Question

The mean of 12 observation is 65.later on it was observed that 75 was misread as 57 .find the correct mean.​

Answer 1

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☛mean of 12 observation is 65

$\sf let\: observation\:be\:x_1\:x_2......x_12$

So,

$65 = \frac{x1 + x2 + x3...............x12}{12}$

$x1 + x2 + x3........x12 = 780$

One observation 75 was misread as 57

☛ 780-57+70

☛780 + 18

☛798

$\bold\green{correct \: mean \: will \: be \: <u>7</u><u>9</u><u>8</u><u>.</u>}$

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Answer 2

mean of 15 observation = 65

wrong sum = 65*15=975

difference BTW correct no. and wrong no. =75-57

= 18

correct sum=975+18=993

correct mean = $\frac{993}{15}$

= $\frac{331}{5}$

= 66.2

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