The mean of 8 observations was found to be 57. Later on, it was discovered that one observation, i.e., 48 was misread as 84. Find the correct mean.

Mean = no. of obs. / sum of all obs.
57= s/8
57 [8] = 8[s/8]
456= s
Since it was later discovered that one of the observations which was actually 48 was mistakenly read as 84, then the Sum S is 8 (84 – 48) too much; therefore, the correct mean is found as follows:

Correct mean = (S – 8)/n
                       = (456 – 8)/8
                       = 448/8
Correct mean = 56

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Mean=sum of observations ÷no.of observations Mean of 8observations=57 Sum of 8observations= 57×8=456 48was misread as 84 Correct mean= 456+48-84 456-36=420 Correct mean= 420/8=52.5
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Arithmetic mean = Sum of observations / Number of observations
In this case, the arithmetic mean ( Incorrect) = 57 ........Given
Number of observations= 8..........Given
Sum of observations = Mean x  No. of observations
= 57 x 8
= 456
As the observation 48 was misread as 84, the correct mean will be The sum of observations - incorrect observation + the correct observation
                                                                                                           = 456                                  -             84                   +            48 =   372 + 48     = 420
So, the correct mean will be = 420 / 8 (as  the number  of  observations remain the same) = 105/2  =  52.5

Hence ,we get the correct arithmetic mean as  52.5.

If we want to check if our answer is correct ,

The Number  of observations = 52.5 x 8

=420

Hence our answer is correct.​​​​​​  
                     

I hope  it helped you.

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