How to Find Assumed Mean?

The assumed mean is a method used to simplify the calculation of the mean (average) for grouped data, especially when dealing with large numbers. Here's how to find it:

Understanding Assumed Mean

The assumed mean method is useful when the data has class intervals and a high number of frequencies. It makes calculating the mean easier by reducing the number of digits we need to deal with. The formula uses a value near the middle of the data range, which we assume to be the mean.

Steps to Find the Assumed Mean

1. Choose an Assumed Mean (A): Select a value from the dataset that seems like a reasonable estimate of the mean. This is typically a value near the center of the data range or any value that is in data.

2. Calculate Deviations (d): Subtract the assumed mean (A) from each data point (X) which would be the mid-value for each class interval. The deviation calculation is: d = X - A

3. Multiply Deviations by Frequencies (fd): Multiply each deviation by the corresponding frequency (f) in the data set. fd = f*d

4. Sum the Frequencies (sf): Add up all the frequencies in your dataset which means the total number of data elements. sf = f1 + f2 + f3 +...+fn

5. Sum the (fd) (sfd): Add up all the values you got in step 3 ( the fd values). This is the summation of frequency multiplied with X-A for all figures. sfd = f1d1 + f2d2 +f3d3+...+fndn

6. Apply the Formula: Calculate the assumed mean using the following formula:

   Assumed Mean = A + (sfd / sf)

Where:

• A is the assumed mean.
• sfd is the summation of (frequency * (X-A)).
• sf is the sum of all frequencies.

Example

Let's say we have the following grouped data:

Class Interval	Mid-Value (X)	Frequency (f)
0-10	5	2
10-20	15	3
20-30	25	5
30-40	35	4
40-50	45	1

1. Assume Mean: Let's assume A = 25

2. Calculate Deviations (d=X-A):

   Class Interval	Mid-Value (X)	Frequency (f)	d=X-A=X-25
   0-10	5	2	-20
   10-20	15	3	-10
   20-30	25	5	0
   30-40	35	4	10
   40-50	45	1	20

3. Calculate fd:

   Class Interval	Mid-Value (X)	Frequency (f)	d=X-A=X-25	fd=f*d
   0-10	5	2	-20	-40
   10-20	15	3	-10	-30
   20-30	25	5	0	0
   30-40	35	4	10	40
   40-50	45	1	20	20

4. Calculate sf: sf = 2 + 3 + 5 + 4 + 1 = 15.

5. Calculate sfd: sfd = -40 -30 + 0 + 40 + 20 = -10

6. Calculate Assumed Mean: A + (sfd/sf) = 25 + (-10 / 15) = 25 - 0.67 = 24.33 (approx)

Key Considerations

• The choice of assumed mean does not affect the final mean of the data. However, it is best to choose a value within or near the middle of your data range to simplify the calculations.
• This method is mostly used for grouped data with class intervals.

By following these steps, you can effectively find the assumed mean and use it to compute the mean of a grouped data set with less complex arithmetic.