Question

The highway mileage (mpg) for a sample of 8 different models of a car company can be found below.

17, 21, 23, 26, 36, 30, 33, 36

Find the 5-number summary, check for any outliers, and use it to create a boxplot.

Answer 1

Ascending order: 17, 21, 23, 26, 30, 33, 36, 36

n = 8

Median = (nth/2 + (n/2th + 1))/2

= (26+30)/2

= 28

Q1 = (21+23)/2

= 22

Q3 = (33+36)/2

= 34.5

Five number summary:

IQR = Q3-Q1

= 34.5-22

= 12.5

Lower boundary for outlier detection = 22-1.5*12.5

= 3.25

Upper boundary for outlier detection = 34.5+1.5*12.5

= 53.25

As we can see there is no data outside the interval[3.25, 53.25] and hence we can say that there is no outlier.

Box Plot:

Please upvote if you have liked my answer, would be of great help. Thank you.