Question

The mean of 50 items was found to be 40. If at the time of calculation 2 items were wrongly taken as 32 and 12 instead of 23 and 11 ,the find the correct mean

Answer 1

$\boxed{ \boxed{\underline \bold \red{find \: correct \: mean \: }}}$

GIVEN -

$\boxed{ \underline \bold \green{wrong \: mean = > 40}} \\ \\ \boxed{ \underline \bold \orange{wrong \: number \: of \: items(n) = > 50}}$

$\boxed{ \underline \bold \red{incorrect \: values = > 32 \: and \: 12}} \\ \\ \boxed{ \underline \bold \blue{correct \: values = > 23 \: and \: 11}}$

Formula used ..

$correct \: mean = > \\ \\ \boxed { \frac{wrong \: (x) + correct \: values - incorrect \: values}{number \: of \: items}}$

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$wrong \: mean = > \frac{wrong \: (x)}{no. \: of \: items} \\ \\ 40 = > \frac{wrong(x)}{50} \\ \\ 2000 = > wrong(x) \\ \\ \boxed{ \underline \bold \green{wrong(x) = > 2000}}$

$correct \: mean = > \frac{2000 + 23 + 11 - 32 - 12}{50} \\ \\ = > \frac{1990}{50} \\ \\ = > 39.8 \: \: or \: \: 40 \\ \\ hence \\ \\ \boxed { \underline \bold \blue{correct \: mean = > 40}}$

Hope it's helps you ☺️

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