Question

Make a box-and-whisker plot for the data:

36, 39, 39, 41, 43, 49, 61, 64

a. smallest value 36
b. Quartile 1: 39
c. Median: 42
d. Quartile 2: 55
e. greatest value: 64

Answer 1

Answer: See the diagram below

The five number summary you wrote out is correct.

The tip of the left whisker is at 36, since this is the smallest value and we don't have outliers. The tip of the right whisker is at 64 which is the max (we don't have outliers here either).

The left and right edges of the box are Q1 and Q3 respectively. The median is the vertical line inside the box. The vertical line does not have to be at the midpoint as the diagram shows.

The IQR (interquartile range) is found by computing IQR = Q3-Q1 = 55-39 = 16

Note that the lower fence is L = Q1 - 1.5*IQR = 39 - 1.5*16 = 15. Anything below this value of L is an outlier.

The upper fence is U = Q3 + 1.5*IQR = 55 + 1.5*16 = 113.5; anything above this value of U is an outlier. All of the values in the given set are between L and U, meaning we don't have outliers. If we had outliers, then we would have island points outside the main box-and-whisker plot.

I used GeoGebra to create the box-and-whisker plot.

Answer 2

The data and 5-number summary is given.

Based on the 5 numbers we have the attached box-and-whisker plot.