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The table shows test scores and their corresponding frequencies. To calculate the mean score, we'll use the formula for the mean of grouped dataThe table shows test scores and their corresponding frequencies. To calculate the mean score, we'll use the formula for the mean of grouped 

\[
\text{Mean} = \frac{\sum (\text{Test Score} \times \text{Frequency})}{\sum \text{Frequency}}
\]

Let's calculate the mean step-by-step:

1. Multiply each test score by its frequency.
2. Sum the results from step 1.
3. Divide the total by the sum of frequencies.

Let's perform these calculations:

- \( 3 \times 2 = 6 \)
- \( 4 \times 6 = 24 \)
- \( 5 \times 2 = 10 \)
- \( 6 \times 3 = 18 \)
- \( 7 \times 3 = 21 \)
- \( 8 \times 2 = 16 \)
- \( 9 \times 2 = 18 \)
- \( 10 \times 2 = 20 \)

Total of products: \( 6 + 24 + 10 + 18 + 21 + 16 + 18 + 20 = 133 \)

Now, sum the frequencies:

\[
2 + 6 + 2 + 3 + 3 + 2 + 2 + 2 = 22
\]

Finally, calculate the mean:

\[
\text{Mean} = \frac{133}{22} \approx 6.05
\]

So, the mean score on this test is approximately **6.05**.

Would you like further details on the calculation or have any questions?

Here are 5 related questions for further practice:
1. How would the mean change if the frequency of the score 10 increased by 1?
2. What is the median score from this data set?
3. How do you calculate the mode for this frequency table?
4. What is the range of the scores from this table?
5. How would the mean change if a score of 1 with a frequency of 1 was added to the table?

**Tip:** When dealing with frequency tables, always make sure to correctly multiply each category by its frequency before summing.

The table below shows the scores of a group of students on a 10-point quiz. The mean score on this test is:

Learn how to find the mean score from a frequency table with a detailed step-by-step solution. This problem involves calculating the mean score of a group of students based on test scores and their frequencies. Suitable for students in Grades 7-9.

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