Question

the mean of 8 observations was found to be 60 later on it was discovered that an observation 42 was misread as 82 to find the correct mean of the observation​

Answer 1

$\large\underline\blue{\bold{Given \:  Question :-  }}$

The mean of 8 observations was found to be 60. Later on, it was discovered that an observation 42 was misread as 82. Find the correct mean of the observation.

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$\huge{AηsωeR} ✍$

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$\large\underline\blue{\bold{Given :-  }}$

$\begin{gathered}\begin{gathered}\bf \begin{cases} &\sf{mean \: of \: 8 \: observations \: is \: 60} \\ &\sf{correct \: observation \: = 42}\\ &\sf{incorrect \: observation \: = 82} \end{cases}\end{gathered}\end{gathered}$

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$\large\underline\blue{\bold{To \: Find :-  }}$

Correct mean of the observations.

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$\large\underline\purple{\bold{Solution :- }}$

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❥︎ Number of observations = 8

❥︎ Mean of 8 observations = 60

❥︎ Incorrect Sum of 8 observations = 8 × 60 = 480

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❥︎ Incorrect observation = 82

❥︎ Correct observation = 42

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❥︎ So, Correct sum of 8 observations =

Incorrect sum of 8 observations - Incorrect observation + Correct observation

❥︎ Correct sum of 8 observations = 480 - 82 + 42 = 440

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We know,

$\bf \:Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations }$

$\sf \:  ⟼So, \: Correct \: Mean = \dfrac{440}{8} = 55$

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