The data set includes 17 values. To determine which boxplot represents the data, we analyzed the quartiles and interquartile range. Only Boxplot B has a matching median and whisker lengths, making it the correct representation of the data set.
The data set is {5, 5, 7, 13, 17, 21, 25, 25, 27, 33, 34, 35, 40, 40, 45, 48, 50}. We can analyze the quartiles to answer this question.
The first quartile (Q1) is the 25th percentile, which is the middle value between the 25% and 50% of the data. In this case, Q1 is 13. The median (Q2) is the 50th percentile, which is the middle value of the data set. Here, the median is 25. The third quartile (Q3) is the 75th percentile, which is the middle value between the 75% and 100% of the data. In this case, Q3 is 35.
The whiskers (or lines) extending from the box represent the spread of the data. If no outliers exist, the whiskers extend to 1.5 times the interquartile range (IQR) from the first and third quartiles. The IQR is the difference between Q3 and Q1, which is 35 - 13 = 22. Therefore, the whiskers should reach 1.5 * 22 = 33 to either side of the box.
Analyzing the answer choices, we can see that only Boxplot B has a median of 25 and whiskers that extend to 33 units on either side. Therefore, Boxplot B represents the data set.