Final answer:
To draw a box plot for the given data set, find the minimum, first quartile, median, third quartile, and maximum values. Draw a box from the first quartile to the third quartile, a vertical line inside the box for the median, and lines from the box to the minimum and maximum values. No outliers were found in this data set.
Step-by-step explanation:
To create a box plot for the given data set: 22, 35, 18, 30, 37, 20, 40, 18, 38, 38, 23, 19, 27, 31, 34, you first need to find the minimum, first quartile, median, third quartile, and maximum values. The minimum value is 18, the maximum value is 40, and the median is the middle value when the data set is ordered, which is 30. To find the first and third quartile, you need to order the data set and find the median of the lower half and upper half, respectively. The first quartile is 22.5 and the third quartile is 36.5.
Now you can draw the box plot using a number line. Draw a horizontal line and label it with the minimum and maximum values. Then draw a box from the first quartile to the third quartile, a vertical line inside the box for the median, and lines (whiskers) from the box to the minimum and maximum values. Place any outliers (values that are more than 1.5 times the interquartile range away from the nearest quartile) as individual points outside the whiskers.
In this case, the box plot will have a minimum of 18, a first quartile of 22.5, a median of 30, a third quartile of 36.5, and a maximum of 40. There are no outliers in this data set, so the box plot will not have any individual points outside the whiskers.
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