Question

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: Analyze option A

The median is the middle - value. In a data - set, it's possible that no data point is exactly equal to the median value. For a sample of 697 (an odd number of data points), the median is the 349th ordered value. It doesn't mean that there must be a data point with value 26. So option A is correct.

Step2: Analyze option B

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

Step3: Analyze option C

The range of the middle 50% of the distribution is the inter - quartile range (IQR), which is \(Q3 - Q1=39 - 20 = 19
eq13\). So option C is incorrect.

Step4: Analyze option D

The median divides the data set into two equal - sized halves. So the percentage of exhibit attendees who are older than 26 years of age is equal to the percentage who are younger than 26 years of age. So option D is incorrect.

Answer:

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