Grouped Data Problems
Find the mean and standard deviation of the following quantitative frequency distributions. These problems were adapted from those on pages 146 to 148 of Michael Sullivan, Fundamentals of Statistics, 2^{nd} edition, Pearson Education, Inc. 2008.
1) A sample of college students was asked how much they spent monthly on a cell phone plan (to the nearest dollar).
Monthly
Cell Phone Plan Cost ($) |
Number of
Students |
10 - 19 |
8 |
20 - 29 |
16 |
30 - 39 |
21 |
40 - 49 |
11 |
50 - 59 |
4 |
2) The following data represent the difference in scores between the winning and losing teams in a sample of 15 college football bowl games from 2004-2005.
Point Difference |
Number of Bowl
Games |
1 - 5 |
8 |
6 - 10 |
0 |
11 - 15 |
2 |
16 - 20 |
3 |
21 - 25 |
1 |
26 - 30 |
0 |
31 - 35 |
1 |
3) The following table represents the distribution of the annual number of days over 100 degrees Fahrenheit for Dallas-Fort Worth for a sample of 80 years from 1905 to 2004.
Days Above 100
Degrees |
Number of Years |
0 - 9 |
25 |
10 - 19 |
33 |
20 - 29 |
14 |
30 - 39 |
5 |
40 - 49 |
2 |
50 - 59 |
1 |
4) The following table shows the distribution of the number of hours worked each week (on average) for a sample of 100 community college students.
Hours
Worked per Week |
Number of Students |
0 - 9 |
24 |
10 - 19 |
14 |
20 - 29 |
39 |
30 - 39 |
18 |
40 - 49 |
5 |
5) The following data represents the age distribution of a sample of 100 people covered by health insurance (private or government). The sample was taken in 2003.
Age |
Number |
25 - 34 |
23 |
35 - 44 |
29 |
45 - 54 |
28 |
55 - 64 |
20 |
6) The following data represent the high temperature
distribution in degrees Fahrenheit for a sample of 40 days from the month of
August in
Temperature |
Days |
60 - 69 |
3 |
70 - 79 |
15 |
80 - 89 |
17 |
90 - 99 |
5 |
7) The following data represent the annual rainfall
distribution in
Rainfall (inches) |
Number of Years |
20 - 24 |
1 |
25 - 29 |
3 |
30 - 34 |
5 |
35 - 39 |
8 |
40 - 44 |
5 |
45 - 49 |
2 |
50 - 54 |
0 |
55 - 59 |
1 |
8) The following data represent the age distribution of a sample of 70 women having multiple-delivery births in 2002.
Age |
Number |
15 - 19 |
1 |
20 - 24 |
5 |
25 - 29 |
16 |
30 - 34 |
28 |
35 - 39 |
17 |
40 - 44 |
3 |
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