Question

The mean of
5
numbers is
77
. If
2
is subtracted from each number, what is the new mean

Answer 1

Answer:

The new mean = 75

Step-by-step explanation:

Given: The mean of 5 numbers are 77 and 2 is subtracted from each number.

To find: The new mean

Solution:

Let the 5 numbers be a,b,c, d,e, and the mean be x

So, mean of 5 numbers, x =   77 = $\frac{a + b + c + d + e}{5}$

⇒  5 x = a + b + c + d + e

⇒5 ( 77 ) = a + b + c + d + e

⇒ 385 = a + b + c + d + e   --------(1)

Now, after subtracting 2 from each of the numbers we get,

New Mean = y = $\frac{ (a - 2) + (b - 2) + ( c - 2) + (d - 2) + (e - 2) }{5}$

⇒  5 y  =  ( a - 2 ) + ( b - 2 ) + ( c - 2 ) + ( d - 2 ) + ( e - 2 )

⇒ 5 y =  a - 2 + b - 2 + c - 2 + d - 2 + e - 2

⇒ 5 y = ( a + b + c + d + e ) - 10         [ From( 1 ) ]

⇒ 5 y =  385  - 10

⇒   y = 375/5

⇒ New mean = 75

Thus, the new mean is 75.

We also can see that, when a number is added or subtracted from the mean, then the mean is also added or subtracted by the same number.