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: Determine the mid-values of the income classes
We need to find the mid-point (mid-value) of each income class. The mid-value \(X_i\) can be calculated as follows:

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