This presentation will explain in detail how to calculate mean for grouped data with the help of an example.

1. By:
Dr.Ashish Kumar Suri
(Ph.D, MBA, B.E.)
CALCULATION OF MEAN FOR GROUPED
DATA BY STEP DEVIATION METHOD

2. Find the Mean Daily Expense for the given data
Daily Expenses (in Rs.) No. of Families (fi)
20-40 6
40-60 9
60-80 11
80-100 14
100-120 20
120-140 15
140-160 10
160-180 8
180-200 7
Total 100

3. Step 1: Calculate Class Mark (Xi) by dividing the sum of Lower
Class Limit and Upper Class Limit of each class by 2
Daily Expenses (in Rs.) No. of Families (fi) Class Mark (Xi)
20-40 6 30
40-60 9 50
60-80 11 70
80-100 14 90
100-120 20 110
120-140 15 130
140-160 10 150
160-180 8 170
180-200 7 190

4. Step 2: Take the middle value of X (110) as Assumed Mean and
subtract it from all values of Xi to get Deviation (di)
Daily Expenses (in Rs.) No. of Families
(fi)
Class Mark
(Xi)
di = (Xi – A)
20-40 6 30 -80
40-60 9 50 -60
60-80 11 70 -40
80-100 14 90 -20
100-120 20 110 0
120-140 15 130 20
140-160 10 150 40
160-180 8 170 60
180-200 7 190 80

5. Step 3: Calculate ui by dividing all values of di by h. “h” is the
largest number which divides all values of di.
Daily Expenses
(in Rs.)
No. of Families
(fi)
Class Mark
(X)
di = (X-A)
(A=110)
ui = di/h
(h=20)
20-40 6 30 -80 -4
40-60 9 50 -60 -3
60-80 11 70 -40 -2
80-100 14 90 -20 -1
100-120 20 110 0 0
120-140 15 130 20 1
140-160 10 150 40 2
160-180 8 170 60 3
180-200 7 190 80 4

6. Step 4: Multiply the value of fi with corresponding values of ui to
calculate fiui. Add all values of fiui to get Ʃfiui
Daily Expenses
(in Rs.)
No. of Families
(fi)
Class Mark
(X)
di = (X-A)
(A=110)
ui = di/h
(h=20)
fiui
20-40 6 30 -80 -4 -24
40-60 9 50 -60 -3 -27
60-80 11 70 -40 -2 -22
80-100 14 90 -20 -1 -14
100-120 20 110 0 0 0
120-140 15 130 20 1 15
140-160 10 150 40 2 20
160-180 8 170 60 3 24
180-200 7 190 80 4 28
Ʃfi = 100 Ʃfiui = 0

7. Step 5: Calculate the mean with the help of following formula
Mean X̅ =
Ʃfiui
Ʃfi
x h + A
X̅ =
0
100
x 20 + 110
X̅ = Rs. 110