Question

A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied at least one hour for the test. The remaining twelve students admitted that they had not studied for the test at all. The test results (expressed as a percent) for the two groups are shown below.

Studied :
87
,

100
,

94
,

79
,

92
,

100
,

95
,

83
,

89
,

99
,

100
,

91
,

89
,

95
,

100
,

93
,

96
,

83


Did Not Study :
82
,

72
,

45
,

91
,

58
,

83
,

65
,

87
,

90
,

77
,

73
,

89

Part 1: Calculate the mean of the group that studied, rounded to the nearest tenth.

Part 2: Calculate the mean absolute deviation of the group that studied, rounded to the nearest tenth.

Part 3: How many of the scores (from the group that studied) are within one mean absolute deviation of the mean.

Answer 1

Explanation:

part1

the mean value is

(87+100+94+79+92+100+95+83+89+99+100+91+89+95+100+93+96+83) / 18

= 1665 / 18 = 92.5

part2

this is the sum of the absolute value of the differences bergen the individual sites and the mean value divided by the number of data points :

(5.5+7.5+1.5+13.5+0.5+7.5+2.5+9.5+3.5+6.5+7.5+1.5+3.5+2.5+7.5+0.5+3.5+9.5)/18

= 94/18 = 5.222222222... ≈ 5.2

part3

how many scores are less than 5.2 away (plus or minus) from the mean value ? in other words, how many differences in the part2 calculation were smaller than or equal to 5.2 ?

there are 9 scores meeting that criteria :

94, 92, 95, 89, 91, 89, 95, 93, 96