To calculate the arithmetic mean from the given data, follow these steps:
1. List the Income Brackets and the Corresponding Number of Persons:
| Income (₹): | below 30 | 40 | 30 | 60 | 70 | 80 | 90 |
|--------------------|----------|----|----|----|----|----|----|
| Number of persons: | 16 | 36 | 61 | 76 | 87 | 95 | 100|
For simplicity and consistency, we'll assume 'below 30' collectively as 30:
| Income (₹): | 30 | 40 | 30 | 60 | 70 | 80 | 90 |
|--------------------|----|----|----|----|----|----|----|
| Number of persons: | 16 | 36 | 61 | 76 | 87 | 95 | 100|
2. Calculate the Total Number of Persons:
The total number of persons is the sum of the number of persons across all income brackets:
[tex]\[ \text{Total Number of Persons} = 16 + 36 + 61 + 76 + 87 + 95 + 100 = 471 \][/tex]
3. Calculate the Total Income:
The total income is found by multiplying each income bracket by the number of persons in that bracket and then summing these products:
[tex]\[
\begin{align*}
\text{Total Income} =& (30 \times 16) + (40 \times 36) + (30 \times 61) + (60 \times 76) + (70 \times 87)\\
&+ (80 \times 95) + (90 \times 100) \\
=& 480 + 1440 + 1830 + 4560 + 6090 + 7600 + 9000 \\
=& 31000
\end{align*}
\][/tex]
4. Calculate the Arithmetic Mean:
The arithmetic mean is calculated by dividing the total income by the total number of persons:
[tex]\[
\text{Arithmetic Mean} = \frac{\text{Total Income}}{\text{Total Number of Persons}} = \frac{31000}{471} \approx 65.817
\][/tex]
Thus, the arithmetic mean of the income is approximately ₹65.82.
