Meanshort cut method. If the values of x and f are large, then the direct method is very tedious and time consuming. As there are big calculations and chance of making mistake in that. So to minimize the time and easy calculations there is another method as meanshort cut method. In this method we take deviations from an arbitrary point.
x_{1}, x_{2},… x_{n}, are observations with respective frequencies f_{1}, f_{2},. . ., f_{n} .
Let deviation A take at any point, we have
d_{i} = x_{i} - A , where, i = 1,2,3,…, n.
⇒ f_{i} d_{i} = f_{i} ( x_{i} - A ) ; i = 1,2,3,…,n
So mean by this method is given by
Steps involved in finding the meanshort cut method :
1) Prepare a frequency table.
2) Choose A and take deviations d_{i} = x_{i} - A of the values of x_{i}.
3) Multiply f_{i} d_{i} and find the sum of it.
4) Use the above formula and find the mean.
Some solved examples :
1) The following table shows the weights of 12 students :
Weight(in kg)
67
70
72
73
75
Number of students
4
3
2
2
1
Find the mean by using short-cut method. Solution :
Let the assumed mean = A = 72
Weight(in kg)
No. of students (fi)
di = xi - A = xi - 72
fi di
67
4
-5
- 20
70
3
-2
- 6
72
2
0
2
73
2
1
2
75
1
3
3
Σ fi = 12
Σfi di = -21
Σ fi = 12 , Σ fi di = -21 , A = 72
⇒ Mean = 72 + (-21) / 12 = 72 – 7 / 4
⇒ Mean = 70.25 kg.
_____________________________________________________________ Example 2 : Find the mean of the following frequency distribution :