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By now you are adept at calculating averages and intuitively can estimate whether something is “normal” (a measurement not too far from average) or unusual (pretty far from the average you might expect). This class helps to quantify exactly how far something you measure is from average using the normal distribution. Basically, you mark the mean down the middle of the bell curve, calculate the standard deviation of your sample, and then add (or subtract) that value to come up with the mile markers (z-scores) that measure the distance from the mean.
For example, if the average height of adult males in the United States is 69 inches with a standard deviation of 3 inches, we could create the graph below.
Men who are somewhere between 63 and 75 inches tall would be considered of a fairly normal height. Men shorter than 63 inches or taller than 75 inches would be considered unusual (assuming our sample data represents the actual population). You could use a z-score to look up exactly what percentage of men are shorter than (or taller than) a particular height.
Think of something in your work or personal life that you measure regularly. (No actual calculation of the mean, standard deviation, or z-scores is necessary.) What value is “average”? What values would you consider to be unusually high or unusually low? If a value were unusually high or low—how would it change your response to the measurement?
