To solve this problem, we need to calculate the mean (average) of each sample and then compare these means to determine which sample has the greatest mean.
Here's the step-by-step solution:
1. Calculate the mean of Sample 1:
The numbers in Sample 1 are: 4, 5, 2, 4, 3.
- Sum of the numbers: [tex]\(4 + 5 + 2 + 4 + 3 = 18\)[/tex]
- Number of elements: 5
- Mean of Sample 1: [tex]\(\frac{18}{5} = 3.6\)[/tex]
2. Calculate the mean of Sample 2:
The numbers in Sample 2 are: 2, 2, 6, 5, 6.
- Sum of the numbers: [tex]\(2 + 2 + 6 + 5 + 6 = 21\)[/tex]
- Number of elements: 5
- Mean of Sample 2: [tex]\(\frac{21}{5} = 4.2\)[/tex]
3. Calculate the mean of Sample 3:
The numbers in Sample 3 are: 4, 6, 3, 4, 2.
- Sum of the numbers: [tex]\(4 + 6 + 3 + 4 + 2 = 19\)[/tex]
- Number of elements: 5
- Mean of Sample 3: [tex]\(\frac{19}{5} = 3.8\)[/tex]
4. Calculate the mean of Sample 4:
The numbers in Sample 4 are: 5, 2, 4, 3, 6.
- Sum of the numbers: [tex]\(5 + 2 + 4 + 3 + 6 = 20\)[/tex]
- Number of elements: 5
- Mean of Sample 4: [tex]\(\frac{20}{5} = 4.0\)[/tex]
5. Compare the means:
- Mean of Sample 1: [tex]\(3.6\)[/tex]
- Mean of Sample 2: [tex]\(4.2\)[/tex]
- Mean of Sample 3: [tex]\(3.8\)[/tex]
- Mean of Sample 4: [tex]\(4.0\)[/tex]
6. Identify the greatest mean:
Among the calculated means, [tex]\(4.2\)[/tex] is the greatest.
Therefore, Sample 2 will result in the greatest mean.
