To find the mean and sample standard deviation of the given weekly commute times, let’s calculate them step by step.

The data provided are: $3.5, 3.0, 4.6, 5.0, 4.6, 3.4, 4.8, 2.9, 4.5, 4.4, 4.7, 4.9, 5.7, 2.7, 5.4$

Step 1: Calculate the Mean

The mean $\bar{x}$ is calculated by summing all the values and dividing by the number of values.

$\bar{x} = \frac{3.5 + 3.0 + 4.6 + 5.0 + 4.6 + 3.4 + 4.8 + 2.9 + 4.5 + 4.4 + 4.7 + 4.9 + 5.7 + 2.7 + 5.4}{15}$

Step 2: Calculate the Sample Standard Deviation

The sample standard deviation $s$ is calculated using the formula: $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$ where:

• $x_i$ are the individual data points,
• $\bar{x}$ is the mean,
• $n$ is the number of data points (15 in this case).

Let's calculate these values to the nearest hundredth.The calculations yield:

• Mean: 4.27 hours
• Sample Standard Deviation: 0.94 hours

Would you like a breakdown of the steps or have any further questions?

Here are some related questions you might consider:

1. How would the calculations change if it were a population standard deviation instead of a sample?
2. What does the standard deviation tell us about the spread of commute times?
3. How would the mean change if a city with a very high commute time was added to the data?
4. Why is it important to distinguish between sample and population standard deviation?
5. How could the commute time data affect city planning?

Tip: The standard deviation gives insight into how much individual data points vary from the mean, helping to understand data consistency.