Question

calculate the mean for each data set. set a: 13 14 18 22 23 25 27 30 set b: 6 8 9 12 15 18 19 22 set a: mean = 13.625 set b: mean = 12 set a: mean = 21.5 set b: mean = 13.5 set a: mean = 22 set b: mean = 12

Explanation:

Step1: Recall mean formula

The mean (average) of a data - set is calculated as $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points.
For Set A: $n_{A}=8$, and the data - set is $\{13,14,18,22,23,25,27,30\}$.
$\sum_{i = 1}^{8}x_{i}=13 + 14+18+22+23+25+27+30=172$.

Step2: Calculate mean of Set A

$\bar{x}_{A}=\frac{172}{8}=21.5$.
For Set B: $n_{B}=8$, and the data - set is $\{6,8,9,12,15,18,19,22\}$.
$\sum_{i = 1}^{8}y_{i}=6 + 8+9+12+15+18+19+22=109$.

Step3: Calculate mean of Set B

$\bar{x}_{B}=\frac{109}{8}=13.625$.

Answer:

Set A mean = 21.5
Set B mean = 13.625