Statistics are often used to describe or predict performance of a total population based on a sample. How accurate the description or prediction will be depends partly on the size of the sample used. For example, if someone were trying to determine the average height of Americans by measuring the height of ten passengers getting on a commercial airliner in Boston, they might randomly choose a flight and time when the Celtics are leaving for a road trip. The average height of passengers on that plane would almost certainly be greater than the average for all Americans. If the researcher selected 5,000 passengers at random times and dates, it is likely that the heights of those passengers would be more like the total population.

The probability that a score could be caused by random occurrence increases greatly as the population being studied decreases. Thus, if we look at the scores of ten students, a single event, such as the death of a pet for one of the students, could have a noticeable impact on the average scores for the students. Although their average score may be 45, it may have been 50 or 55 had it not been for the trauma that one or two students experienced. Likewise, the students may, by shear chance, have studied an important concept the day before the test that caused their scores to go up by 5 or 10 points. The Standard Error of Estimate for those 10 students may be 20 points, indicating that the recorded average of 45 could, under different circumstances, have fallen anywhere between 35 and 55. As the sample of students gets larger, the Standard Error of Estimate gets smaller, so that the range in a large school may be ± 2 or 3 points.

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