The gas mileages​ (in miles per​ gallon) for 34 cars are shown in the frequency distribution. Approximate the mean of the frequency distribution. Gas Mileage (in miles per gallon)	Frequency
26-31	11
32-37	13
38-43	3
44-49	7

To approximate the mean of the frequency distribution, we follow these steps:

1. Find the midpoint of each class interval.
2. Multiply each midpoint by the frequency of that class.
3. Sum these products.
4. Divide the sum by the total frequency.

Let's go through these steps with the given dataTo approximate the mean of the frequency distribution, we follow these steps:

1. Find the midpoint of each class interval.
2. Multiply each midpoint by the frequency of that class.
3. Sum these products.
4. Divide the sum by the total frequency.

Let's go through these steps with the given 

1. Calculate the midpoints for each class interval:

- For 26-31: \((26 + 31) / 2 = 28.5\)
- For 32-37: \((32 + 37) / 2 = 34.5\)
- For 38-43: \((38 + 43) / 2 = 40.5\)
- For 44-49: \((44 + 49) / 2 = 46.5\)

2. Multiply each midpoint by the corresponding frequency:

- \(28.5 \times 11 = 313.5\)
- \(34.5 \times 13 = 448.5\)
- \(40.5 \times 3 = 121.5\)
- \(46.5 \times 7 = 325.5\)

3. Sum these products:

\[313.5 + 448.5 + 121.5 + 325.5 = 1209\]

4. Divide the sum by the total frequency (which is the sum of all frequencies):

Total frequency:
\[11 + 13 + 3 + 7 = 34\]

Approximate mean:
\[\frac{1209}{34} \approx 35.56\]

So, the approximate mean gas mileage is 35.56 miles per gallon.

Would you like more details or have any questions about this calculation?

Here are 5 questions you might want to ask next:
1. How do you calculate the standard deviation for this frequency distribution?
2. What is the difference between the mean and median in a frequency distribution?
3. How do you construct a histogram from this frequency distribution?
4. How can you use the mean to interpret the central tendency of this data?
5. What are some limitations of using frequency distributions?

**Tip:** When dealing with frequency distributions, always ensure to accurately find the midpoints of the class intervals, as they are crucial for calculating the mean and other statistical measures.

Learn how to approximate the mean gas mileage from a frequency distribution with detailed steps and calculations. This problem involves statistical concepts such as frequency distribution and mean calculation. Suitable for advanced high school students and beyond.

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