Find the missing frequency from the following data, if arithmetic mean is 62.Class 0-40 40-80 80-120 120-160f 6 9 ? 2

To find the missing frequency, we first need to understand the formula for the arithmetic mean. The arithmetic mean is calculated by summing all the values in a set and then dividing by the number of values in that set.

In this case, the arithmetic mean is given as 62. We also know the total frequency (n), which is the sum of all frequencies. We have three frequencies: 6, 9, and 2. The missing frequency is denoted as 'f'. So, the total frequency n = 6 + 9 + 2 + f.

The classes given are 0-40, 40-80, 80-120, and 120-160. We need to find the mid-point (xi) of each class, which is calculated as (lower limit + upper limit)/2. So, the mid-points for the classes are 20, 60, 100, and 140 respectively.

The formula for the arithmetic mean is:

Mean = Σfixi / n

Where: fi = frequency of the ith class xi = mid-point of the ith class n = total frequency

Substituting the given values into the formula:

62 = [(620) + (960) + (f100) + (2140)] / (6 + 9 + f + 2)

Solving the equation will give us the value of the missing frequency 'f'.