Question

The mean of 100 items was found to be 30.At the time of calculations two items were wrongly taken as 32 and 12 instead of 23 and 11 respectively. Find the correct mean.

Answer 1

this is ur required answer

Answer 2

AnswEr:

$\\ \sf \: \: Here \: , \: \: n = 100 \: \: , \: \bar x = 30$

$\\ \: \sf \: \bar X = \frac{1}{n} \: \bigg( \sum \: x_i \bigg) \\ \\ \\ \implies \sf \sum \: x_i = n \: \bar X \\ \\ \\ \implies \sf \sum \: X_i = 100 \times 30 \\ \\ \\ \implies \boxed{\rm{\blue {\sum \: x_i = 3000}}}$

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$\therefore \: \: \sf \: \: \: Incorrect \: \: value \: \: of \: \: \sum \: x_i = 3000$

Now,

$\\ \rm \: \: Correct \: \: value \: \: of \: \: \sum \: x_i = \: \: Incorrect \: \: value \: \: of \: \: \\ \\ \rm \: \: \sum \: x_i - (Sum \: of \: incorrect \: values) + (sum \: of \: \\ \rm \: \: correct \: values) \\ \\ \\ \implies \sf \: Correct \: \: value \: \: of \: \: \sum \: x_i = 3000 - (32 + 12) \\ \\ \sf + (23 + 11) \\ \\ \\ \implies \boxed{\rm{\pink{2990}}}$

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$\therefore \sf \: Correct \: mean = \bigg ( \frac{correct \: mean \: of \: \sum \: x_i}{n} \bigg) \\ \\ \\ \implies \sf \: \frac{2990}{100} \\ \\ \\ \implies \sf \orange { 29.9}$