Question

the following are the distances (in miles) to the nearest airport for 14 towns:
9, 10, 13, 18, 18, 23, 29, 34, 35, 38, 39, 40, 43, 44
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 the minimum and maximum

The minimum is the smallest number in the data set: $9$.
The maximum is the largest number in the data set: $44$.

Step2: Find the median

The data set has $14$ numbers. The median is the average of the $7^{th}$ and $8^{th}$ numbers.
The $7^{th}$ number is $34$ and the $8^{th}$ number is $35$.
Median $=\frac{34 + 35}{2}=\frac{69}{2}=34.5$.

Step3: Find the lower quartile ($Q_1$)

The lower half of the data set is $9,10,13,18,18,23,29,34$.
Since there are $8$ numbers in the lower half, the lower quartile is the average of the $4^{th}$ and $5^{th}$ numbers.
The $4^{th}$ number is $18$ and the $5^{th}$ number is $18$.
$Q_1=\frac{18+18}{2}=18$.

Step4: Find the upper quartile ($Q_3$)

The upper half of the data set is $35,38,39,40,43,44$.
Since there are $6$ numbers in the upper half, the upper quartile is the average of the $3^{rd}$ and $4^{th}$ numbers.
The $3^{rd}$ number is $39$ and the $4^{th}$ number is $40$.
$Q_3=\frac{39 + 40}{2}=39.5$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1$.
$IQR=39.5-18=21.5$.

Answer:

Minimum: $9$; Lower quartile: $18$; Median: $34.5$; Upper quartile: $39.5$; Maximum: $44$; Inter - quartile range: $21.5$