Calculate the mean, variance and standard deviation for the following distribution:
Class       30-40    40-50      50-60     60-70      70-80      80-90       90-100
Frequency   3             7             12          15             8            3               2

Explanation

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

### Step 1: Create a Frequency Distribution Table
We will create a table with the classes, class marks (x_i), frequencies (f_i), and the products of class marks and frequencies (x_i * f_i).

| Class | Class Mark (x_i) | Frequency (f_i) | x_i * f_i |
|-----------|------------------|----------------|-----------|
| 30-40 | 35 | 3 | 105 |
...