Question

The mean of 40 observation 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

$\huge\mathbb{SOLUTION:-}$

$\sf\bullet Mean\:of\:40\: observation=160\\ \\ \sf\bullet 165\:in\: place\:of\:125$

Now we have to find the correct mean

$\boxed{\sf{Mean=\dfrac{Sum\:of\: observation}{No.\:of\: observation}}}$

$\sf\underline{\red{A.T.Q:-}}$

$\sf\bullet let\: observation\:be\\ \\ \sf\:\:x_1,\:x_2\:x_3,\:x_4.............x_{40}$

$\sf\implies 160=\dfrac{x_1+x_2+x_3+x_4+x_5\:\:....x_{40}}{40}\\ \\ \sf\implies 160\times 40=x_1+x_2+x_3+x_4.......x_{40}\\ \\ \sf\implies 6400=x_1+x_2+x_3..........x_{40}$

So sum of correct observation

$\sf\bullet 6400-125+165\\ \\ \sf\bullet 6565-125\\ \\ \sf\bullet 6440$

Now the mean of new observation

$\boxed{\sf{Correct\:mean=\dfrac{correct\:sum\:of\: observation}{Number\:of\: observation}}}$

$\sf\implies correct\:mean=\cancel{\dfrac{6440}{40}}\\ \\ \sf\implies correct\:mean=161$

$\boxed{\bigstar{\sf{correct\:mean=161}}}$

Answer 2

$\huge\bold\green{Question}$

The mean of 40 observation was 160 .it was detected on rechecking that the value 165 was wrongly copied as 125 for computation of mean . Find the correct mean.

$\huge\bold\green{AnsWer}$

According to the question we have

•°• Mean of 40 observation is 160

Hence, we have to find correct mean of the data

$\tt\blue{Mean=\dfrac{Sum\:of\: observation}{No.\:of\: observation}}$

So, by using formula we can get the mean

$\begin{lgathered}\tt let\: observation\:be\\ \\ \sf\:\:x_1,\:x_2\:x_3,\:x_4.............x_{40}\end{lgathered}$

$\begin{lgathered}\tt 160=\dfrac{x_1+x_2+x_3+x_4+x_5\:\:....x_{40}}{40}\\ \\ \tt 160\times 40=x_1+x_2+x_3+x_4.......x_{40}\\ \\ \tt 6400=x_1+x_2+x_3..........x_{40}\end{lgathered}$

Hence the sum of all observation is :-

$\begin{lgathered}\tt = 6400-125+165\\ \\ \tt = 6565-125\\ \\ \tt = 6440\end{lgathered}$

Now the mean of new observation be :-

$\tt\blue{Correct\:mean=\dfrac{correct\:sum\:of\: observation}{Number\:of\: observation}}$

By applying this formula we can get mean

$\begin{lgathered}\tt = correct\:mean=\cancel{\dfrac{6440}{40}}\\ \\ \tt = correct\:mean=161\end{lgathered}$

Hence , the required correct mean is 161