Question

Consider the horizontal box plot shown below.

a.What is the median of the data set (approximately)?

b.What are the upper and lower quartiles of the data set (approximately)?

c.What is the interquartile range of the data set (approximately)?

d.Is the data set skewed to the left, skewed to the right, or symmetric?

e.What percentage of the measurements in the data set lie to the right of the median? To the left of the upper quartile?

f.Identify any outliers in the data.

Short answer

(a) 4

(b) 6, 3

(c) 3

(d) Skewed to the right

(e) 50%, 75%

(f) 12, 13, 16

Step-by-step solution

Identifying the median

The median here is approximately 4.

Finding the upper and lower quartiles

Upper Quartile (Q_U) = 6

Lower Quartile (Q_L) = 3

Calculating the the interquartile range(IQR)

IQR = Q_U - Q_L

= 6 – 3

= 3

The interquartile range is 3.

Determining the skewness

The box plot is skewed to the rightbecause the right whisker is longer than the left.

Computing the percentage of the measurements the right of the median and to the left of the upper quartile

Median is the centermost value of the dataset. Therefore, there will be 50% measurements to the right of the median.

The upper quartile is the 75^th percentile. Therefore, there are 75% of measurements to the left of the upper quartile.

Finding the outliers

The threeoutliers are 12, 13, and 16.