PROJECT: GRAPHS FOR
QUALITATIVE DATA
Objective:
Construct graphs for categorical data.
I.
Perform the following operations
A.
Add "Relative Frequency" and “Degrees” columns to the
tables.
B.
Calculate the "Relative Frequencies" by dividing each “$
Billions” by the sum
of the “$ Billions”. Put
the result in the "Relative Frequency" column.
C.
Multiply the “Rel. Freq.” by 360 and fill in the "Degrees"
column.
| PROGRAM |
$ BILLIONS |
REL. FREQ. |
DEGREES |
|
Social Security |
684 |
684 / 1,900 ≈ 0.36 |
0.36(360) ≈130 |
|
National Defense |
342 |
342 / 1,900 ≈ 0.18 |
0.18(360) ≈ 65 |
|
Interest on the National Debt |
190 |
190 / 1,900 = 0.10 |
0.10(360) = 36 |
|
Communities |
190 |
190 / 1,900 = 0.10 |
0.10(360) = 36 |
|
Social Programs |
342 |
342 / 1,900 ≈ 0.18 |
0.18(360) ≈ 65 |
|
Law Enforcement |
38 |
38 / 1,900 ≈ 0.02 |
0.02(360) ≈ 7 |
|
Pay Down the National Debt |
114 |
114 / 1,900 ≈ 0.06 |
0.06(360) ≈22 |
|
Total |
1,900 |
1,900 / 1,900 =1.00 |
361* |
* Acceptable rounding error.
| PROGRAM |
$ BILLIONS |
REL. FREQ. |
DEGREES |
|
Social Security |
798 |
798 / 2,100 ≈ 0.38 |
0.38(360) ≈ 137 |
|
National Defense |
420 |
420 / 2,100 = 0.20 |
0.20(360) =72 |
|
Interest on the National Debt |
168 |
168 / 2,100 ≈ 0.08 |
0.08(360) ≈ 29 |
|
Communities |
210 |
210 / 2,100 = 0.10 |
0.10(360) = 36 |
|
Social Programs |
441 |
441 / 2,100 ≈ 0.21 |
0.21(360) ≈ 76 |
|
Law Enforcement |
63 |
63 / 2,100 ≈ 0.03 |
0.03(360) ≈ 11 |
|
Total |
2,100 |
2,100 / 2,100 ≈ 1.00 |
361 |
* Acceptable rounding error.
II.
Use the table from Part I to construct the graphs.
A. Vertical frequency bar
graph for 2001.
B. Relative frequency pie chart for 2001.
C. Horizontal relative frequency bar graph for 2002
D. Relative frequency pie chart for 2002.
III. Compare the pie charts of US expenditures for 2001 and
2002. What differences do you find?
Write at least one paragraph describing what you feel are
the factors responsible for these
differences?
Answers will vary, possible responses will include:
1. Payments on the National Debt were made in 2001 but were not made in
2002.
2. References to September 11, 2001 that caused changes in the
government spending
in 2002.
3. The government had a surplus in 2001.
4. The government had to borrow to meet expenditures in 2002.
5. Even though the government was spending more money, it passed
legislation allowing tax
breaks. This lowered its income.
Note 1: It
is amazing (frightening) the number of students who do not connect Sept. 11,
with the change in government
spending.
Note 2:
Many
students will attribute the change in spending to the "baby boomers"
who are retiring. The increase
costs of Social Security is responsible for
the changes in government spending.
Note #3: Reason #5 is unknown to may students but some students may be aware of it.
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