Calculate mean, variance and standard deviation of the following frequency distribution:

Class ` \ \ \ \ \ \ \ \ \ \ \ \ \ ` Frequency

`1-10` ` \ \ \ \ \ \ \ \ \ \ \ \ \ ` `11`

`10-20` ` \ \ \ \ \ \ \ \ \ \ \ \ \ ` `29`

`20-30` ` \ \ \ \ \ \ \ \ \ \ \ \ \ ` `18`

`30-40` ` \ \ \ \ \ \ \ \ \ \ \ \ \ ` `4`

`40-50` ` \ \ \ \ \ \ \ \ \ \ \ \ \ ` `5`

`50-60` ` \ \ \ \ \ \ \ \ \ \ \ \ \ ` `3`

Explanation

To calculate the mean, variance, and standard deviation of the given frequency distribution, we will follow these steps:

### Step 1: Calculate the Midpoint (x_i) of Each Class
The midpoint (x_i) for each class is calculated as follows:
- For the class 1-10, midpoint = (1 + 10) / 2 = 5
- For the class 10-20, midpoint = (10 + 20) / 2 = 15
- For the class 20-30, midpoint = (20 + 30) / 2 = 25
- For the class 30-40, midpoint = (30 + 40) / 2 = 35
...