The mean marks of 100 students were found to be 40 later it was discovered score of 53 was misread as 83 find the correct mean cor

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1. Given :

   • Mean marks of 100 students were found to be 40. Later it was discovered score of 53 misread as 83.

   To calculate :

   • The mean after correcting the wrong score.

   Calculation :

   For calculating the sum of observations, formula is given by :-

   [tex] \underline{\boxed{\sf{Sum \: of \: observations = Mean \times No. \: of \: observations}}} [/tex]

   Plugging the values,

   [tex] : \implies \rm 40 \times 100 = 4000 [/tex]

   [tex] \underline{ \underline{ \boldsymbol{According \: to \: the \: Question : }}} [/tex]

   Let’s calculate the correct mean!

   [tex] : \implies \rm 4000 – 83 + 53 [/tex]

   Simplifying,

   [tex] : \implies \underline{ \boxed{3970}} [/tex]

   Now, we need to divide 3970 by 100 to get our final answer.

   [tex] : \implies \rm Correct \: mean = \dfrac{3970}{100} [/tex]

   Cancelling the numbers,

   [tex] : \implies \underline{ \boxed{\rm{Correct \: mean = 39.7}}} \blue{\bigstar} [/tex]

   Therefore,

   • The correct mean is 39.7

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