**Step Deviation Method**

Step deviation method is a method to calculate the mean deviation by converting the given data into a continuous distribution by assuming a common difference or step size. This method helps in simplifying the calculation process.

**Question 10**

The marks obtained by 40 students in a mathematics test are given below:

12, 15, 16, 18, 20, 20, 21, 22, 22, 24, 24, 25, 25, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 34, 35, 38, 39, 40, 41

Calculate the mean deviation using the step deviation method.

**Step 1: Find the Mean**

To find the mean, we add up all the data points and divide by the total number of data points.

Mean = (12 + 15 + 16 + 18 + 20 + 20 + 21 + 22 + 22 + 24 + 24 + 25 + 25 + 26 + 26 + 27 + 27 + 27 + 27 + 28 + 28 + 28 + 28 + 29 + 29 + 29 + 29 + 30 + 30 + 31 + 32 + 32 + 33 + 33 + 34 + 34 + 35 + 38 + 39 + 40 + 41)/40

Mean = 27.3

**Step 2: Find the Step Deviation**

To find the step deviation, we subtract the assumed common difference from each data point and divide by the common difference.

Assuming the common difference is 3, we get:

Step deviation = (Data point - Mean)/Common difference

For example, for the first data point:

Step deviation = (12 - 27.3)/3 = -5.1/3 = -1.7

By repeating this process for all data points, we get the following table:

| Marks | Step Deviation |
|--------|----------------|
| 12 | -1.7 |
| 15 | -1.1 |
| 16 | -0.8 |
| 18 | -0.4 |
| 20 | -0.1 |
| 20 | -0.1 |
| 21 | 0 |
| 22 | 0.3 |
| 22 | 0.3 |
| 24 | 0.7 |
| 24 | 0.7 |
| 25 | 1 |
| 25 | 1 |
| 26 | 1.3 |
| 26 | 1.3 |
| 27 | 1.6 |
| 27 | 1.6 |
| 27 | 1.6 |
| 27 | 1.6 |
| 28 | 1.9 |
| 28