Question

The average (arithmetic mean) of 8 numbers is 42. One of the numbers is removed from the set, and the resulting average (arithmetic mean) of the remaining numbers is 40. What number was removed from the set?

Answer 1

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Mean of 8 numbers is 42

IF ONE NUMBER IS REMOVED FROM THE SET

Mean of 7 numbers is 40

As we know the formula

Mean= Sum of all numbers/ Total numbers

Sum of all numbers = Mean x Total numbers

Sum of 8 numbers = 8 x 42
= 336

Sum of 7 numbers = 7 x 40
= 280

So The missing number = 336 - 280
=56

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Answer 2

Answer:

The removed number is $56$.

Step-by-step explanation:

Let the removed number be $x$

Given that :

After removing the number, the mean of $7$numbers is $40$.

Mean  $=\frac{sum of 7 numbers}{7}$

The new mean is given to be $40$

$40 = \frac{sum of 7 numbers}{7}$

Sum of 7 numbers $=40*7$

$=280$

Now,

Mean of all $8$ numbers (including the removed number $x$) $= 42$

Mean $=\frac{sum of 8 numbers}{8}$

Mean $=\frac{Sum of 7 numbers + x }{8}$

$42 = \frac{280+x}{8}$

$280 + x = 336$

$x = 56$