**Assumed Mean Method**

The assumed mean method is a technique used to calculate the mean of a given set of data when the data is presented in the form of class intervals. In this method, we assume a value as the mean and then calculate the deviations from this assumed mean. By using these deviations, we can find the actual mean of the data set.

**Step 1: Calculate the Midpoint of Each Class Interval**

To start with, we need to find the midpoint of each class interval. The midpoint is calculated by adding the lower limit and upper limit of each class interval and dividing the sum by 2.

Midpoint of 100-150 = (100 + 150) / 2 = 125
Midpoint of 150-200 = (150 + 200) / 2 = 175
Midpoint of 200-250 = (200 + 250) / 2 = 225
Midpoint of 250-300 = (250 + 300) / 2 = 275
Midpoint of 300-350 = (300 + 350) / 2 = 325

**Step 2: Calculate the Deviations from the Assumed Mean**

Next, we assume a value as the mean. Let's assume the mean as M. We will calculate the deviations of each midpoint from this assumed mean.

Deviation of 125 from M = 125 - M
Deviation of 175 from M = 175 - M
Deviation of 225 from M = 225 - M
Deviation of 275 from M = 275 - M
Deviation of 325 from M = 325 - M

**Step 3: Calculate the Product of Deviations and Frequencies**

Now, we multiply each deviation with its corresponding frequency.

Product of deviation of 125 from M and frequency 4 = (125 - M) * 4
Product of deviation of 175 from M and frequency 5 = (175 - M) * 5
Product of deviation of 225 from M and frequency 12 = (225 - M) * 12
Product of deviation of 275 from M and frequency 2 = (275 - M) * 2
Product of deviation of 325 from M and frequency 2 = (325 - M) * 2

**Step 4: Calculate the Sum of the Products of Deviations and Frequencies**

Next, we find the sum of all the products of deviations and frequencies.

Sum = (125 - M) * 4 + (175 - M) * 5 + (225 - M) * 12 + (275 - M) * 2 + (325 - M) * 2

**Step 5: Calculate the Mean**

To find the mean, we divide the sum of the products of deviations and frequencies by the total frequency.

Mean = Sum / Total Frequency

In this case, the total frequency is 4 + 5 + 12 + 2 + 2 = 25.

Mean = Sum / 25

**Step 6: Solve for M**

Now, we solve the equation Sum / 25 = M to find the value of M, which is the assumed mean.

Once we find the value of M, we can substitute it back into the equation to calculate the mean.

By following these steps, you can find the mean using the assumed mean method when the