Question

population data
if serena selects 4 samples from the table, which row will give her the largest mean?
which row will give her the smallest mean?
the actual population mean will be between

Explanation:

Step1: Recall mean formula

The mean of a set of numbers $x_1,x_2,x_3,x_4$ is $\bar{x}=\frac{x_1 + x_2+x_3+x_4}{4}$.

Step2: Calculate mean of first - row

For the first row with numbers $4,8,6,10$, the mean is $\frac{4 + 8+6+10}{4}=\frac{28}{4}=7$.

Step3: Calculate mean of second - row

For the second row with numbers $5,2,9,8$, the mean is $\frac{5 + 2+9+8}{4}=\frac{24}{4}=6$.

Step4: Calculate mean of third - row

For the third row with numbers $9,20,10,1$, the mean is $\frac{9+20 + 10+1}{4}=\frac{40}{4}=10$.

Step5: Calculate mean of fourth - row

For the fourth row with numbers $15,1,8,2$, the mean is $\frac{15 + 1+8+2}{4}=\frac{26}{4}=6.5$.

Step6: Compare means

$10>7>6.5>6$. So the third row gives the largest mean. And the second row gives the smallest mean.

Step7: Find range for population mean

The smallest value in the table is $1$ and the largest is $20$. The population mean will be between the smallest and largest values of the data points. So the actual population mean will be between $1$ and $20$.

Answer:

The row that gives the largest mean: Third row
The row that gives the smallest mean: Second row
The actual population mean will be between: $1$ and $20$