Question

practice 2b score: 17.99/46 answered: 14/23 question 15 find the 5 number summary for the data shown. 14 33 40 41 59 64 68 70 72 77 88 92 93 98 5 number summary: question help: video 1 video 2 submit question

Explanation:

Step1: Arrange data in ascending order

14, 33, 40, 41, 59, 64, 68, 70, 72, 77, 88, 92, 93, 98

Step2: Find the minimum

The minimum value is 14.

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

There are $n = 14$ data points. The position of $Q_1$ is $i=\frac{n + 1}{4}=\frac{14+ 1}{4}=3.75$. So $Q_1=40+(41 - 40)\times0.75 = 40.75$.

Step4: Find the median

The position of the median for $n = 14$ (even number of data - points) is $\frac{n}{2}=7$ and $\frac{n}{2}+1 = 8$. The median is $\frac{68 + 70}{2}=69$.

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

The position of $Q_3$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(14 + 1)}{4}=11.25$. So $Q_3=88+(92 - 88)\times0.25=89$.

Step6: Find the maximum

The maximum value is 98.

Answer:

14, 40.75, 69, 89, 98