According to a recent report from the U.S. National Center forHealth Statistics,

Question

According to a recent report from the U.S. National Center forHealth Statistics, for males with age 25-34 years, 2% of theirheights are 64 inches or less, 8% are 66inches or less, 27% are 68inches or less, 39% are 69 inches or less, 54% are 70 inches orless, 68% are 71 inches or less, 80% are 72 inches or less, 93% are74 inches or less, and 98% are 76 inches or less. a) Which category has the median height? Explain b) Nearly all the hights fall between 60 and 80 inches, withfewer than 1% falling outside that range. If the heights areapproximately bell-shaped, give a rough approximation for thestandard deviation of the heights. Explain yourreasoning According to a recent report from the U.S. National Center forHealth Statistics, for males with age 25-34 years, 2% of theirheights are 64 inches or less, 8% are 66inches or less, 27% are 68inches or less, 39% are 69 inches or less, 54% are 70 inches orless, 68% are 71 inches or less, 80% are 72 inches or less, 93% are74 inches or less, and 98% are 76 inches or less. a) Which category has the median height? Explain b) Nearly all the hights fall between 60 and 80 inches, withfewer than 1% falling outside that range. If the heights areapproximately bell-shaped, give a rough approximation for thestandard deviation of the heights. Explain yourreasoning

Explanation / Answer

a. The category 70 in contains the median,because approx. 50% of the data is above 70 in and approx. 50% ofthe data is below 70 in. b. If the heights are bell shaped then themedian is equal to the mean, so the mean is 70. Using the empiricalrule, we know that about 99.7% of the data is three standarddeviations from the mean. We can evaluate the standard deviationfrom either the upper or lower side, I choose to do it from theupper side. 80 - 70 = 10 in from the mean. 10 in / 3 standarddeviations gives us the estimated standard deviation of 3.33.

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