practice 5 (from unit 1, lesson 9)\na. what is the five - number summary for the data?\n2 2 4 4 5 5 6 7 9…

Explanation:

Step1: Define five - number summary

The five - number summary consists of the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum.

Step2: For part a

Minimum

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

First quartile ($Q_1$)

There are $n = 10$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{10+ 1}{4}=2.75$. So, $Q_1=4$.

Median ($Q_2$)

The position of the median for $n = 10$ is $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The median $Q_2=\frac{5 + 5}{2}=5$.

Third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. So, $Q_3=7$.

Maximum

The maximum value is 15.

Step3: For part b

New data set

The new data set after removing 15 is 2, 2, 4, 4, 5, 5, 6, 7, 9. Now $n = 9$.

Minimum

The minimum value is 2.

First quartile ($Q_1$)

The position of $Q_1$ is $\frac{n + 1}{4}=\frac{9+1}{4}=2.5$. So, $Q_1=\frac{4+4}{[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]