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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 sample means?

\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{5}{|c|}{ Hours of Swim Practice } \\
\hline 4 & 5 & 3 & 6 & 3 \\
\hline 8 & 3 & 5 & 4 & 7 \\
\hline 6 & 2 & 4 & 5 & 3 \\
\hline 5 & 2 & 3 & 4 & 6 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To find the range of the sample means from the hours of swim practice recorded by Charles, we need to follow a detailed, step-by-step process.

### Step 1: Record the Hours of Swim Practice
Here's the table of hours Charles recorded:
```
| 4 | 5 | 3 | 6 | 3 |
| 8 | 3 | 5 | 4 | 7 |
| 6 | 2 | 4 | 5 | 3 |
| 5 | 2 | 3 | 4 | 6 |
```

### Step 2: Calculate the Sample Means
To calculate the sample mean for each row, we add up all the hours in the row and divide by the number of entries in that row (which is 5 in this case).

#### Row 1: `4, 5, 3, 6, 3`
Sum = 4 + 5 + 3 + 6 + 3 = 21
Mean = 21 / 5 = 4.2

#### Row 2: `8, 3, 5, 4, 7`
Sum = 8 + 3 + 5 + 4 + 7 = 27
Mean = 27 / 5 = 5.4

#### Row 3: `6, 2, 4, 5, 3`
Sum = 6 + 2 + 4 + 5 + 3 = 20
Mean = 20 / 5 = 4.0

#### Row 4: `5, 2, 3, 4, 6`
Sum = 5 + 2 + 3 + 4 + 6 = 20
Mean = 20 / 5 = 4.0

The calculated sample means are:
[tex]\[4.2, 5.4, 4.0, 4.0\][/tex]

### Step 3: Find the Range of the Sample Means
To find the range, we identify the maximum and minimum values from the sample means list and subtract the minimum from the maximum.

- Maximum value: 5.4
- Minimum value: 4.0

Range = Maximum - Minimum = 5.4 - 4.0 = 1.4

### Conclusion
The range of the sample means is 1.4

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