Answered

A box plot is drawn using a 12-inch ruler as the scale. The box ext
3.5 in. to 6.0 in. Which of the following represents the upper boundary for
outliers (that is, the smallest value beyond which you will find outliers)?
A. 9.75 in.
B. 10.5 in.
C. 7.25 in.
D. 6 in.
E. 3.75 in.

Verified Answer :

GinnyAnswer

To determine the upper boundary for outliers in a box plot, follow these steps:

1. Identify the first quartile (Q1) and the third quartile (Q3):
- In this problem, the first quartile \(\( Q1 = 3.5 \)\) inches.
- The third quartile \(\( Q3 = 6.0 \)\) inches.

2. Calculate the interquartile range (IQR):
- The interquartile range (IQR) is the difference between the third quartile and the first quartile.
- \(\( \text{IQR} = Q3 - Q1 \)\).

So, \(\( \text{IQR} = 6.0 - 3.5 = 2.5 \)\) inches.

3. Determine the upper boundary for outliers:
- The formula to find the upper boundary for outliers is \(\( \text{Upper Boundary} = Q3 + 1.5 \times \text{IQR} \)\).
- Substituting the values into the formula:

\(\( \text{Upper Boundary} = 6.0 + 1.5 \times 2.5 \)\)

\(\( = 6.0 + 3.75 = 9.75 \)\) inches.

Therefore, the smallest value beyond which you will find outliers is \(\( 9.75 \)\) inches.

Correct answer: A. 9.75 in.