Question

analyzing a box plot
the average age of the children at a campout is shown in the box plot below.
age of campers
which statement is true about the box plot?
the youngest age is 7.
it is skewed right.
more of the children were close to 12 years old than 6 years old.
half of the children were between 6 and 9 years old.

Explanation:

Step1: Analyze box - plot properties

A box - plot (box - and - whisker plot) shows the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum values. The box represents the inter - quartile range ($IQR=Q_3 - Q_1$), which contains 50% of the data.

Step2: Check each option

• Option 1: The youngest age is 7

Looking at the box - plot, the minimum value (left - most whisker) is 6, not 7. So this option is wrong.

• Option 2: It is skewed right

For a symmetric box - plot, the median is in the middle of the box and the whiskers are approximately of equal length. Here, the box and whiskers do not show a right - skew (where the right whisker is longer and the median is closer to $Q_1$). So this option is wrong.

• Option 3: More of the children were close to 12 years old than 6 years old

The length of the whiskers and the position of the box do not indicate that more data is near 12. The whiskers just show the range of the data. So this option is wrong.

• Option 4: Half of the children were between 9 and 11 years old

The box in a box - plot represents the middle 50% of the data. If the lower end of the box is at 9 and the upper end is at 11 (assuming standard box - plot interpretation where the box is from $Q_1$ to $Q_3$), then half of the data (50% of the children) lies within this interval.

Answer:

Half of the children were between 9 and 11 years old.