Let me extract the relevant data and solve the problem. The task is to calculate the mean from the given frequency distribution.

Extracted Data:

The table contains two columns:

• $x_i$ (No.) = [7, 8, 9, 10, 11, 12, 13]
• $f_i$ (Frequency) = [3, 8, 12, 15, 10, 9, 5]

We also calculate $f_i \cdot x_i$ (the product of frequency and value): $f_i \cdot x_i = [21, 64, 108, 150, 110, 108, 65]$

Solution:

1. Formula for the Mean: $\text{Mean} (\bar{x}) = \frac{\sum f_i \cdot x_i}{\sum f_i}$

2. Step 1: Calculate $\sum f_i$: $\sum f_i = 3 + 8 + 12 + 15 + 10 + 9 + 5 = 62$

3. Step 2: Calculate $\sum f_i \cdot x_i$: $\sum f_i \cdot x_i = 21 + 64 + 108 + 150 + 110 + 108 + 65 = 626$

4. Step 3: Calculate the Mean: $\bar{x} = \frac{626}{62} = 10.1$

Final Answer:

The mean of the frequency distribution is: $\boxed{10.1}$

Would you like a step-by-step breakdown of this calculation?

Related Questions:

1. How is the weighted mean different from the arithmetic mean?
2. What is the significance of frequency in determining the mean?
3. Can the mean alone describe a dataset? Why or why not?
4. How can we use this mean to identify outliers in the dataset?
5. How would the mean change if one more data point was added?

Tip:

Always verify your calculations by summing $\sum f_i$ and $\sum f_i \cdot x_i$ to ensure accuracy in your final mean value.