Question

A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. Which statement is true of the box plot of this data set?
The box will go from 10 to 12.
A line dividing the box will be at 12.
The left whisker will go from 4 to 15.
The right whisker will go from 12 to 20.

Answer 1

To analyze the box plot based on the provided statistics:

- **Minimum**: 4
- **Lower Quartile (Q1)**: 10
- **Median (Q2)**: 12
- **Upper Quartile (Q3)**: 15
- **Maximum**: 20

Now, we can construct the box plot:

1. The box itself will go from the lower quartile (Q1 = 10) to the upper quartile (Q3 = 15).
2. A line will be drawn inside the box at the median (Q2 = 12).
3. The left whisker will extend from the minimum value (4) to Q1 (10).
4. The right whisker will extend from Q3 (15) to the maximum value (20).

Now, we can evaluate the statements:

1. **The box will go from 10 to 12.** - **False**. The box goes from 10 (lower quartile) to 15 (upper quartile).

2. **A line dividing the box will be at 12.** - **True**. The median (12) will have a line inside the box.

3. **The left whisker will go from 4 to 15.** - **False**. The left whisker goes from 4 to 10 (the lower quartile).

4. **The right whisker will go from 12 to 20.** - **False**. The right whisker goes from 15 to 20 (the upper quartile to the maximum).

The true statement is: **A line dividing the box will be at 12.**