Question

the mean of eight observation was found to be 57. letter on, it was discovered that one observation that is 48 is measured at 84. find the correct mean​

Answer 1

Answer:

Let sum of eight observations is=x

x/8=57

x=456

correction is

x=456-84

x=372

x=372+48

x=420

The correct mean is

x=420/8

x=52.5

Answer 2

$\underline{\underline{\underline{\underline{\mathfrak{\blue{ \:\:\: Given:-\:\:\:}}}}}}$

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• The mean of eight observations was found to be 57. Later on, it was discovered that one observation, i.e 48 was misread as 84.

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$\underline{\underline{\underline{\underline{\mathfrak{\blue{ \:\:\: Find \: out:-\:\:\:}}}}}}$

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• The required correct mean = ?

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$\underline{\underline{\underline{\underline{\mathfrak{\green{ \:\:\: Solution:-\:\:\:}}}}}}$

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$\sf \: Mean \: of \: eight \: observations = 57 \\ \\ \sf \: Sum \: of \: all \: the \: observations = 57 \times 8 \\ \\ \sf \: Sum \: of \: all \: the \: observations = \boxed{ \bf \red{456}} \: \bigstar \\ \\ \bf \underline \pink{Since \: 48 \: was \: misread \: as \: 84,}$

$\footnotesize\bold{\underline{\underline{\sf{\red{Therefore:-}}}}}$

$\underline{\sf \: The \: correct \: sum \: of \: all \: the \: observations \: is }\\ \: \: \: \: \: \: \leadsto \sf456 - 84 + 48 \\ \\ \: \: \: \: \: \: \leadsto \sf456 + 48 - 84 \\ \\ \: \: \: \: \: \: \leadsto \sf504 - 84 \\ \\ \: \: \: \: \: \: \leadsto \sf \boxed{ \bf \red{420}} \: \bigstar$

$\footnotesize\bold{\underline{\underline{\sf{\red{Hence:-}}}}}$

$\sf Correct \: mean = \cancel\dfrac{420}{8} \\ \\ \sf Correct \: mean = \boxed{ \tt \pink{52.5}} \: \star$

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$\underline{\underline{\underline{\underline{\mathfrak{\pink{ \:\:\: AnswEr:-\:\:\:}}}}}}$

• The required correct mean is 52.5