Mean ( Direct method)
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Mean (or average) of observations, as we know, is the sum of the values of all the observations divided by the total number of observations.If x _{1} , x _{2} ,… x _{n} , are observations with respective frequencies f _{1} , f _{2} ,, . . ., f _{n} then this means observation x _{1} , occurs f _{1} times, x _{2} , occurs f _{2} , times, and so on. Now, the sum of the values of all the observations = f _{1} x _{1} + f _{2} x _{2} + . . . + f _{n} x _{n} , and the number of observations = f _{1} + f _{2} + . . . + f _{n} .
f_{1} x_{1} + f_{2} x_{2} + . . . + f_{n} x_{n} x =  f_{1} + f_{2} + . . . + f_{n} 
This can be written in short way using Greek letter Σ
Σf_{i} x_{i} x =  Σ f_{i} 
Example 1 :
Weight (in Kgs)  67  70  72  73  75 
Number of students  4  3  2  2  1 
Find the average weight.
Solution :





















Σf_{i} x_{i} 843 x =  =  = 70.25 kg Σ f_{i} 12 
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Example 2 :
If the average of the following data is 20.2, find the value of p:
































Σf_{i} x_{i} x =  Σ f_{i} 
20.2 = ( 610 + 20P) / ( 30 + P)
20.2 ( 30 + P ) = 610 + 20P
606 + 20.2P = 610 + 20P
20.2P – 20P = 610 – 606
0.2 P = 4
∴ P = 4 / 0.2
P = 20
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Example 3: Find the average of the following data :












Solution: First find the class mark,
Class Mark = ( upper class limit + Lower class limit ) /2
Example : Class Mark = ( 10 + 0 ) / 2 = 10 / 2 = 5
Prepare the frequency table :


























Σf_{i} x_{i} x =  Σ f_{i} 
= 26.2
• Direct method.
• Short cut method.
• Step  Deviation method.
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