Question

the following table shows the distribution of hours worked each week on average for a sample of 100 community college students.

hours per week number of students

0-9 24

10-19. 14

20-29. 39

30-39. 18

40-49. 5

1) what is mean? round 3 decimals

2) standard deviation of sample? round 3 decimals

3) what is the mid point of the class 20-29?

4) do a histograms of the data ; shape of distribution?

5) what is quartile 75 of distribution?

Answer 1

Class interval	Midpoint, x	Frequency, f	fx	fx²	cf
0 - 9	4.5	24	108	486	24
10 - 19	14.5	14	203	2943.5	38
20 - 29	24.5	39	955.5	23409.75	77
30 - 39	34.5	18	621	21424.5	95
40 - 49	44.5	5	222.5	9901.25	100
Total		100	2110	58165

1. Mean, x̅ = ∑fx / n = 2110/100 = 21.1

2. Standard deviation, s = √((∑fx² - (∑fx)²/n)/(n-1)) = √((58165 - 2110²/100)/(100- 1)) = 11.740

3. Mid-point of class 20-29 = 24.5

4. Histogram:

5. Class with 75th value of the observation in cf column lies in the class 20-29.

Q3 class : 19.5-29.5

The lower boundary point of 19.5-29.5, L = 19.5.

Q3 = L + c*((3n/4 - cf)/f)

=19.5 + 10*((75-38)/39)

= 28.99