Question

1. the ages in years are recorded for a sample of 697 visitors to a museum exhibit. summary statistics were computed based on this sample of data, and they are included in the table below. a boxplot of the data set is also given below. what can we conclude based on this information?

mean	standard deviation	minimum	q1	median	q3	maximum
30.3	13.1	10	20	26	39	77

a. it’s possible that none of the individuals in the sample were exactly 26 years old.
b. on average, the individuals in the sample have ages that are 13.1 years away from the median age.
c. the range of the middle 50% of the distribution is equal to approximately 13 years.
d. the percentage of exhibit attendees who are older than 26 years of age is larger than the percentage who are younger than 26 years of age.
e. none of the above interpretations are correct.

Explanation:

Step1: Recall median concept

The median is the middle - value when data is ordered. It's possible that no data point has the exact value of the median. For a large data set like this one (697 visitors), it's entirely feasible that none of the ages is exactly 26.

Step2: Analyze option B

The standard deviation (13.1) is the average distance from the mean, not the median. So option B is incorrect.

Step3: Calculate inter - quartile range

The inter - quartile range (IQR), which represents the range of the middle 50% of the data, is $Q_3 - Q_1=39 - 20 = 19$ years, not approximately 13 years. So option C is incorrect.

Step4: Understand median property

The median divides the data set into two equal parts. So the percentage of exhibit attendees older than 26 years of age is equal to the percentage of those younger than 26 years of age. Option D is incorrect.

Answer:

A. It's possible that none of the individuals in the sample were exactly 26 years old.