Question

chloe created the box - plot below to represent the heights of the sixth - graders in her class. select all the statements that must be correct about the heights of the sixth - graders in chloes class. there are 40 students in chloes class. the interquartile range is 13 centimeters. of the students, 25% are 152 centimeters tall. half of the students are between 158 and 182 centimeters tall. the height of the tallest student is 182 centimeters, and the height of the second tallest student is 165 centimeters.

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 contains the middle 50% of the data, with the lower half of the middle 50% between $Q_1$ and $Q_2$ and the upper half between $Q_2$ and $Q_3$. The inter - quartile range (IQR) is $IQR = Q_3−Q_1$.

Step2: Analyze each statement

• There is no information in the box - plot to determine the number of students. So, the statement "There are 40 students in Chloe's class" is incorrect.
• If we assume the box - plot values: let's say $Q_1\approx150$, $Q_3\approx163$. Then $IQR=Q_3 - Q_1\approx163 - 150=13$ centimeters. This statement could be correct.
• Just because the first quartile is around 150 does not mean 25% of the students are exactly 152 centimeters tall. This statement is incorrect.
• The box in the box - plot represents the middle 50% of the data. If the lower end of the box is around 150 and the upper end is around 163, it is not correct to say half of the students are between 158 and 182 centimeters tall. This statement is incorrect.
• The maximum value shown in the box - plot is around 180, but there is no information about the height of the second - tallest student. This statement is incorrect.

Answer:

The inter - quartile range is 13 centimeters.