The numbers 3, 5, 7 and 9 have their respective frequencies x – 2, x + 2, x – 3 and x + 3. If the arithmetic mean is 6.5 then the value of x is

To solve this problem, we need to use the formula for the arithmetic mean, which is the sum of all numbers divided by the count of numbers.

The sum of all numbers can be calculated as follows:

Sum = (3*(x-2)) + (5*(x+2)) + (7*(x-3)) + (9*(x+3))

The count of numbers is the sum of all frequencies, which is:

Count = (x-2) + (x+2) + (x-3) + (x+3)

Given that the arithmetic mean is 6.5, we can set up the equation:

6.5 = Sum / Count

Substituting the expressions for Sum and Count into this equation, we get:

6.5 = [(3*(x-2)) + (5*(x+2)) + (7*(x-3)) + (9*(x+3))] / [(x-2) + (x+2) + (x-3) + (x+3)]

Solving this equation will give us the value of x.