Question

The following back to back stemplot represents the amount a sample of students spent on their last haircut. Because there are significant differences between males and females the data was selerated by gender.
Please answer to all of the questions!

Answer 1

The 5 - number summary of the distribution obtained from the boxplot is :

• Minimum = 20
• Maximum = 85
• Lower quartile = 35
• Median = 44
• Upper quartile = 58
• Outlier = 100

Firstly, we need to extract the values for the amount spent by females :

20, 25, 25, 35, 37, 38, 39, 43, 45, 46, 50, 53, 60, 70, 85, 100

The five number summary include ;

• Minimum, lower Quartile, Median, Upper Quartile and Maximum values.

Rearranging the data in ascending order :

20, 25, 25, 35, 37, 38, 39, 43, 45, 46, 50, 53, 60, 70, 85, 100

The boxplot clearly and easily gives the five number summary of the distribution :

• Minimum = 20 (starting point of the whisker)
• Lower quartile = 35 (starting point of the box)
• Median = 44 (vertical line in between the box)
• Upper quartile = 58 (endpoint of the box)
• Maximum = 85 (endpoint of the upper whisker).

Outlier :

• Lower boundary = LOWER QUARTILE - (1.5 × IQR)
• Upper boundary = UPPER QUARTILE + (1.5 × IQR)
• IQR = UPPER QUARTILE - LOWER QUARTILE
• IQR = (58 - 35) = 23

Lower boundary = 35 - (1.5 × 23) = 0.5

Upper boundary = 58 + (1.5 × 23) = 92.5

• The point denoted by a dot on the boxplot is an outlier = 100

Hence, values lesser than 0.5 or greater than 92.5 are outliers.

Therefore, 100 is an outlier.

Learn more : brainly.com/question/24582786