Question

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: Find the minimum

The minimum value in the data - set 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 is 2.

Step2: Find the first quartile ($Q_1$)

The data - set has $n = 10$ values. First, find the position of $Q_1$. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{10+1}{4}=2.75$. So, $Q_1$ is the value at the 2.75 - th position. Interpolating between the 2nd and 3rd ordered values: $Q_1=2+(4 - 2)\times0.75 = 3.5$.

Step3: 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 the average of the 5th and 6th ordered values, so $Median=\frac{5 + 5}{2}=5$.

Step4: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. Interpolating between the 8th and 9th ordered values: $Q_3=7+(9 - 7)\times0.25=7.5$.

Step5: Find the maximum

The maximum value in the data - set is 15.

Answer:

2, 3.5, 5, 7.5, 15