Question

the mean of 200 items was 50. later on, it was discovered that two items was misread as 92 and 8 instead of 192 and 88. find the correct mean

Answer 1

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GIVEN :

MEAN OF 200 ITEMS :

=> 50

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STEP 1 :

=> SUM OF ALL OBSERVATIONS

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$\sf\green{sum \: of \: all \: observations}$

=> NO. OF OBSERVATIONS * MEAN

=> 200 * 50

$\red{10000}$

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CONDITION :

=> 192 WAS CONSIDERED AS 92

=> AND 88 WAS CONSIDERED AS 8

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THE SUM OF TAKEN TWO OBSERVATIONS :

=> 92 + 8

=> 100

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SUM OF ACTUAL 2 OBSERVATIONS :

=> 192 + 88

=> 280

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SO,

=> THE SUM OF OBSERVATIONS SHOULD BE INCREASED BY ;

=> ACTUAL SUM - TAKEN SUM OF OBSERVATIONS

=> 280 - 100

=> 180

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CORRECT SUM OF TOTAL OBSERVATIONS :

=> PREVIOUS SUM + 180

=> 10,000 + 180

$\purple{10180}$

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MEAN :

$\bold\blue{total \: sum \: \div no. \: of \: observations}$

=> 10,180 / 200

$\green{50.9}$

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$\huge\red{thanks}$

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