01 &amp; 02 STAT HWB a

# 01 &amp; 02 STAT HWB a - Dr V.R Bencivenga Economics...

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Dr. V.R. Bencivenga Economics 329 PRACTICE HOMEWORK #1B: ANSWERS 1.a. Approximately continuous. Technically discrete, because the units of measurement are “dollars,” but the number of values of the variable in the data set is going to be large (probably each value will be unique), and the typical value of the variable is large compared to the unit of measurement. b. Continuous. A proportion can take on any value from zero to one (or zero to one hundred if in percentage points). c. Discrete. Any given state probably has one, two, or three state university systems (I’m pretty sure every state has at least one, and I’m not aware of any state that has more than three, although if there is a state with four, the variable would still be considered to be discrete). d. Discrete. Dummy variable, since any state university is either a land grant institution or not. e. Approximately continuous. Technically discrete, because the units of measurement are “students,” but the criteria for modeling the variable as continuous (given above) are satisfied. 2.a. Median. This variable will have an asymmetric distribution, with a long right “tail,” similar to that of the distribution of income. The relatively small number of large cities would pull the mean up compared to the median, distorting the impression given by the mean. b. Either the median or mean could be justified. Probably the distribution of this variable is somewhat asymmetric with a right “tail,” suggesting that the median is most appropr iate. But probably it is not very asymmetric to some extent people who get married late will be offset by people who get married young, and most marriages probably occur between people in their twenties and thirties, suggesting that the mean is a reasonable measure. c. Mode. This information is qualitative. The concepts of the mean and median do not make sense in this context. d. Again, either the median or mean could be justified. Probably the distribution is somewhat asymmetric with a right “tail,” but probably the degree of asymmetry is not great. In practice, it would be reasonable to report both the median and the mean, with the difference between them indicating the degree of skewness.

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