The data below represents the number of desks on each floor of Texter Corporate. 54, 60, 65, 66, 67, 69, 70, 72, 73, 75, 76

Which box plot correctly summarizes the data?

Choose 1

50

53

56

59

62

65

68

71

80

74 77

80

62

65

68

71

74

59

50

53

56

53

50

56

59

62 65 68 71 74 77 80

Box-plot = {54, 65, 69, 73, 76}

Step-by-step explanation:

The data provided for the number of desks on each floor of Texter Corporate is as follows:

S = {54, 60, 65, 66, 67, 69, 70, 72, 73, 75, 76}

There are a total of n = 11 floors.  

A boxplot, also known as a box and whisker plot is a method to demonstrate the distribution of a data-set based on the following 5 number summary,

Arrange the data in ascending order as follows:

S': = {54 , 60 , 65 , 66 , 67 , 69 , 70 , 72 , 73 , 75 , 76}

The minimum value is:

Minimum = 54

The maximum value is:

Maximum = 76

As there are odd number of values the median is the middle value.

Median = 6th value = 69

The first quartile is the median of the first half of the data.

S'₁ = {54 , 60 , 65 , 66 , 67}

First quartile = 3rd value = 65

The third quartile is the median of the second half of the data.

S'₂ = {70 , 72 , 73 , 75 , 76}

Third quartile = 3rd value = 73

Thus, summarized data for the box plot is:

Box-plot = {54, 65, 69, 73, 76}

The box plot is attached below.