Question

the following are the distances (in miles) to the nearest airport for 15 families.
6, 11, 12, 14, 16, 21, 26, 29, 32, 33, 34, 38, 38, 46, 47.
notice that the numbers are ordered from least to greatest.
make a box-and-whisker plot for the data.
image of a box-and-whisker plot template with a number line labeled distance from 5 to 50

Explanation:

Step1: Find the minimum value

The minimum value is the first data point.
Minimum = 6

Step2: Find the first quartile (Q1)

The data set has 15 values. The position of Q1 is $ \frac{n + 1}{4} = \frac{15 + 1}{4} = 4 $th term.
The 4th term is 14. So, Q1 = 14

Step3: Find the median (Q2)

The position of the median is $ \frac{n + 1}{2} = \frac{15 + 1}{2} = 8 $th term.
The 8th term is 29. So, Median = 29

Step4: Find the third quartile (Q3)

The position of Q3 is $ \frac{3(n + 1)}{4} = \frac{3(15 + 1)}{4} = 12 $th term.
The 12th term is 38. So, Q3 = 38

Step5: Find the maximum value

The maximum value is the last data point.
Maximum = 47

Now, to draw the box - and - whisker plot:

• The left whisker goes from the minimum (6) to Q1 (14).
• The box goes from Q1 (14) to Q3 (38), with a line inside the box at the median (29).
• The right whisker goes from Q3 (38) to the maximum (47).

Answer:

The box - and - whisker plot has:

• Minimum: 6
• Q1: 14
• Median: 29
• Q3: 38
• Maximum: 47

To plot:

• Mark the minimum (6) and maximum (47) on the number line.
• Draw a box from 14 (Q1) to 38 (Q3).
• Draw a vertical line inside the box at 29 (median).
• Draw whiskers from 6 to 14 and from 38 to 47.