Question

the following are the ages of 17 music teachers in a school district. 31, 33, 34, 36, 37, 38, 39, 42, 44, 45, 46, 47, 48, 48, 50, 51, 52. notice that the ages are ordered from least to greatest. make a box-and-whisker plot for the data.

Explanation:

Step1: Find the minimum value

The smallest data point is 31.

Step2: Find the first quartile (Q1)

For $n=17$, position of Q1 is $\frac{17+1}{4}=4.5$, so average 4th & 5th values:
$\frac{36+37}{2}=36.5$

Step3: Find the median (Q2)

Position of median is $\frac{17+1}{2}=9$, so 9th value: 44

Step4: Find the third quartile (Q3)

Position of Q3 is $3\times\frac{17+1}{4}=13.5$, so average 13th & 14th values:
$\frac{48+48}{2}=48$

Step5: Find the maximum value

The largest data point is 52.

Step6: Map values to the plot

Align min=31, Q1=36.5, median=44, Q3=48, max=52 to the age axis (30-55), then draw the box-and-whisker plot:

• Left whisker from 31 to Q1=36.5
• Box from Q1=36.5 to Q3=48, with a line at median=44
• Right whisker from Q3=48 to 52

Answer:

The box-and-whisker plot is constructed with:

• Minimum value at 31,
• First quartile (Q1) at 36.5,
• Median (Q2) at 44,
• Third quartile (Q3) at 48,
• Maximum value at 52,

aligned to the provided age axis (30 to 55) as described in the steps.