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From the image, it looks like you're working on a problem involving statistics. Specifically, you are asked to calculate the **range**, **variance**, and **standard deviation** of the times (in minutes) spent in rush-hour traffic by a sample of 14 drivers. Here's a breakdown of the tasks and solutions based on the dataFrom the image, it looks like you're working on a problem involving statistics. Specifically, you are asked to calculate the **range**, **variance**, and **standard deviation** of the times (in minutes) spent in rush-hour traffic by a sample of 14 drivers. Here's a breakdown of the tasks and solutions based on the 

### Part 1: Find the Range
You’ve correctly identified the **range** as 25. The range is calculated by subtracting the smallest value from the largest value:
\[
\text{Range} = 71 - 46 = 25
\]

### Part 2: Find the Variance
It appears that the value you entered, 539.4, was incorrect, and the correct variance is 82.7. Variance (\( \sigma^2 \)) measures how spread out the numbers are. 

To find the variance, you would use the formula:
\[
\text{Variance} = \frac{1}{n-1} \sum (x_i - \bar{x})^2
\]
Where:
- \( n \) is the number of data points (14 in this case).
- \( x_i \) represents each individual data point.
- \( \bar{x} \) is the mean of the data points.

The correct variance given in your problem is **82.7**.

### Part 3: Find the Standard Deviation
The standard deviation is the square root of the variance:
\[
\text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{82.7}
\]
Let me calculate the correct standard deviation for you.

The standard deviation is approximately **9.1**.

Would you like more details on how these values were calculated or have any questions? 

Here are five additional related questions you might find helpful:
1. How is the variance formula derived?
2. What is the difference between population variance and sample variance?
3. Why is the range a less reliable measure of spread than variance or standard deviation?
4. How would the results change if there were an outlier in the data?
5. What are some common applications of standard deviation in real-world data analysis?

**Tip**: Standard deviation is a useful measure to understand how much variation exists in a dataset. The larger the standard deviation, the more spread out the data.

Find the range, variance, and standard deviation for the time (in minutes) spent in rush-hour traffic by a sample of 14 drivers: 52, 70, 60, 49, 46, 48, 53, 51, 70, 71, 59.

Learn how to calculate the range, variance, and standard deviation for the time (in minutes) spent in rush-hour traffic by 14 drivers. This guide covers key statistics concepts such as variance and standard deviation, with a worked example.

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