If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x and hence find the mean of the last three observations.
Answers
Number of observations = 5
It is given that mean = 13
We can write it as
[x + (x + 2) + (x + 4) + (x + 6) + (x + 8)]/5 = 13
On further calculation
5x + 20 = 13 (5)
So we get
5x + 20 = 65
By subtraction
5x = 45
By division
x = 9
By substituting the value of x
We know that the last three observations are
9 + 4 = 13
9 + 6 = 15
9 + 8 = 17
We know that
Mean of last three observations = (13 + 15 + 17)/3
On further calculation
Mean of last three observations = 45/3
By division
Mean of last three observations = 15
Therefore, the mean of last three observations is 15.
Step-by-step explanation:
Observations= X,X+2,X+4,X+6,X+8
No of observations=5
Mean of observations= 13
Sum of observations= Mean of observations × No of observations
= 13 × 5 = 65.
Sum of observations in terms of X = X+2+X+4+X+6+X+8 = 5X+20
According to the problem
5X + 20 = 65
5X = 65 — 20
5X = 45
X = 9
The value of X is 9.