Question

1. Time to degree has become a "hot" topic with federal legislators. At one state university, it was necessary to do a quick calculation when one of the local congressmen called the president. Twenty students were randomly selected from the most recent graduating class and the number of semesters they were enrolled was calculated as: 7, 8, 10, 11, 8, 6, 10, 9, 9, 8, 13, 12, 8, 11, 11, 14, 8, 7, 10, and 12. What is the standard deviation?

Answer 1

Standard deviation = 2.16

Explanation:

Data provided:

7, 8, 10, 11, 8, 6, 10, 9, 9, 8, 13, 12, 8, 11, 11, 14, 8, 7, 10, and 12

Total number of observations, n = 20

Now,

Mean of the data =
`\frac{\textup{Sum of all observations}}{\textup{Total number of observations}}`

or

Mean of the data =
`\frac{\textup{192}}{\textup{20}}`

or

Mean of the data = 9.6

Thus,

Observed value (x) value - Mean (Value - Mean)²

7 -2.6 6.76

8 -1.6 2.56

10 0.4 0.16

11 1.4 1.96

8 -1.6 2.56

6 -3.6 12.96

10 0.4 0.16

9 -0.6 0.36

9 -0.6 0.36

8 -1.6 2.56

13 3.4 11.56

12 2.4 5.76

8 -1.6 2.56

11 1.4 1.96

11 1.4 1.96

14 4.4 19.36

8 -1.6 2.56

7 -2.6 6.76

10 0.4 0.16

12 2.4 5.76

=====================================================

∑x = 192 ∑(Value - Mean)² = 88.8

Now,

Standard deviation =
`\sqrt{\frac{\sum{(Value - Mean)^2}}{n-1}}`

or

Standard deviation =
`\sqrt{(88.8)/(20-1)}`

or

Standard deviation = 2.16