Question

cholesterol (in milligrams per deciliter)
about 25% of the adults have cholesterol levels of at most 210.
one half of the cholesterol levels are between 182 and 197.8.
one half of the cholesterol levels are between 182 and 210.
about 75% of the adults have cholesterol levels less than 182.

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: Analyze the given box - and - whisker plot

From the box - and - whisker plot, the minimum value is 133.0, $Q_1 = 182$, the median ($Q_2$) = 197.8, $Q_3=210$, and the maximum value is 261.0.

Step3: Evaluate each statement

• Statement 1: About 25% of the adults have cholesterol levels of at most 210. Since $Q_3 = 210$, about 75% of the adults have cholesterol levels of at most 210, so this statement is false.
• Statement 2: One - half of the cholesterol levels are between 182 and 197.8. The inter - quartile range (IQR) is from $Q_1$ to $Q_3$. The median divides the data set into two halves. The number of data points between $Q_1$ and the median ($Q_2$) is 25% of the data set, not 50%. So this statement is false.
• Statement 3: One - half of the cholesterol levels are between 182 and 210. Since the IQR is from $Q_1 = 182$ to $Q_3 = 210$, the inter - quartile range contains 50% of the data. So this statement is true.
• Statement 4: About 75% of the adults have cholesterol levels less than 182. Since $Q_1=182$, about 25% of the adults have cholesterol levels less than 182, so this statement is false.

Answer:

One half of the cholesterol levels are between 182 and 210.