I'm creating a large number of practice problems for my statistics students. These problems are for an elementary stats course where students:
- measure central tendency
- measure dispersion
- use linear regression to extrapolate and interpolate
- calculate the mean, and standard deviation for a discrete distribution
- generate binomial probability distributions
- use normal distributions to calculate probabilities
- use the central limit theorem to calculate probabilities for $\bar x$
- calculate confidence intervals
- perform simple hypothesis testing
It is tempting to make up numbers for these problems. However, I wonder if it is better practice to use numbers based on real-world measurements? I know what when most people make up lists of values that are meant to be random, or centered about a mean, the distribution of their made-up numbers is not always the same as measured data.
That said, my students are not expected to deal with sets of data with more than 35 elements, and I do not want confusing examples. I must minimize student frustration.
The ideal? Sets of values that seem reasonable, come from a real source and that give answers that build intuition over the core concepts in the course. Will real data help students form a more concrete mental image of the problem? Our book often has sourced data, yet I find far too many of the problems are highly technical to the point of obscuring the chapter's central concept. Complexity isn't a bad thing for the stronger students. I don't want to get hung up on converting between units, or bogged down trying hard to get my students to picture what "3.7 acre-feet of water per hour per person" might mean. At least not just yet.
I've found it very time-consuming to source "real" data. Are there any libraries online with samples that could work well in this situation? Do you have any recommendations for finding good data? I have no fanatical desire to have a real source for everything. I seek reasonable data and with the kind of noise and randomness that arises from real-world measurements.