5. given the following set of data: 15, 22, 19, 31, 20, 14, 17, 23, 28, calculate the\na. mean,\nb…

Explanation:

Step1: Arrange data in ascending order

$14, 17, 19, 20, 22, 23, 28, 31$

Step2: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 8$ and $\sum_{i=1}^{8}x_{i}=14 + 17+19+20+22+23+28+31=174$. So $\bar{x}=\frac{174}{8}=21.75$

Step3: Calculate the median

Since $n = 8$ (even), the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered values. $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4 - th value is $20$ and the 5 - th value is $22$. Median $=\frac{20 + 22}{2}=21$

Step4: Calculate the mode

There is no value that appears more frequently than others, so there is no mode.

Step5: Calculate the 60th percentile

First, find the index $i$. $i=\frac{p}{100}\times n$, where $p = 60$ and $n=8$. $i=\frac{60}{100}\times8 = 4.8$. Rounding up, the 60th percentile is the 5 - th ordered value, which is $22$.

Answer:

a. $21.75$ b. $21$ c. No mode d. $22$