Meanshort cut Method
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 shortcut 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.
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Example 2 : Find the mean of the following frequency distribution :
Class interval 
010 
1020

2030

3040 
4050

Number of workers (f)

7 
10 
15 
8 
10

Solution :
Class interval 
Class mark (xi) 
Frequency (fi) 
di = xi  25 
fi di 
0  10 
5 
7 
20 
140 
10  20 
15 
10 
10 
100 
20  30 
25 
15 
0 
0 
30  40 
35 
8 
10 
80 
40  50 
45 
10 
20 
200 


Σ fi = 50 

40 
A = 25; N = 50 and Σfi di = 40
⇒ Mean = 25 + 40 / 50
⇒ Mean = 25.8
• Direct method
• Short cut method.
• Step  Deviation method.
From short cut method to measures of central tendency
Statistics
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