Question

the mean of 12 observation is 8 if 5 is subtracted from each observation and then its result is multiplied by 3 then find the mean of new observation so obtained

Answer 1

heya

mean = sum of observations ÷ number of observations
sum of observation = mean × number of observations
= 12 × 8
= 96

new mean = ( 96 ) -5 × 12 ÷ 12
new mean = 3
3 × 3
9
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Answer 2

It is not possible as it goes in negative when multiplied by 3. 

Without multiplication of 3

Given:

 The mean of 12 observations is 8.

Solution:

Number of observations = 12

                             Mean = 8
We know that ,

Mean = Total observations / Number of observations

Total observations =  Mean × Number of observations
Total observations = 8 × 12
                 
                              = 96
If 5 is subtracted to each of the 12 observations, then the sum of the

values will decrease by  (5 × 12)= 60.
New total no of observations = 96 - 60
 
                                               = 36Then,

New mean = New total no of observations / no of observations

                  = 36 / 12
                  
                  = 3

Answer :

New mean = 3

___________________________________________________________

With multiplication of 3, which is not possible but according to your ques,

Total no of values decreased = 60 × 3

                                               = 120

New total no of observations = 96 - 120
  
                                               = -24Then,

New mean = New total no of observations / no of observations

                  = -24 / 12
                  
                  = -2

Answer : 

New mean = -2 (which is impossible)

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