Answer:
If M is the arithmetic mean of n observations and if a is the sum of n-4 observations, then the mean of the remaining 4 numbers is [tex]\frac{8M-a}{4}[/tex]
Step-by-step explanation:
Given
Arithmetic mean of n observations = M
That is,
the sum of n observations / n = M
So, the sum of n observations = Mn
Given
Sum of n-4 observations = a
So there mean of remaining observations = sum of n observations - the sum of n-4 observations / (n-4)
[tex]= \frac{Mn-a}{n-4}[/tex]
So the mean of remaining observations is [tex]= \frac{Mn-a}{n-4}[/tex]
Give there are 4 observations remaining
that is,
n-4 = 4
So n= 4 +4 = 8
So [tex]= \frac{Mn-a}{n-4}[/tex] = [tex]\frac{8M-a}{4}[/tex]