Question

select the correct answer.

jeremy is recording the weights, in ounces, of different rock samples in a lab. the weights of seven rocks are listed below.

11, 13, 14, 6, 10, 9, 10

the eighth rock that he weighed was 5 ounces. how would the interquartile range of the data be affected if jeremy includes the weight of the eighth rock?

• the interquartile range increases.
• the interquartile range decreases.
• the interquartile range does not change.
• the interquartile range cannot be determined.

Explanation:

⚡ Using what you learned: Interquartile Range (IQR)

Step 1: Calculate the initial IQR

Original data set of 7 rocks:

$$ 11, 13, 14, 6, 10, 9, 10 $$

Ordered data set:

$$ 6, 9, 10, 10, 11, 13, 14 $$

Median (\(Q_2\)):

$$ Q_2 = 10 $$

Lower half (values below the median):

$$ 6, 9, 10 \implies Q_1 = 9 $$

Upper half (values above the median):

$$ 11, 13, 14 \implies Q_3 = 13 $$

Initial IQR:

$$ \text{IQR}_{\text{initial}} = Q_3 - Q_1 = 13 - 9 = 4 $$

Step 2: Calculate the new IQR with the eighth rock

New data set of 8 rocks (adding 5):

$$ 5, 6, 9, 10, 10, 11, 13, 14 $$

Median (\(Q_2\)):

$$ Q_2 = \frac{10 + 10}{2} = 10 $$

Lower half (lower 4 values):

$$ 5, 6, 9, 10 \implies Q_1 = \frac{6 + 9}{2} = 7.5 $$

Upper half (upper 4 values):

$$ 10, 11, 13, 14 \implies Q_3 = \frac{11 + 13}{2} = 12 $$

New IQR:

$$ \text{IQR}_{\text{new}} = Q_3 - Q_1 = 12 - 7.5 = 4.5 $$

Step 3: Compare the IQR values

$$ \text{IQR}_{\text{initial}} = 4 $$

$$ \text{IQR}_{\text{new}} = 4.5 $$

$$ 4.5 > 4 $$

The interquartile range increases.

Answer:

The interquartile range increases.