find the 5 number summary for the data shown\nx\n3\n11.7\n13.2\n16.1\n22.8\n24.7\n26.6\n28.2\n29.2\n5 number…

Explanation:

Step1: Sort the data (already sorted)

The data is 3, 11.7, 13.2, 16.1, 22.8, 24.7, 26.6, 28.2, 29.2

Step2: Find the minimum

The minimum value is 3

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

There are $n = 9$ data points. The position of $Q_1$ is $i=\frac{1}{4}(n + 1)=\frac{1}{4}(9+1)=2.5$. So $Q_1=\frac{11.7 + 13.2}{2}=12.45$

Step4: Find the median ($Q_2$)

The position of the median is $i=\frac{1}{2}(n + 1)=\frac{1}{2}(9 + 1)=5$. So the median $Q_2=22.8$

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

The position of $Q_3$ is $i=\frac{3}{4}(n + 1)=\frac{3}{4}(9+1)=7.5$. So $Q_3=\frac{26.6+28.2}{2}=27.4$

Step6: Find the maximum

The maximum value is 29.2

Answer:

3, 12.45, 22.8, 27.4, 29.2