FIND ARITHMETIC MEAN BY ASSUMED MEAN METHOD
About "Find arithmetic mean by assumed mean method"
Find arithmetic mean by assumed mean method :
Here we are going to see how to find arithmetic mean by assumed mean method.
Arithmetic mean for grouped data can be obtained in two methods which are
(i) Direct Method and (ii) Assumed Mean Method
Formula for assumed mean method
Arithmetic mean by assumed mean method - Examples
Example 1 :
Obtain the A.M of 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
Hence the required arithmetic mean for the given data is 15.6
Example 2 :
Obtain the A.M of 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
Hence the required arithmetic mean for the given data is 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
Hence the required arithmetic mean for the given data is 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
Hence the required arithmetic mean for the given data is 45
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