Question

thirteen students in a statistics class were asked how many siblings they have. their responses are listed below. 0, 1, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6 which of the following is the five - number summary for the data? 0, 3, 3, 3, 6 0, 3, 3, 4, 6 0, 2.5, 3, 3, 6 0, 2.5, 3, 4, 6

Explanation:

Step1: Arrange data in ascending order

0, 1, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6

Step2: Find the minimum

The minimum value is 0.

Step3: Find the first - quartile ($Q_1$)

There are $n = 13$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{13+1}{4}=3.5$. So, $Q_1=\frac{2 + 3}{2}=2.5$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{13+1}{2}=7$. So, the median $Q_2 = 3$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(13 + 1)}{4}=10.5$. So, $Q_3=\frac{3+5}{2}=4$.

Step6: Find the maximum

The maximum value is 6.

Answer:

0, 2.5, 3, 4, 6