Question

question 9 of 10
these box plots show daily low temperatures for a sample of
days in two different towns.

which statement is the most appropriate comparison of the
spreads?

a. the interquartile range (iqr) for town a, 45°, is less
than the iqr for town b, 50°.

b. the interquartile range (iqr) for town a, 15°, is less
than the iqr for town b, 20°.

c. the standard deviation for town a, 15°, is less than the
standard deviation for town b, 20°.

d. the interquartile ranges (iqrs) for towns a and b are both 30°.

text description for graph
town a box plot: minimum 10, q1 15, median 20, q3 30, maximum 55.
town b box plot: minimum 5, q1 20, median 30, q3 40, maximum 55.

Explanation:

Step1: Recall IQR formula

IQR is calculated as \( \text{IQR} = Q_3 - Q_1 \), where \( Q_3 \) is the third quartile and \( Q_1 \) is the first quartile.

Step2: Find \( Q_1 \) and \( Q_3 \) for Town A

From the box plot, for Town A: \( Q_1 = 10 \), \( Q_3 = 25 \). So \( \text{IQR}_A = 25 - 10 = 15 \).

Step3: Find \( Q_1 \) and \( Q_3 \) for Town B

For Town B: \( Q_1 = 20 \), \( Q_3 = 40 \). So \( \text{IQR}_B = 40 - 20 = 20 \).

Step4: Analyze options

• Option A: IQR for A is 15, not 45. Incorrect.
• Option B: IQR for A (15) is less than IQR for B (20). Correct.
• Option C: The question is about spreads via IQR, not standard deviation. Also, standard deviation values given are wrong. Incorrect.
• Option D: IQRs are 15 and 20, not both 30. Incorrect.

Answer:

B. The interquartile range (IQR) for town A, 15°, is less than the IQR for town B, 20°.