calculate the five - number summary of the given data. 16, 14, 2, 10, 19, 21, 3, 13, 18, 7, 18, 4, 23, 20…

Explanation:

Step1: Sort the data

$2,3,4,7,10,13,14,16,18,18,19,20,21,23$

Step2: Find the minimum

The minimum value is $2$.

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

There are $n = 14$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{14+1}{4}=3.75$. So $Q_1=4+(7 - 4)\times0.75 = 6.25$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{14 + 1}{2}=7.5$. So $Q_2=\frac{14 + 16}{2}=15$.

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

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(14 + 1)}{4}=11.25$. So $Q_3=18+(19 - 18)\times0.25 = 18.25$.

Step6: Find the maximum

The maximum value is $23$.

Answer:

$2,6.25,15,18.25,23$