Question

the following table shows statistics on the ages, in years, of the people who attended a lecture last week. the data are summarized in the boxplot shown. age of people attending lecture boxplot with age axis 10–70 n 45 mean 43 stdev 12 minimum 20 q1 33 median 44 q3 53 maximum 65 which of the following statements is supported by the table and boxplot? a the range of the distribution is 20 years. b there were 43 people who attended the lecture. c at least 50% of the people who attended the lecture were 43 years or younger. d at least 75% of the people who attended the lecture were age 53 years or younger. e at least 25% of the people who attended the lecture were 33 years old.

Explanation:

• Option A: Range = Max - Min = 65 - 20 = 45, not 20. Incorrect.
• Option B: N = 45 means 45 people attended, not 43. Incorrect.
• Option C: Median is 44, so 50% are ≤44, not 43. Incorrect.
• Option D: Q3 = 53, so 75% are ≤53 (at least 75% younger or equal). Correct.
• Option E: Q1 = 33, so 25% are ≤33, not "at least 25%" being 33. Incorrect.

Answer:

D. At least 75% of the people who attended the lecture were age 53 years or younger.