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 five - number summary concept

In a five - number summary (minimum, first quartile $Q_1$, median $Q_2$, third quartile $Q_3$, maximum), 25% of the data is less than $Q_1$, 50% is less than $Q_2$, and 75% is less than $Q_3$. Given the five - number summary 143, 162, 168, 180, 202, where 143 is the minimum, 162 is $Q_1$, 168 is $Q_2$, 180 is $Q_3$, and 202 is the maximum.

Step2: Analyze each option

• Option 1: Since 180 is the third quartile ($Q_3$), approximately 75% of the data is less than 180 cm. This is true.
• Option 2: Since 168 is the median ($Q_2$), approximately 50% of the data is less than 168 cm. This is true.
• Option 3: Approximately 25% of the data is less than 162 cm (the first quartile $Q_1$), not 180 cm. This is false.
• Option 4: Since 162 is the first quartile ($Q_1$), approximately 75% of the data is greater than 162 cm. This is true.

Answer:

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