Question

practice 5 (from unit 1, lesson 9)
a. what is the five - number summary for the data?
2 2 4 4 5 5 6 7 9 15
type the answers in the boxes.

Explanation:

Step1: Organize data in order

The data is already in ascending - order: 2, 2, 4, 4, 5, 5, 6, 7, 9, 15.

Step2: Find the minimum

The minimum value is the first number in the ordered list, so the minimum is 2.

Step3: Find the first quartile ($Q_1$)

There are $n = 10$ data points. The position of $Q_1$ is $0.25\times(n + 1)=0.25\times(10 + 1)=2.75$. Interpolating between the 2nd and 3rd values: $Q_1=2+(4 - 2)\times0.75 = 3.5$.

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 ($Q_3$)

The position of $Q_3$ is $0.75\times(n + 1)=0.75\times(10+1)=8.25$. Interpolating between the 8th and 9th values: $Q_3=7+(9 - 7)\times0.25 = 7.5$.

Step6: Find the maximum

The maximum value is the last number in the ordered list, so the maximum is 15.

Answer:

2, 3.5, 5, 7.5, 15