Question

he test scores of 32 students are listed below. Construct a boxplot for the data set and include the values of the 5-number summary

Answer 1

Five number summary is:

Minimum Value = 32

First Quartile = 56

Median = 69.5

Third Quartile = 80

Maximum Value = 99

Box plot is used to represented by Option C.

Explanation:

The box plot is made up of five number summary.

The five number summary consists of:

Minimum Value

First Quartile

Median

Third Quartile

Maximum Value

So, Looking at the data set and finding five number summary,

Minimum Value = 32

First Quartile

We find median of lower half of data (i.e all data before median)

(55+57)/2 =112/2 =56

So, First Quartile = 56

Median

Mean of middle most numbers: 69+70/2 = 69.5

So, Median = 69.5

Third Quartile

We find median of upper half of data (i.e all data after median)

(79+81)/2 =160/2 =80

So, Third Quartile = 80

Maximum Number = 99

So, Five number summary is:

Minimum Value = 32

First Quartile = 56

Median = 69.5

Third Quartile = 80

Maximum Value = 99

Box plot is used to represent this five number summary.

Option C is correct.