Question

Draw a box-and-whisker plot of the data. Dogs' weights (in pounds): \(88,23,75,46,77,22,83,75,97,89,46,79,69,72,91,20,75,78,83,35,39,98,59,77,84,69,82,79,57,91\)

Short answer

The box-and-whisker plot for the data involves a number line from 20 to 100 with a box extending from 46 (Q1) to 83 (Q3), and a line within the box at 76 (median). Lines extend from this box to 20 (minimum) and 98 (maximum).

Step-by-step solution

Sort the Dataset

Start off by sorting the dogs' weights in ascending order: \(20, 22, 23, 35, 39, 46, 46, 57, 59, 69, 69, 72, 75, 75, 75, 77, 77, 78, 79, 79, 82, 83, 83, 84, 88, 89, 91, 91, 97, 98\)

Find the Median

The median is the middle number of the sorted dataset. With 30 data points, the median is the average of the 15th and 16th data points, which are 75 and 77, respectively. So the median is \((75 + 77) / 2 = 76\).

Determine Lower and Upper Quartiles

The lower quartile (Q1) is the median of the lower half of the data, not including the median itself. There are 15 data points in the lower half. The median of this is the 8th value, which is 46. The upper quartile (Q3) is the median of the upper half of data, excluding the median. The 8th value here is 83.

Find the Minimum and Maximum

The minimum value is the smallest data point, which is 20. The maximum value is the largest data point, which is 98.

Draw the Box-and-Whisker Plot

Now, draw a number line from 20 to 100. Mark the positions of the minimum value, lower quartile, median, upper quartile, and maximum value on the line. Draw a box from the lower quartile to upper quartile position, with a line inside the box at the median. Then draw lines (whiskers) from the box to the minimum and maximum values.