Question

the ogive represents the heights of males in a particular country in the 20-29 age group. what height represents the 60th percentile? how should you interpret this? the 60th percentile represents about 69 inches. (round to nearest whole number as needed.) interpret this percentile. choose the correct answer below. a. this means that about 60 percent of males in this country ages 20-29 are exactly this height. b. this means that about 40 percent of males in this country ages 20-29 are shorter than this height. c. this means that about 60 percent of males in this country ages 20-29 are taller than this height. d. this means that about 60 percent of males in this country ages 20-29 are shorter than this height.

Explanation:

To interpret a percentile, recall that the \( n^{\text{th}} \) percentile of a data set means that \( n\% \) of the data values are less than or equal to that value. For the 60th percentile, this means about 60% of the males in the 20 - 29 age group are shorter than (or equal to) this height.

• Option A is incorrect because a percentile does not mean 60% are exactly that height (heights are continuous, and the probability of being exactly a single value is 0 in a continuous distribution).
• Option B is incorrect because if 60% are shorter, then 40% are taller, not shorter.
• Option C is incorrect as it says 60% are taller, which is the opposite of the percentile definition.
• Option D correctly states that about 60% of males in this age group are shorter than this height.

Answer:

D. This means that about 60 percent of males in this country ages 20 - 29 are shorter than this height.