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To calculate the mean for this frequency distribution, we need to apply the formula for the mean of grouped dataTo calculate the mean for this frequency distribution, we need to apply the formula for the mean of grouped 

\[
\text{Mean} = \frac{\sum (x \times f)}{\sum f}
\]

Where:
- \( x \) is the value of the variable.
- \( f \) is the frequency of the corresponding value.

Using the table you provided:

| \(x\) | \(f\) |
|------|------|
| 11   | 13   |
| 12   | 20   |
| 13   | 2    |
| 14   | 1    |

1. Multiply \(x\) by \(f\):
   - \(11 \times 13 = 143\)
   - \(12 \times 20 = 240\)
   - \(13 \times 2 = 26\)
   - \(14 \times 1 = 14\)

2. Sum of \(x \times f\):
   \[
   143 + 240 + 26 + 14 = 423
   \]

3. Sum of frequencies (\(\sum f\)):
   \[
   13 + 20 + 2 + 1 = 36
   \]

4. Now calculate the mean:
   \[
   \text{Mean} = \frac{423}{36} \approx 11.8
   \]

So, the mean is approximately **11.8** (rounded to 1 decimal place).

Would you like more details or have any other questions? Here are five related questions:

1. How would the mean change if one of the frequencies was altered?
2. Can you explain why the mean is not necessarily one of the \(x\) values?
3. How do you calculate the median for a frequency distribution like this?
4. What is the impact of outliers on the mean in such distributions?
5. How would you calculate the mode for this frequency table?

**Tip:** The mean is a measure of central tendency, but it can be influenced heavily by extreme values (outliers). Always consider other measures like the median for a fuller understanding of the data.

Calculate the mean for the provided frequency distribution.

This guide provides a comprehensive tutorial on how to calculate the mean of grouped data using a frequency distribution table. The example covers the process of multiplying values by their frequencies, summing them up, and dividing by the total frequency. Suitable for students in Grades 6-12 and those learning basic statistics.

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