 as follows. 4, 7, 8, 13, 14, 17, 18, 21, 21, 23, 24, 25, 26, 27, 28, 30, 30, 31, 41, 73 (a) Select the box-and-whisker plot. (i) 0 Find the interquartile range. IQR = 16 (b) Below is the box-and-whisker plot of data from a survey of 20 nurses at Center Hospital.

A 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 as follows. 4, 7, 8, 13, 14, 17, 18, 21, 21, 23, 24, 25, 26, 27, 28, 30, 30, 31, 41, 73 (a) Select the box-and-whisker plot. (i) 0 Find the interquartile range. IQR = 16 (b) Below is the box-and-whisker plot of data from a survey of 20 nurses at Center Hospital.
Transcript text: A 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 as follows. 4, 7, 8, 13, 14, 17, 18, 21, 21, 23, 24, 25, 26, 27, 28, 30, 30, 31, 41, 73 (a) Select the box-and-whisker plot. (i) 0 Find the interquartile range. \[ I Q R=16 \times \] (b) Below is the box-and-whisker plot of data from a survey of 20 nurses at Center Hospital.
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Solution

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Solution Steps

Step 1: Identify the correct box-and-whisker plot
  • The given data set is: 4, 8, 9, 13, 17, 18, 21, 21, 23, 24, 26, 26, 30, 30, 31, 41, 41, 73.
  • To identify the correct box-and-whisker plot, we need to determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
Step 2: Calculate the quartiles and median
  • Minimum value: 4
  • Maximum value: 73
  • Median (Q2): The median is the middle value of the ordered data set. Since there are 18 data points, the median is the average of the 9th and 10th values: (23 + 24) / 2 = 23.5
  • First quartile (Q1): The median of the first half of the data (4, 8, 9, 13, 17, 18, 21, 21, 23) is the 5th value: 17
  • Third quartile (Q3): The median of the second half of the data (24, 26, 26, 30, 30, 31, 41, 41, 73) is the 5th value: 30
Step 3: Select the correct box-and-whisker plot
  • The box-and-whisker plot should have:
    • Minimum: 4
    • Q1: 17
    • Median: 23.5
    • Q3: 30
    • Maximum: 73
  • The correct box-and-whisker plot is the third one from the left.

Final Answer

  • The correct box-and-whisker plot is the third one from the left.
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