Question

1. based on the box - and - whisker plot below, which statement is false?
2. the median is 7.
3. the range is 12.
4. the first quartile is 4.
5. the third quartile is 11.

Explanation:

To solve this, we analyze each statement using the box - and - whisker plot:

Step 1: Recall the components of a box - and - whisker plot

• The median (second quartile, \(Q_2\)) is the line inside the box.
• The first quartile (\(Q_1\)) is the left end of the box.
• The third quartile (\(Q_3\)) is the right end of the box.
• The range is calculated as \( \text{Maximum}-\text{Minimum}\), where the minimum is the left end of the left whisker and the maximum is the right end of the right whisker.

Step 2: Analyze statement 1 (Median is 7)

Looking at the box - and - whisker plot, the line inside the box is at 7. So the median is 7. This statement is true.

Step 3: Analyze statement 2 (Range is 12)

The left end of the left whisker is at 1 (minimum value) and the right end of the right whisker is at 13 (maximum value). The range is \(13 - 1=12\). This statement is true.

Step 4: Analyze statement 3 (First quartile is 4)

The left end of the box is at 4. So the first quartile (\(Q_1\)) is 4. This statement is true.

Step 5: Analyze statement 4 (Third quartile is 11)

The right end of the box is at 10, not 11. So the third quartile (\(Q_3\)) is 10, not 11. This statement is false.

Answer:

1. The third quartile is 11.