Question

comparing the mean of a sample with the mean of the population
population data
2 5 10 2
4 1 5 3
8 1 4 3
sample data
4 1 5 3
compare the mean of the population with the mean of a sample.
the mean of the population is
the mean of the sample is
the difference between the mean of the sample and the mean of the population is
0
0.50
0.75
5

Explanation:

Step1: Sum all population data

$2+5+10+2+4+1+5+3+8+1+4+3 = 48$

Step2: Count population data points

$n_{\text{pop}} = 12$

Step3: Calculate population mean

$\text{Mean}_{\text{pop}} = \frac{48}{12} = 4$

Step4: Sum all sample data

$4+1+5+3 = 13$

Step5: Count sample data points

$n_{\text{sam}} = 4$

Step6: Calculate sample mean

$\text{Mean}_{\text{sam}} = \frac{13}{4} = 3.25$

Step7: Find mean difference

$\text{Mean}_{\text{sam}} - \text{Mean}_{\text{pop}} = 3.25 - 4 = -0.75$
(Note: The absolute value matches 0.75 from the options)

Answer:

The mean of the population is 4
The mean of the sample is 3.25
The difference between the mean of the sample and the mean of the population is 0.75