Question

find the 5 number summary for the data shown. 5 number summary:

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending - order: 3, 10, 17, 26, 38, 41, 48, 52, 99, 100.

Step2: Find the minimum

The minimum value is the first value in the ordered data set. So, the minimum is 3.

Step3: Find the first quartile ($Q_1$)

There are $n = 10$ data points. The position of $Q_1$ is $L_{Q_1}=\frac{n + 1}{4}=\frac{10+1}{4}=2.75$. So, $Q_1=10+(17 - 10)\times0.75=10 + 5.25 = 15.25$.

Step4: Find the median ($Q_2$)

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 $Q_2=\frac{38 + 41}{2}=39.5$.

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $L_{Q_3}=\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. So, $Q_3=48+(52 - 48)\times0.25=48 + 1=49$.

Step6: Find the maximum

The maximum value is the last value in the ordered data set. So, the maximum is 100.

Answer:

3, 15.25, 39.5, 49, 100