Peter wants to estimate the mean value rolled on a fair number cube. He has generated four samples containing five rolls of the number cube as shown in the table below. Which sample will result in the greatest mean?

Question

Sample Data
Sample 1
4
5
2
4
3
Sample 2
2
2
6
5
6
Sample 3
4
6
3
4
2
Sample 4
5
2
4
3
6
Sample 1
Sample 2
Sample 3
Sample 4

Answer 1

To find which sample will result in the greatest mean, we need to calculate the mean for each sample. The mean is calculated by summing all the values in the sample and then dividing by the number of values (which is 5 for each sample).

Calculations:

1. Sample 1:

   • Data: 4, 5, 2, 4, 3
   • Sum: \(4 + 5 + 2 + 4 + 3 = 18\)
   • Mean: \(18 / 5 = 3.6\)

2. Sample 2:

   • Data: 2, 2, 6, 5, 6
   • Sum: \(2 + 2 + 6 + 5 + 6 = 21\)
   • Mean: \(21 / 5 = 4.2\)

3. Sample 3:

   • Data: 4, 6, 3, 4, 2
   • Sum: \(4 + 6 + 3 + 4 + 2 = 19\)
   • Mean: \(19 / 5 = 3.8\)

4. Sample 4:

   • Data: 5, 2, 4, 3, 6
   • Sum: \(5 + 2 + 4 + 3 + 6 = 20\)
   • Mean: \(20 / 5 = 4.0\)

Now, we can summarize the means:

• Sample 1 Mean: 3.6
• Sample 2 Mean: 4.2
• Sample 3 Mean: 3.8
• Sample 4 Mean: 4.0

The sample with the greatest mean is Sample 2, with a mean of 4.2.