Question

The following are final exam scores for 30 students in an elementary statistics class.

91            59            82            91            79            76            90            69            77            83

59            88            95            72            88            81            77            52            80            96

62            97            76            75            75            89            61            72            90            85

a.              Find the quartiles for this data______________________________.

b.             What is the Interquartile Range (IQR)_________________________?

c.              What percent of students got at least a 72 on their final exam______________?

d.              Build a boxplot using the graphing calculator.

Answer 1

a)

Entire data set (sorted):
52 ; 59 ; 59 ; 61 ; 62 ; 69 ; 72 ; 72 ; 75 ; 75 ; 76 ; 76 ; 77 ; 77 ; 79 ; 80 ; 81 ; 82 ; 83 ; 85 ; 88 ; 88 ; 89 ; 90 ; 90 ; 91 ; 91 ; 95 ; 96 ; 97

First Half of Data Set (Sorted):
52 ; 59 ; 59 ; 61 ; 62 ; 69 ; 72 ; 72 ; 75 ; 75 ; 76 ; 76 ; 77 ; 77 ; 79

Second Half of Data Set (Sorted):
80 ; 81 ; 82 ; 83 ; 85 ; 88 ; 88 ; 89 ; 90 ; 90 ; 91 ; 91 ; 95 ; 96 ; 97

Minimum = 52

Q1 = First Quartile = Middle of First Half of Data Set = 72

Q2 = Median = Second Quartile = Middle of Entire Data Set = 79.5

Q3 = Third Quartile = Middle of Second Half of Data Set = 89

Maximum = 97

.b)

The interquartile range is the difference between the third and first quartiles.

The third quartile is 89.

The first quartile is 72.

The interquartile range = 89 - 72 = 17.

c)

percent of students got at least a 72 on their final exam =

P( X >72) = 72 - 78.9   / 11.92 = -0.5788

P( Z > -0.5788) =P ( Z<0.5788 )=0.719

d)