Question

analyzing data
population data
4 8 6 10
5 2 9 8
9 20 10 1
15 1 8 2
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
6 and 10
6.5 and 10
7 and 12
10 and 12

Explanation:

Step1: Calculate Row 1 mean

$\text{Mean}_1 = \frac{4+8+6+10}{4} = \frac{28}{4} = 7$

Step2: Calculate Row 2 mean

$\text{Mean}_2 = \frac{5+2+9+8}{4} = \frac{24}{4} = 6$

Step3: Calculate Row 3 mean

$\text{Mean}_3 = \frac{9+20+10+1}{4} = \frac{40}{4} = 10$

Step4: Calculate Row 4 mean

$\text{Mean}_4 = \frac{15+1+8+2}{4} = \frac{26}{4} = 6.5$

Step5: Find population mean

First sum all values: $4+8+6+10+5+2+9+8+9+20+10+1+15+1+8+2 = 118$
$\text{Population Mean} = \frac{118}{16} = 7.375$

Step6: Compare means for largest/smallest

Largest row mean = 10 (Row 3), Smallest row mean = 6 (Row 2)

Step7: Match population mean range

$7.375$ is between 6.5 and 10

Answer:

1. Row with the largest mean: Row 3
2. Row with the smallest mean: Row 2
3. Population mean range: 6.5 and 10