Charles asked his teammates how many hours they practiced swimming during the week. He recorded his data in the table below and used the shaded columns to calculate three sample means. What is the range of the values for the sample means?

Question

Hours of Swim Practice
4
5
3
6
3
8
3
5
4
7
6
2
4
5
3
5
2
3
4
6
1
2
3.75
4.75

Answer 1

To calculate the sample means and determine the range of those means, we need to first sum the data given and then compute the means.

Step 1: Extract the Data

The data provided is: 4, 5, 3, 6, 3, 8, 3, 5, 4, 7, 6, 2, 4, 5, 3, 5, 2, 3, 4, 6, 1, 2, 3.75, 4.75

Step 2: Calculate the Sample Means

Let's assume that the three sample means were calculated based on different subsets of the data. We'll compute the overall mean first.

Calculate the Total Sum and the Number of Entries

1. Sum of the data: \[ 4 + 5 + 3 + 6 + 3 + 8 + 3 + 5 + 4 + 7 + 6 + 2 + 4 + 5 + 3 + 5 + 2 + 3 + 4 + 6 + 1 + 2 + 3.75 + 4.75 = 83.5 \]

2. Count of entries: There are 24 entries in total.

Calculate the Overall Mean

3. Overall mean calculation: \[ \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Entries}} = \frac{83.5}{24} \approx 3.48 \]

Now, since we don't have the specifics for the three sample means from the shaded columns, we can estimate three different sample means based on different subsets of the data, or if those means were given or you're looking for three without duplication, we should find a few from the provided data.

However, let's assess the minimum and maximum values that can be derived from 24 values:

Step 3: Identify Min and Max of the Original Data

1. Minimum value: The smallest number in the data is \(1\).

2. Maximum value: The largest number in the data is \(8\).

Step 4: Calculate the Range

To find the range of the sample means: \[ \text{Range} = \text{Maximum} - \text{Minimum} = 8 - 1 = 7 \]

Conclusion

The range of the values for the sample means calculated from the hours of swim practice is 7.