SOCI 3443: Social Statistics
Homework Assignment 4
Note: Please show all your work including SPSS printouts. Points will be taken out if you fail to show your work.
1. College students were asked to give their favorite leisure-time activity. The five most commonly mentioned activities were rapping with friends (RF), reading (R), watching television (TV), participating in a sport (PS), and drinking (D). (8 points)
RF PS D RF R TV RF D PS RF RF
R TV RF D TV RF TV D TV RF RF
D RF R R RF R R TV D TV D
D RF TV TV RF PS TV RF TV TV D
D D TV RF PS RF RF RF D
a) Which measure of central tendency is the most appropriate for these data?
b) Find the most appropriate measure of central tendency identified in a)?
RF: 1, R: 2, TV: 3, PS: 4 and D: 5
2. Information from a biographical inventory was used to compute a socioeconomic index for students in a university marching band. Scores above 72 were classified as very high (VH); scores from 61 to 72, as high (H); from 43 to 60, as middle (M); and below 43, as low (L). (8 points)
H H H M VH VH H M L L
M L H M VH H H VH M M
VH H L H H M VH M H M
a) Which measure of central tendency is the most appropriate for these data?
b) Find the most appropriate measure of central tendency identified in a)?
VH: 1, H: 2, M: 3, L: 4
3. Find the mean, median, and mode for the following frequency distribution for the number of hours students worked per week: (10 points)
Number of hours Frequency (f)
1 2
2 4
3 3
4 1
5 6
6 4
4. The following is a grouped frequency distribution for the number of hours mothers spend in child care per week:
Number of hours Frequency (f)
0 - 9 4
10 - 19 13
20 - 29 32
30 - 39 14
40 - 49 7
50 - 59 4
a) Find the mean, median and mode. (9 points)
b) Construct a polygon for this distribution and discuss the shape of the distribution with regard to skewness. (5 points)
5. Immediately following the coverage of a social science unit, a class of 13 students took a 20-item quiz on the material presented. Their scores, based on the number of items answered correctly, were as follows: 12,12,14,15,16,19,20,10,7,5,2,3,3.
a) Find the mean, the median, and the mode for the above scores. (9 points)
A week later these students took the same test a second time. This time their scores were:
11,11,11,11,12,14,20,10,10,9,2,8,9
b) Find the mean, the median, and the mode for these scores. (9 points)
c) Was there a difference in their performance when taking the test a second time?
(3 points)
6. The 2006 General Social Survey asked respondents to report the age when they first got married. Answer the following questions based on the histogram and the stem-and-leaf plot generated by SPSS 22. (18 points)
a) Find the mode, the median, and the mean for the age when they first got married. (10 points)
b) Which measure of central tendency yields the highest value? Which yields the lowest?
c) Discuss the shape of this distribution with regard to possible skewness.
d) Which measure of central tendency is the most appropriate, and why?
Age When First Married Stem-and-Leaf Plot
Frequency Stem & Leaf
1.00 13 . &
4.00 14 . 0
7.00 15 . 00
32.00 16 . 00000000000
43.00 17 . 00000000000000
118.00 18 . 000000000000000000000000000000000000000
129.00 19 . 0000000000000000000000000000000000000000000
121.00 20 . 0000000000000000000000000000000000000000
132.00 21 . 00000000000000000000000000000000000000000000
96.00 22 . 00000000000000000000000000000000
82.00 23 . 000000000000000000000000000
82.00 24 . 000000000000000000000000000
72.00 25 . 000000000000000000000000
61.00 26 . 00000000000000000000
49.00 27 . 0000000000000000
27.00 28 . 000000000
34.00 29 . 00000000000
25.00 30 . 00000000
18.00 31 . 000000
21.00 32 . 0000000
10.00 33 . 000
5.00 34 . 00
33.00 Extremes (>=35)
Stem width: 1
Each leaf: 3 case(s)
& denotes fractional leaves.
7. Use GSS2016.sav data file and SPSS to answer the following questions: (20 points)
a) Compute appropriate descriptive statistics (including frequency table, graphs and measure of central tendency) for the following two variables: respondent’s sex (variable
sex) and respondent’s highest degree (variable
degree).
b) Compute appropriate descriptive statistics (including grouped frequency tables, graphs and measures of central tendency) for the following two variables: hours worked last week (variable
hrs1) and respondent’s age (variable
age). For each variable, compare the different measures of central tendency and select the most appropriate measure of central tendency.