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The given plot shows the number of tennis matches won by players last summer, indicated by orange crosses along a horizontal axis.

Here’s how we can find the mean:

1. Count how many times each value appears (each "X" represents one occurrence):

   - 0 matches won: 1 time
   - 1 match won: 4 times
   - 2 matches won: 3 times
   - 3 matches won: 2 times
   - 4 matches won: 2 times
   - 5 matches won: 2 times
   - 6 matches won: 1 time

2. To find the mean, use the formula for the mean of a frequency distribution:
   \[
   \text{Mean} = \frac{\sum (\text{value} \times \text{frequency})}{\sum (\text{frequency})}
   \]
   
   First, calculate the sum of the products:
   \[
   (0 \times 1) + (1 \times 4) + (2 \times 3) + (3 \times 2) + (4 \times 2) + (5 \times 2) + (6 \times 1) = 0 + 4 + 6 + 6 + 8 + 10 + 6 = 40
   \]

   Now, sum the frequencies:
   \[
   1 + 4 + 3 + 2 + 2 + 2 + 1 = 15
   \]

   Finally, divide the sum of the products by the sum of the frequencies to find the mean:
   \[
   \text{Mean} = \frac{40}{15} \approx 2.67
   \]

The mean number of tennis matches won is approximately **2.67**.

Would you like further details or have any questions?

Here are some related questions to think about:

1. What is the mode of the data in this frequency distribution?
2. How would you calculate the median of this dataset?
3. What does the mean represent in the context of this problem?
4. How would the mean change if one more player won 5 matches?
5. Can you explain the difference between the mean, median, and mode for this set?

**Tip:** Always double-check the frequency count and your calculations to avoid simple errors when working with data distributions!

A tennis fan counted the number of matches won by her favorite players last summer. The data is displayed as a frequency distribution graph. What is the mean of the numbers?

Learn how to calculate the mean of tennis matches won using a frequency distribution chart. This example helps students understand how to use the formula for mean in a dataset involving different occurrences of values. Suitable for Grades 5-7.

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