Question

1. the boxplot summarizes the scores on mrs. carpenters last math test. based on the information in the boxplot, which statement must be true? a. only one student scored a 92. b. most scores were between 72 and 82. c. three students scored between 60 and 65. d. approximately half the students scored at least 77.

Explanation:

Step1: Recall box - plot properties

A box - plot divides the data into quartiles. The median is the middle value (second quartile, Q2), the lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half of the data. The inter - quartile range (IQR) is Q3 - Q1. Approximately 25% of the data lies between Q1 and Q2, and another 25% lies between Q2 and Q3. So, approximately 50% of the data lies between Q1 and Q3.

Step2: Analyze each option

• Option A: A box - plot does not give information about the number of times a particular value occurs. So, we cannot say that only one student scored a 92.
• Option B: There is no indication from the box - plot that most scores were between 72 and 82. A box - plot shows quartiles, not the most frequent scores.
• Option C: A box - plot does not give information about the number of data points in a particular non - quartile range like 60 - 65.
• Option D: The median (Q2) of the box - plot is around 77. By the definition of the median, approximately half of the data values are at least as large as the median. So, approximately half the students scored at least 77.

Answer:

D. Approximately half the students scored at least 77.