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On election night, TV commentators routinely predict the outcome of elections before the polls close. Most of the time they’re right. How do they do that?

The trick is to interview a sample of voters right after they cast their ballots. Assuming the voters tell the truth about whom they voted for, and assuming the sample truly represents the population, network analysts use the sample data to generalize to the population of voters.

This is the job of a statistician — to use the findings from a sample to make a decision about the population from which the sample comes. But sometimes those decisions don’t turn out the way the numbers predict. History buffs are probably familiar with the memorable photo of President Harry Truman holding up a copy of the Chicago Daily Tribune with the famous, but incorrect, headline “Dewey Defeats Truman” after the 1948 election. Part of the statistician’s job is to express how much confidence they have in the decision.

Another election-related example speaks to the idea of the confidence in the decision. Pre-election polls (again, assuming a representative sample of voters) tell you the percentage of sampled voters who prefer each candidate. The polling organization adds how accurate it believes the polls are. When you hear a newscaster say something like “accurate to within 3 percent,” you're hearing a judgment about confidence.

Here’s another example. Suppose you’ve been assigned to find the average reading speed of all fifth grade children in the United States but you haven’t got the time or the money to test them all. What would you do?

Your best bet is to take a sample of fifth-graders, measure their reading speeds (in words per minute), and calculate the average of the reading speeds in the sample. You can then use the sample average as an estimate of the population average.

Estimating the population average is one kind of inference that statisticians make from sample data. I discuss inference in more detail in the upcoming section “Inferential Statistics: Testing Hypotheses.”

Here’s some terminology you have to know: Characteristics of a population (like the population average) are called parameters, and characteristics of a sample (like the sample average) are called statistics. When you confine your field of view to samples, your statistics are descriptive. When you broaden your horizons and concern yourself with populations, your statistics are inferential.

And here’s a notation convention you have to know: Statisticians use Greek letters ((μ, σ, ρ) to stand for parameters, and English letters , s, r) to stand for statistics. Figure 1-1 summarizes the relationship between populations and samples, and between parameters and statistics.

FIGURE 1-1: The relationship between populations and samples, and between parameters and statistics.