Question

what is the five - number summary for the data: {2,2,4,4,5,5,6,7,9,15}? 5 number summary values minimum q1 median q3 maximum

Explanation:

Step1: Sort the data

The sorted data is $\{2,2,4,4,5,5,6,7,9,15\}$.

Step2: Find the minimum

The minimum value is the first - value in the sorted list, so the minimum is $2$.

Step3: Find the first quartile (Q1)

There are $n = 10$ data points. The position of Q1 is $i=\frac{n + 1}{4}=\frac{10+1}{4}=2.75$. So, $Q1=4$.

Step4: Find the median

The position of the median for $n = 10$ (an even - numbered data set) is $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The median is $\frac{5 + 5}{2}=5$.

Step5: Find the third quartile (Q3)

The position of Q3 is $i=\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. So, $Q3=7$.

Step6: Find the maximum

The maximum value is the last value in the sorted list, so the maximum is $15$.

Answer:

5 Number summary	Values
Q1	4
median	5
Q3	7
maximum	15