Question

How to find mean for grouped data

Answer 1

To find the mean for grouped data, you can follow these steps:

1. **Create a Frequency Distribution Table**: Start with your grouped data organized in classes or intervals, along with their corresponding frequencies.

Example:

| Class Interval | Frequency (f) |
|----------------|----------------|
| 1 - 10 | 5 |
| 11 - 20 | 12 |
| 21 - 30 | 8 |

2. **Calculate the Midpoint for Each Class**: The midpoint (often denoted as \(x_i\)) of each class interval is found by averaging the lower and upper bounds of the interval.

\[
x_i = \frac{\text{Lower limit} + \text{Upper limit}}{2}
\]

For the table above:

| Class Interval | Frequency (f) | Midpoint (x_i) |
|----------------|----------------|-----------------|
| 1 - 10 | 5 | 5.5 |
| 11 - 20 | 12 | 15.5 |
| 21 - 30 | 8 | 25.5 |

3. **Calculate \(f_i \cdot x_i\)**: Multiply the frequency of each class by the corresponding midpoint.

| Class Interval | Frequency (f) | Midpoint (x_i) | \(f_i \cdot x_i\) |
|----------------|----------------|-----------------|--------------------|
| 1 - 10 | 5 | 5.5 | 27.5 |
| 11 - 20 | 12 | 15.5 | 186 |
| 21 - 30 | 8 | 25.5 | 204 |

4. **Sum \(f_i\) and \(f_i \cdot x_i\)**: Calculate the total frequency (\(N\)) and the total of \(f_i \cdot x_i\) values.

- Total Frequency \(N\) = \(5 + 12 + 8 = 25\)
- Sum of \(f_i \cdot x_i\) = \(27.5 + 186 + 204 = 417.5\)

5. **Calculate the Mean**: Use the formula for the mean of grouped data:

\[
\text{Mean} = \frac{\sum (f_i \cdot x_i)}{N}
\]

\[
\text{Mean} = \frac{417.5}{25} = 16.7
\]

So, the mean of the grouped data would be 16.7.