Chapter 4, Problem 4.3P

In problem 3.1 at the end of Chapter 3, you calculated measures of central tendency for six variables for freshmen and seniors. Three of those variables are reproduced here. Calculate the mean (if necessary), the range, and the standard deviation for each variable. What information is added by the measures of dispersion? Write a paragraph summarizing the differences between freshmen and seniors.

Out-of-Pocket Expenses		Number of Movies		Rating of Cafeteria Food
Freshmen	Seniors	Freshmen	Seniors	Freshmen	Seniors
43	75	0	0	10	1
49	72	14	5	7	2
55	70	10	11	2	8
57	95	7	3	1	4
72	72	5	4	8	3
58	67	1	14	6	6
62	50	0	0	10	2
75	59	14	7	0	9
61	55	3	5	5	4
53	95	4	3	6	7
	88		5		4

3.1 $\boxed{SOC}$ A variety of information has been gathered from a sample of college freshmen and seniors, including

• Their region of birth;

• The extent to which they support legalization of marijuana (measured on a scale on which $7=\text{strong}\text{support}$, $4=\text{neutral}$, and $1=\text{strong Opposition}$);

• The amount of money they spend each week out of—pocket for food, drinks, and entertainment;

• How many movies they watched in their dorm rooms last week;

• Their opinion of cafeteria food ( $10=\text{excellent}$, $0=\text{very}\text{bad}$); and

• Their religious affiliation.

Some results are presented here. Find the most appropriate measure of central tendency for each variable for freshmen and then for seniors. Report both the measure you selected and its value for each variable (e.g., “ $\text{<x-custom-btb-me data-me-id="2395" class="microExplainerHighlight">Mode</x-custom-btb-me> }=3$” or “ $\text{<x-custom-btb-me data-me-id="2409" class="microExplainerHighlight">Median</x-custom-btb-me>}=3.5$”). (HINT: Determine the level of measurement for each variable first. In general, this will tell you which measure of central tendency is appropriate. See the section “Choosing a Measure of central Tendency” to review the relationship between measure of central tendency and level of measurement. Also, remember that the mode is the most common score, and especially remember to array scores from high to low before finding the median.)

FRESHMEN
Student	Region of Birth	Legalization	Out-of-Pocket Expenses	Movies	Cafeteria Food	Religion
A	North	7	43	0	10	Protestant
B	North	4	49	14	7	Protestant
C	South	3	55	10	2	Catholic
D	Midwest	2	57	7	1	None
E	North	3	72	5	8	Protestant
F	North	5	58	1	6	Jew
G	South	1	62	0	10	Protestant
H	South	4	75	14	0	Other
I	Midwest	1	61	3	5	Other
J	West	2	53	4	6	Catholic

SENIORS
Student	Region of Birth	Legalization	Out-of-Pocket Expenses	Movies	Cafeteria Food	Religion
K	North	7	75	0	1	None
L	Midwest	6	72	5	2	Protestant
M	North	7	70	11	8	Protestant
N	North	5	95	3	4	Catholic
O	South	1	72	4	3	Protestant
P	South	5	67	14	6	Protestant
Q	West	6	50	0	2	Catholic
R	West	7	59	7	9	None
S	North	3	55	5	4	None
T	West	5	95	3	7	Other
U	North	4	88	5	4	None

Some results are presented here. Find the most appropriate measure of central tendency for each variable for freshmen and then for seniors. Report both the measure you selected and its value for each variable (e.g., “ $\text{Mode }=3$” or “ $\text{Median}=3.5$”). (HINT: Determine the level of measurement for each variable first. In general, this will tell you which measure of central tendency is appropriate. See the section “Choosing a Measure of central Tendency” to review the relationship between measure of central tendency and level of measurement. Also, remember that the mode is the most common score, and especially remember to array scores from high to low before finding the median.)

FRESHMEN
Student	Region of Birth	Legalization	Out-of-Pocket Expenses	Movies	Cafeteria Food	Religion
A	North	7	43	0	10	Protestant
B	North	4	49	14	7	Protestant
C	South	3	55	10	2	Catholic
D	Midwest	2	57	7	1	None
E	North	3	72	5	8	Protestant
F	North	5	58	1	6	Jew
G	South	1	62	0	10	Protestant
H	South	4	75	14	0	Other
I	Midwest	1	61	3	5	Other
J	West	2	53	4	6	Catholic

SENIORS
Student	Region of Birth	Legalization	Out-of-Pocket Expenses	Movies	Cafeteria Food	Religion
K	North	7	75	0	1	None
L	Midwest	6	72	5	2	Protestant
M	North	7	70	11	8	Protestant
N	North	5	95	3	4	Catholic
O	South	1	72	4	3	Protestant
P	South	5	67	14	6	Protestant
Q	West	6	50	0	2	Catholic
R	West	7	59	7	9	None
S	North	3	55	5	4	None
T	West	5	95	3	7	Other
U	North	4	88	5	4	None