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: Analyze option A

The median is just the middle - value when data is ordered. It's possible no data - point has the exact value of the median. For example, if we have an even number of data points and the two middle values are different, the median is their average, and no data point may have that exact median value. So option A is correct.

Step2: Analyze option B

The standard deviation (13.1) is the average distance of the 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 \(Q3 - Q1=39 - 20 = 19\) years, not approximately 13 years. So option C is incorrect.

Step4: Analyze option D

The median (26) divides the data into two equal parts. 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.