EXAMPLE 17 Heights of American Women: Finding the Quartiles

The distribution of heights of young American women (ages 18 to 24) is approximately normal, with a mean of 64.5 inches (that is, 5 feet 4.5 inches) and a standard deviation of 2.5 inches. Figure 5.23 shows this normal curve. The quartiles are 0.67 standard deviation, or inches away from the mean. The first quartile is , or 62.8 inches. The third quartile is , or 66.2 inches. The middle 50% of women’s heights lie approximately between 62.8 inches and 66.2 inches. These numbers are exact for the normal distribution with a mean of 64.5 inches and a standard deviation of 2.5 inches, but only approximately true for the actual heights of the women because real-life distributions of biological measurements such as heights are only approximately normal.

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Figure 5.25: Figure 5.23 The quartiles of a normal distribution are located at 0.67 standard deviation on either side of the mean. For this normal curve, the mean is 64.5 inches and the standard deviation is 2.5 inches.