Suppose we are interested in the mean speed of vehicles on interstate highways in the U.S. We checked the speed of 40 cars near exit 115 on the I-45 and the result is as below (in mph): 



80, 75, 65, 70, 73, 72, 79, 73, 75, 77, 80, 75, 65, 70, 73, 72, 79, 73, 75, 77, 80, 75, 65, 70, 73, 72, 79, 73, 75, 77, 80, 75, 65, 70, 73, 72, 79, 73, 75, 77.  What is the point estimate of the mean speed of vehicles on interstate highways in the U.S.? 



To calculate the point estimate of the mean speed of vehicles, we simply take the average (arithmetic mean) of the observed speeds.

The formula for the mean is:

\[
\bar{x} = \frac{\sum x_i}{n}
\]

where:
- \( \bar{x} \) is the mean,
- \( \sum x_i \) is the sum of all the speeds,
- \( n \) is the number of cars (which in this case is 40).

Let's calculate it.

### Given dataTo calculate the point estimate of the mean speed of vehicles, we simply take the average (arithmetic mean) of the observed speeds.

The formula for the mean is:

\[
\bar{x} = \frac{\sum x_i}{n}
\]

where:
- \( \bar{x} \) is the mean,
- \( \sum x_i \) is the sum of all the speeds,
- \( n \) is the number of cars (which in this case is 40).

Let's calculate it.

### Given 
- Speeds (in mph):  
80, 75, 65, 70, 73, 72, 79, 73, 75, 77, 80, 75, 65, 70, 73, 72, 79, 73, 75, 77,  
80, 75, 65, 70, 73, 72, 79, 73, 75, 77, 80, 75, 65, 70, 73, 72, 79, 73, 75, 77

Let me compute this for you.The point estimate of the mean speed of vehicles near exit 115 on I-45 is approximately **73.9 mph**.

Would you like more details or further explanations on this? Here are a few related questions:

1. What is the median speed of the vehicles?
2. How would you calculate the variance or standard deviation of the speeds?
3. How does the point estimate differ from a confidence interval?
4. What is the difference between point estimate and population mean?
5. How can you account for outliers in the data?

**Tip:** The point estimate gives a single value as an estimate of a population parameter, but it doesn't provide any information about the uncertainty or variability of the estimate.

Suppose we are interested in the mean speed of vehicles on interstate highways in the U.S. We checked the speed of 40 cars near exit 115 on the I-45 and the result is as below (in mph): 80, 75, 65, 70, 73, 72, 79, 73, 75, 77, 80, 75, 65, 70, 73, 72, 79, 73, 75, 77, 80, 75, 65, 70, 73, 72, 79, 73, 75, 77, 80, 75, 65, 70, 73, 72, 79, 73, 75, 77. What is the point estimate of the mean speed of vehicles on interstate highways in the U.S.?

Find out how to calculate the mean speed of vehicles on interstate highways using the speeds of 40 cars near exit 115 on the I-45. This problem applies key statistical concepts, including the mean formula. Suitable for students in Grades 9-12.

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