Question

find the 5 number summary for the data shown
x
4.6
6
6.3
9.7
10.3
11.1
11.5
12.6
12.8
16.1
17
20.2
22.1
22.3
28
5 number summary:

Explanation:

Step1: Sort the data

The data is already sorted: 4.6, 6, 6.3, 9.7, 10.3, 11.1, 11.5, 12.6, 12.8, 16.1, 17, 20.2, 22.1, 22.3, 28

Step2: Find the minimum

The minimum value is the first - value in the sorted list. So, the minimum is 4.6.

Step3: Find the first quartile ($Q_1$)

There are $n = 15$ data points. The position of $Q_1$ is $i=\frac{n + 1}{4}=\frac{15+1}{4}=4$. So, $Q_1$ is the 4th value in the sorted list, $Q_1 = 9.7$.

Step4: Find the median ($Q_2$)

The position of the median is $i=\frac{n + 1}{2}=\frac{15 + 1}{2}=8$. So, the median $Q_2$ is the 8th value in the sorted list, $Q_2=12.6$.

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(15 + 1)}{4}=12$. So, $Q_3$ is the 12th value in the sorted list, $Q_3=20.2$.

Step6: Find the maximum

The maximum value is the last - value in the sorted list. So, the maximum is 28.

Answer:

4.6, 9.7, 12.6, 20.2, 28