Question

the following are the distances (in miles) to the nearest airport for 14 families.
6, 11, 11, 15, 16, 17, 18, 23, 23, 25, 27, 29, 34, 35
notice that the numbers are ordered from least to greatest.
give the five - number summary and the interquartile range for the data set.
five - number summary
minimum:
lower quartile:
median:
upper quartile:
maximum:
interquartile range:

Explanation:

Step1: Find Minimum and Maximum

Minimum is the smallest value, so \( 6 \). Maximum is the largest value, so \( 35 \).

Step2: Find Median (Q2)

There are \( n = 14 \) data points. Median is the average of the \( \frac{n}{2} = 7 \)-th and \( \frac{n}{2}+1 = 8 \)-th values. 7th value: \( 18 \), 8th value: \( 23 \). Median \( = \frac{18 + 23}{2} = 20.5 \).

Step3: Find Lower Quartile (Q1)

Lower half: first \( 7 \) values (\( 6, 11, 11, 15, 16, 17, 18 \)). Median of lower half (Q1) is the 4th value: \( 15 \).

Step4: Find Upper Quartile (Q3)

Upper half: last \( 7 \) values (\( 23, 23, 25, 27, 29, 34, 35 \)). Median of upper half (Q3) is the 4th value: \( 27 \).

Step5: Find Interquartile Range (IQR)

IQR = Q3 - Q1 = \( 27 - 15 = 12 \).

Answer:

Minimum: \( 6 \)
Lower quartile: \( 15 \)
Median: \( 20.5 \)
Upper quartile: \( 27 \)
Maximum: \( 35 \)
Interquartile range: \( 12 \)