Arithmetic mean : Definition, Formula, Examples.

Arithmetic mean :
Arithmetic Mean Definition :
" The arithmetic mean means sum of the given numbers divided by total numbers."

             Mode       Median        Quartile

Arithmetic Mean Formula :
Arithmetic Mean = ( Sum of given numbers ) / Total numbers.
X = ( a1 + a2 + a3 + ----- + an ) / N
where, X = Arithmetic Mean,
N = Total numbers.

Arithmetic Mean Examples based on Individual data. :
Que.1: Calculate mean of the following values.
24, 43, 34, 65, 78, 20.
Ans. :
Arithmetic Mean = ( Sum of given numbers ) / Total numbers.
Arithmetic Mean = ( 24 + 43 + 34 + 65 + 78 + 20 ) / 6
Arithmetic Mean = 264 / 6
Arithmetic Mean = 44

Que. 2 : Calculate mean of the following values.
21, 25, 35, 40, 39.
Ans. :
Arithmetic Mean = ( Sum of given numbers ) / Total numbers.
Arithmetic Mean  = ( 21 + 25 + 35 + 40 + 39 ) / 5
Arithmetic Mean  = 160 / 5
Arithmetic Mean  = 32.

Que.3) The mean of a group of 7 observation is 12 and 20 are added to the group. find the mean of 8 observations.
Ans. :
Arithmetic Mean = ( Sum of given numbers ) / Total numbers.
sum of given numbers = Arithmetic Mean × Total numbers.
= 12 × 7
= 84.
The new sum after adding an observation 20 becomes 84 + 20 = 104.
Now mean of 8 observations becomes
Arithmetic Mean = 104 / 8
                                = 13.

Que.4) The mean of a group of 10 observation is 6 and 17 are added to the group. find the mean of 11 observations.
Ans. :
Arithmetic Mean = ( Sum of given numbers ) / Total numbers.
sum of given numbers = Arithmetic Mean × Total numbers.
= 6 × 10
= 60.
The new sum after adding an observation 17 becomes 60 + 17 = 77.
Now mean of 11 observations becomes
Arithmetic Mean = 77 / 11
                                = 7.

Que. 5) If the average of 19, 16, 18, 14, a, 17 and 13 is 16, what will be the value of a?
Ans. :
Arithmetic Mean = ( Sum of given numbers ) / Total numbers.
16 = ( 19 + 16 + 18 + 14 + a + 17 + 13 ) / 7
16 × 7 = 97 + a
112 = 97 + a
therefore, a = 112 - 97
a = 15.

Que. 6) Mean of 50 items is found to be 20. if at the time of calculations two items are wrongly taken as 22 and 14 instead of 10 and 16, find the correct mean.
Ans. :
Arithmetic Mean = ( Sum of given items) / Total items
mean = 20 , Total items = 50
therefore, Sum of given items = mean × total items
= 20 × 50
= 1000.
Now, the correct sum of items = ( incorrect sum of items ) - ( sum of wrong figures ) + ( sum of correct figures )
= 1000 - ( 22 + 14 ) + ( 10 + 16 )
= 1000 -  36 + 26
= 1000 - 10
= 990
therefore, Correct mean = ( correct sum ) / total items
= 990 / 50
= 19.8


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