Question

the boxplot below displays the arm spans for 44 students. the five - number summary for the data is 143, 162, 168, 180, and 202. which of the following is not a true statement? approximately 75% of the arm spans are less than 180 cm. approximately 50% of the arm spans are less than 168 cm. approximately 25% of the arm spans are less than 180 cm. approximately 75% of the arm spans are greater than 162 cm.

Explanation:

Step1: Recall the properties of five - number summary

The five - number summary consists of the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum. Here, minimum = 143, $Q_1$ = 162, median ($Q_2$)=168, $Q_3$ = 180, maximum = 202.

Step2: Analyze each option

• Option 1:

Since $Q_3$ = 180, by the definition of quartiles, approximately 75% of the data is less than $Q_3$. So, approximately 75% of the arm spans are less than 180 cm. This statement is True.

• Option 2:

Since the median ($Q_2$)=168, by the definition of the median, approximately 50% of the data is less than the median. So, approximately 50% of the arm spans are less than 168 cm. This statement is True.

• Option 3:

Since $Q_3$ = 180, approximately 75% of the data is less than 180 cm (not 25%). This statement is False.

• Option 4:

Since $Q_1$ = 162, approximately 25% of the data is less than $Q_1$. So, approximately 75% of the data is greater than $Q_1$ (162 cm). This statement is True.

Answer:

Approximately 25% of the arm spans are less than 180 cm.