Question

The average of marks of 14 students was calculated as 71. But it was later found that the mark of one student had been wrongly entered as 42 instead of 56 and of another as 74 instead of 32 . The correct average is? solve the question by using allegation and mixture formula.
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Answer 1

The correct average is 69  if average of 14 students calculated as 71 but 56 was entered as 42 & 32 was entered as 74

Step-by-step explanation:

The average of marks of 14 students was calculated as 71

=> Total Marks Calculated = 14 * 71  =  994

t it was later found that the mark of one student had been wrongly entered as 42 instead of 56  and of another as 74 instead of 32 .

Correct Total = 994  - 42 + 56  - 74 + 32

= 966

Correct Average = 966/14

= 69

The correct average is 69

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$1. \: \: \displaystyle \sf{Average = \frac{Sum \: of \: the \: given \: observations \: }{Number \: of \: observations} \: }$

$2. \: \: \displaystyle \sf{Sum \: of \: the \: given \: observations = Average \times Number \: of \: observations\: }$

GIVEN

The average of marks of 14 students was calculated as 71. But it was later found that the mark of two students had been wrongly entered as 42 instead of 56 and of another as 74 instead of 32

TO DETERMINE

The correct average

CALCULATION

Here The average of marks of 14 students was calculated as 71

So sum of marks of 14 students

$= 71 \times 14$

$= 994$

Now it was later found that the mark of two students had been wrongly entered as 42 instead of 56 and of another as 74 instead of 32

So after making correction the correct sum of marks of 14 students

$= 994 + (32 + 56) - (74 + 42)$

$= 994 + 88 - 116$

$= 994 - 28$

$= 966$

So the required correct average is

$\displaystyle \sf{= \frac{Sum \: of \: the \: given \: observations \: }{Number \: of \: observations} \: }$

$\displaystyle \sf{= \frac{966}{14} }$

$= 69$