To calculate the arithmetic mean, we need to find the sum of all the incomes and divide it by the total number of families.

First, we need to find the cumulative frequency for each income category. The cumulative frequency is the sum of the number of families in that category and all the categories before it.

Cumulative frequency for “more than 75” = 150 Cumulative frequency for “more than 85” = 150 + 140 = 290 Cumulative frequency for “more than 95” = 290 + 115 = 405 Cumulative frequency for “more than 105” = 405 + 95 = 500 Cumulative frequency for “more than 115” = 500 + 70 = 570 Cumulative frequency for “more than 125” = 570 + 60 = 630 Cumulative frequency for “more than 135” = 630 + 40 = 670 Cumulative frequency for “more than 145” = 670 + 25 = 695

Now, we can calculate the sum of all the incomes. We will multiply each income category by its corresponding cumulative frequency and add them all together.

Sum of incomes = (75 * 150) + (85 * 140) + (95 * 115) + (105 * 95) + (115 * 70) + (125 * 60) + (135 * 40) + (145 * 25)

Finally, we can calculate the arithmetic mean by dividing the sum of incomes by the total number of families.

Arithmetic mean = Sum of incomes / Total number of families

Note: The formula for the arithmetic mean is Σx / n, where Σx represents the sum of all the values and n represents the total number of values.