Question

find the 5 number summary for the data shown
5 8
13 19
28 42
59 60
72 75
79 84
5 number summary:
use the locator/percentile method described in your book, not your calculator.
check answer

Explanation:

Step1: Arrange data in ascending order

$5,8,13,19,28,42,59,60,72,75,79,84$

Step2: Find the minimum

The minimum value is $5$.

Step3: Calculate the first - quartile ($Q_1$)

$n = 12$. The locator for $Q_1$ is $L_{Q_1}=\frac{1}{4}(n + 1)=\frac{1}{4}(12 + 1)=3.25$. So $Q_1$ is the value at the 3rd position plus $0.25$ times the difference between the 4th and 3rd values. $Q_1=13+0.25\times(19 - 13)=13 + 1.5 = 14.5$.

Step4: Calculate the median ($Q_2$)

The locator for the median is $L_{Q_2}=\frac{1}{2}(n + 1)=\frac{1}{2}(12+1)=6.5$. So $Q_2$ is the value at the 6th position plus $0.5$ times the difference between the 7th and 6th values. $Q_2=42+0.5\times(59 - 42)=42 + 8.5 = 50.5$.

Step5: Calculate the third - quartile ($Q_3$)

The locator for $Q_3$ is $L_{Q_3}=\frac{3}{4}(n + 1)=\frac{3}{4}(12 + 1)=9.75$. So $Q_3$ is the value at the 9th position plus $0.75$ times the difference between the 10th and 9th values. $Q_3=72+0.75\times(75 - 72)=72+2.25 = 74.25$.

Step6: Find the maximum

The maximum value is $84$.

Answer:

$5,14.5,50.5,74.25,84$