Question

cholesterol (in milligrams per deciliter)
o about 75% of the adults have cholesterol levels less than 180.
o one half of the cholesterol levels are between 180 and 198.
o one half of the cholesterol levels are between 180 and 212.
o about 25% of the adults have cholesterol levels of at most 212.

Explanation:

Step1: Recall box - and - whisker plot properties

In a box - and - whisker plot, the first quartile ($Q_1$) represents the 25th percentile, the median ($Q_2$) represents the 50th percentile, and the third quartile ($Q_3$) represents the 75th percentile. The minimum value is the lower - most value and the maximum value is the upper - most value.

Step2: Identify values from the box - and - whisker plot

From the box - and - whisker plot, the minimum value is 158.0, $Q_1 = 180$, the median ($Q_2$) = 198, $Q_3=212$, and the maximum value is 266.0.

Step3: Analyze each statement

• Statement 1: About 75% of the adults have cholesterol levels less than 180. Since 180 is $Q_1$ (25th percentile), about 25% of the adults have cholesterol levels less than 180, so this statement is false.
• Statement 2: One half of the cholesterol levels are between 180 and 198. Since 180 is $Q_1$ and 198 is the median, the proportion between them is 25% (not 50%), so this statement is false.
• Statement 3: One half of the cholesterol levels are between 180 and 212. Since 180 is $Q_1$ and 212 is $Q_3$, the inter - quartile range ($IQR=Q_3 - Q_1$) contains 50% of the data. So, one half of the cholesterol levels are between 180 and 212, and this statement is true.
• Statement 4: About 25% of the cholesterol levels are between 180 and 212. Since 180 is $Q_1$ and 212 is $Q_3$, about 50% of the cholesterol levels are between 180 and 212, so this statement is false.
• Statement 5: About 25% of the adults have cholesterol levels of at most 212. Since 212 is $Q_3$ (75th percentile), about 75% of the adults have cholesterol levels of at most 212, so this statement is false.

Answer:

One half of the cholesterol levels are between 180 and 212.