FIND ARITHMETIC MEAN BY ASSUMED MEAN METHOD
Formula to find arithmetic mean for a grouped data using assumed mean :
= A + [∑fd / N]
Here A is the assumed mean.
Example 1 :
Calculate arithmetic mean for the following data.
|
x 5 10 15 20 25 30 |
f 4 5 7 4 3 2 |
Solution :
Now we have to use the formula given above to find the arithmetic mean.
Take the assumed mean A = 15
|
x 5 10 15 20 25 30 Total |
f 4 5 7 4 3 2 N = 25 |
d = x - A -10 -5 0 5 10 15 |
fd -40 -25 0 20 30 30 ∑fd = 15 |
Arithmetic mean = A + [∑fd / N]
= 15 + (15/25)
= 15 + (3/5)
= (75 + 3)/5
= 78/5
= 15.6
Example 2 :
Calculate arithmetic mean for the following data.
|
Marks 65 70 75 80 85 90 95 100 |
Number of students 6 11 3 5 4 7 10 4 |
Solution :
Now we have to use the formula given above to find the arithmetic mean.
Take the assumed mean A = 80
|
x 65 70 75 80 85 90 95 100 Total |
f 6 11 3 5 4 7 10 4 N = 50 |
d = x - A -15 -10 -5 0 5 10 15 20 |
fd -90 -110 -15 0 20 70 150 80 ∑fd = 115 |
Arithmetic mean = A + [∑fd / N]
= 80 + (115/50)
= 80 + (23/10)
= 80 + 2.3
= 82.3
Example 3 :
The following data give the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students
|
Age (in years) 13 14 15 16 17 18 |
Number of students 3 8 9 11 6 3 |
Solution :
Now we have to use the formula given above to find the arithmetic mean.
Take the assumed mean A = 16
|
x 13 14 15 16 17 18 Total |
f 3 8 9 11 6 3 N = 40 |
d = x - A -3 -2 -1 0 1 2 |
fd -9 -16 -9 0 6 6 ∑fd = -22 |
Arithmetic mean = A + [∑fd / N]
= 16 + (-22/40)
= 16 - 0.55
= 15.45
Example 4 :
Calculate the Arithmetic mean of the following data:
|
x 15 25 35 45 55 65 75 85 |
f 12 20 15 14 16 11 7 8 |
Solution :
Now we have to use the formula given above to find the arithmetic mean.
Take the assumed mean A = 45
|
x 15 25 35 45 55 65 75 85 Total |
f 12 20 15 14 16 11 7 8 N = 103 |
d = x - A -30 -20 -10 0 10 20 30 40 |
fd -360 -400 -150 0 160 220 210 320 ∑fd = 0 |
Arithmetic mean = A + [∑fd / N]
= 45 + (0/103)
= 45
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