Question

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

18, 20, 24, 26, 36, 29, 32, 36

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

Answer 1

Given:

The highway mileage for a sample of 8 different models of a car company can be found below.
18, 20, 24, 26, 36, 29, 32, 36.

Arrange the given data in ascending order

18, 20, 24, 26, 29, 32, 36, 36.

Five number summary consists of

Minimum value of the sorted data

First quartile, Q1 : Q1 is the median of the first half of the sorted data

Median : Median is the middle value

Third quartile, Q3 : Q3 is the median of the second half of the sorted data

Maximum value of sorted data

So

* Minimum = 18

* First quartile, Q1 = 20+24/2 = 22

* Median = 26+29/2 = 27.5

* Third quartile, Q3 = 32+36/2 = 34

* Maximum = 36

Inter quartile range = Q3 - Q1 = 34 - 22 = 12

Lower quartile = Q1 - 1.5 × IQR = 22-1.5×12 = 4

Upper quartile = Q3 - 1.5 × IQR = 34-1.5×12 = 16

An outlier in a distribution is a number that is more than 1.5 times the length of the box away from either the lower or upper quartiles

So there is no any outlier.