Mean ( Direct method)
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 .
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f1 x1 + f2 x2 + . . . + fn xn x = --------------------------------- f1 + f2 + . . . + fn |
This can be written in short way using Greek letter Σ
| Σfi xi x = ------ Σ fi |
Example 1 :
| Weight (in Kgs) | 67 | 70 | 72 | 73 | 75 |
| Number of students | 4 | 3 | 2 | 2 | 1 |
Find the average weight.
Solution :
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| Σfi xi 843 x = ------- = ------- = 70.25 kg Σ fi 12 |
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Example 2 :
If the average of the following data is 20.2, find the value of p:
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| Σfi xi x = ------- Σ fi |
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 :
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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 :
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| Σfi xi x = ------- Σ fi |
= 26.2
• Direct method.
• Short cut method.
• Step - Deviation method.
Statistics
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