Question

use the box - and - whisker plot below to determine which statement is accurate.
153.0 178.0 196.6 211.0 260.0

150 175 200 225 250 275
cholesterol (in milligrams per deciliter)
about 75% of the adults have cholesterol levels less than 178.
one half of the cholesterol levels are between 178 and 211.
about 25% of the adults have cholesterol levels of at most 211.
one half of the cholesterol levels are between 178 and 196.6.

Explanation:

Step1: Recall box - and - whisker plot properties

In a box - and - whisker plot, the left - hand side of the box is the first quartile ($Q_1$), the line inside the box is the median ($Q_2$), and the right - hand side of the box is the third quartile ($Q_3$). The whiskers represent the minimum and maximum values. Here, $Q_1 = 178$, $Q_2=196.6$, $Q_3 = 211$.

Step2: Analyze each statement

• Statement 1: About 75% of the adults have cholesterol levels less than 178. Since 178 is $Q_1$, about 25% of the data is less than $Q_1$ and 75% is greater than $Q_1$, so this statement is false.
• Statement 2: One - half of the cholesterol levels are between 178 and 211. Since $Q_1 = 178$ and $Q_3=211$, the inter - quartile range ($IQR = Q_3 - Q_1$) contains 50% of the data. So, one - half of the cholesterol levels are between 178 and 211. This statement is true.
• Statement 3: About 25% of the adults have cholesterol levels of at most 211. Since 211 is $Q_3$, about 75% of the data is less than or equal to $Q_3$, so this statement is false.
• Statement 4: One - half of the cholesterol levels are between 178 and 196.6. 196.6 is the median. The data between $Q_1$ and $Q_2$ is 25% of the data, not 50%, so this statement is false.

Answer:

One half of the cholesterol levels are between 178 and 211.