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 shows the five - number summary: minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum. The box represents the inter - quartile range (IQR) from $Q_1$ to $Q_3$, and the median is the line inside the box. Approximately 25% of the data is below $Q_1$, 25% is between $Q_1$ and the median, 25% is between the median and $Q_3$, and 25% is above $Q_3$.

Step2: Analyze option A

The box - plot does not give information about the frequency of a single score like 92. We cannot say that only one student scored 92.

Step3: Analyze option B

The box - plot shows that the middle 50% of the data (the box) is from approximately 65 to 80. The interval 60 - 65 is outside the box and we cannot say most scores were in this range.

Step4: Analyze option C

The box - plot does not give information about the exact number of students in a particular range. We cannot say exactly three students scored between 60 and 65.

Step5: Analyze option D

The median divides the data into two halves. The median of the box - plot is around 77. So approximately half the students scored at least 77.

Answer:

D. Approximately half the students scored at least 77.