60 Chapter 2 Describing and Exploring Data
2.29 The following data represent the total number of households, the number of households
headed by women, and family size from 1960 to 1990. Present these data in such a way to
reveal any changes in U.S. demographics. What do the data suggest about how a social scien-
tist might look at the problems facing the United States? (Households are given in thousands.)Households
Total Headed by Family
Year Households Females Size
1960 52,799 4,507 3.33
1970 63,401 5,591 3.14
1975 71,120 7,242 2.94
1980 80,776 8,705 2.76
1985 86,789 10,129 2.69
1987 89,479 10,445 2.66
1988 91,066 10,608 2.64
1989 92,830 10,890 2.62
1990 92,347 10,890 2.632.30 Make up a set of data for which the mean is greater than the median.
2.31 Make up a positively skewed set of data. Does the mean fall above or below the median?
2.32 Make up a unimodal set of data for which the mean and median are equal but are different
from the mode.
2.33 A group of 15 rats running a straight-alley maze required the following number of trials to
perform at a predetermined criterion level:
Trials required to reach criterion: 18 19 20 21 22 23 24
Number of rats (frequency): 1 0 4 3 3 3 1
Calculate the mean and median of the required number of trials for this group.
2.34 Given the following set of data, demonstrate that subtracting a constant (e.g., 5) from every
score reduces all measures of central tendency by that constant: [8, 7, 12, 14, 3 7].
2.35 Given the following set of data, show that multiplying each score by a constant multiplies
all measures of central tendency by that constant: 8 3 5 5 6 2.
2.36 Create a sample of 10 numbers that has a mean of 8.6. How does this illustrate the point we
discussed about degrees of freedom?
2.37 The accompanying output applies to the data on ADDSC and GPA described in Appendix:
Data Set. How do these answers on measures of central tendency compare to what you
would predict from the answers to Exercises 2.12 and 2.13?Descriptive StatisticsDescriptive Statistics for ADDSC and GPAADDSC GPA Valid N(listwise)
N 88 88 88
Minimum 26 1
Maximum 85 4
Mean 52.60 2.46
Std. Deviation 12.42 .86
Variance 154.311 .742