The following table gives the distribution of income of 100 families in a village. Calculate the standard deviation: Income Rs., 0-1000, 1000-2000, 2000-3000, 3000-4000, 4000-5000, 5000-6000 No. of Families, 18, 26, 30, 12, 10, 4

Explanation

To calculate the standard deviation of the income distribution of 100 families in a village, we will follow these steps:

### Step 1: Create a Table with Mid Values
We need to determine the mid values of each income class. The mid value \(X_i\) for each class can be calculated as follows:

- For the class 0-1000, \(X_1 = \frac{0 + 1000}{2} = 500\)
- For the class 1000-2000, \(X_2 = \frac{1000 + 2000}{2} = 1500\)
- For the class 2000-3000, \(X_3 = \frac{2000 + 3000}{2} = 2500\)
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