Descriptive Statistics

Statistics that inform you about a set of participants or a measurement are descriptive. Statistics, such as the mean, median, and mode, tell you about the numbers in the middle of the distribution. The range and SD tell you how spread out the data are. The mean, or average, is an estimate of what was typical of the sample. If the mean score on a test is 82, that says that most people’s results were near that 82; it does not mean that everyone scored an 82. The median is the number or score that is exactly middle of the range of the data, so that 50% of the data are below it and 50% are above it. This is why the median is sometimes referred to as the 50th percentile. The most common score in the sample is the mode. If 8 people took an examination and 5 people earned 85 points and 3 people earned an 80 points, then 85 points would be the mode. When data are normally distributed, the mean, median, and mode are all in the center of the normal curve (Figure 3-6).

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Knowing how wide the numbers range in the data is as important as knowing the mean, median, or mode. The mean does not tell you how many people had high scores and how many people had low scores. Consider that the average of 60, 72, 86, 92, and 100 is 82. If you only looked at the

Percentages of data fall within each standard deviation mean, you would not know that one score was very low and one score was the highest possible. When there is a large range to the data, the mean is not a good representation of the sample. That is why the median is used when reporting data from a large population. Income, for example, is typically reported as the median of all incomes collected. SD is a commonly used statistic to describe the variation within a dataset. An SD represents a set distance from the mean. This distance could be to the right or left of the mean. SDs are reported as a ± after the mean. For example, the mean weight of a team is 165 lb with a SD of ± 1.5 looks like 165 ±1.5 lb. SDs are distances from the mean, not units, such as pounds. The numbers below the normal curve represent the SDs (see Figure 3-6). A specific percentage of the data will fall within each of the SDs based on a normal distribution. Data can be sectioned off into percentiles based on these percentages. Quartiles are a common way epidemiologists separate data and look for differences between people in the lowest quartile (bottom 25%) and the highest quartile (top 25%).