Looking at that graph, you might conclude that most kids scored between 1000
and 1200. But any statistician worth his Statistician Badge would take a look at
that data and smirk. “This is terrible data, the group is too small, and it’s not
random. Those kids are all from the same neighborhood, in a similar
socioeconomic class, have had the same level of education. If you want real
data, you should pick 3,000 kids randomly from all across America.” What that
statistician just recommended, in stat-talk, is enlarging the population
parameter. In general, a larger population parameter yields more accurate data.
Let’s say we asked 3,000 American kids. Our table would look more like this:
number of students score range 420 800–10001,057 1000–12001,072 1200–1400
458 1400–1600
Which we could graph like this: