Question

find the five - number summary for the data below:
11 3 8 18 1
9 11 8 9 0
13 7 14 13 20
16 19 0 5 20
8 19 4
minimum
quartile 1
median
quartile 3
maximum

Explanation:

Step1: Organize data in ascending order

$0,0,1,3,4,5,7,8,8,8,9,9,11,11,13,13,14,16,18,19,19,20,20$

Step2: Find the minimum

The smallest value is $0$.

Step3: Calculate the position of Q1

There are $n = 23$ data - points. The position of Q1 is $i=\frac{n + 1}{4}=\frac{23+1}{4}=6$. So Q1 is the 6th value in the ordered list, which is $5$.

Step4: Calculate the position of the median

The position of the median is $i=\frac{n + 1}{2}=\frac{23 + 1}{2}=12$. So the median is the 12th value in the ordered list, which is $9$.

Step5: Calculate the position of Q3

The position of Q3 is $i=\frac{3(n + 1)}{4}=\frac{3\times(23 + 1)}{4}=18$. So Q3 is the 18th value in the ordered list, which is $16$.

Step6: Find the maximum

The largest value is $20$.

Answer:

Minimum: $0$
Quartile 1: $5$
Median: $9$
Quartile 3: $16$
Maximum: $20$