Question

3. The mean of 40 observations was 160. It was detected on rechecking that the value 165
was wrongly copied as 125 for computation of mean. Find the correct mean.​

Answer 1

The correct mean of the required observations is 161. = > 6400 = sum of 40 observations. Later on, it was detected on rechecking that the value of 165 was wrongly copied as 125 for computation of mean. Hence, the correct mean is 161.

Here,

Here,n=40,

Here,n=40, X

Here,n=40, X =160

Here,n=40, X =160So,

Here,n=40, X =160So, X

Here,n=40, X =160So, X =

Here,n=40, X =160So, X = n

Here,n=40, X =160So, X = n1

Here,n=40, X =160So, X = n1 (∑x

Here,n=40, X =160So, X = n1 (∑x i )

Here,n=40, X =160So, X = n1 (∑x i )160=

Here,n=40, X =160So, X = n1 (∑x i )160= 40

Here,n=40, X =160So, X = n1 (∑x i )160= 401

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400Therefore, incorrect value of ∑x

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400Therefore, incorrect value of ∑x i=6400

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400Therefore, incorrect value of ∑x i=6400Now,

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400Therefore, incorrect value of ∑x i=6400Now,Correct value of ∑x

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400Therefore, incorrect value of ∑x i=6400Now,Correct value of ∑x i =6400−125+165=6440

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400Therefore, incorrect value of ∑x i=6400Now,Correct value of ∑x i =6400−125+165=6440Therefore,

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400Therefore, incorrect value of ∑x i=6400Now,Correct value of ∑x i =6400−125+165=6440Therefore,Correct mean = 40

Here,n=40, X =160So, X = n1 (∑x i )160= 401 (∑x ∑x i =6400Therefore, incorrect value of ∑x i=6400Now,Correct value of ∑x i =6400−125+165=6440Therefore,Correct mean = 406440 =161

Answer 2

Answer:

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Step-by-step explanation:

ANSWER

Here,

n=40,

X

=160

So,

X

=

n

1

(∑x

i

)

160=

40

1

(∑x

i

)

∑x

i

=6400

Therefore, incorrect value of ∑x

i

=6400

Now,

Correct value of ∑x

i

=6400−125+165=6440

Therefore,

Correct mean =

40

6440

=161