The mean of the squares of the number 1,2,3,4 ........ n-1 is
Answers
Answer:
Mean=
6
(n+1)(2n+1)
step by step explaination :
Formula for mean:
Mean=\frac{\sum x}{n}Mean=
n
∑x
where, x is observations and n is number of observations.
The given numbers are 0,1,2,3,........,n.
We need to find the mean of the squares of the numbers 0,1,2,3,........,n.
Sum of squares of the numbers 0,1,2,3,........,n is
\sum x^2=0^2+1^2+2^2+3^2+...+n^2∑x
2
=0
2
+1
2
+2
2
+3
2
+...+n
2
\sum x^2=\frac{n(n+1)(2n+1)}{6}∑x
2
=
6
n(n+1)(2n+1)
The mean of the squares of the numbers 0,1,2,3,........,n.
Mean=\frac{\sum x^2}{n}Mean=
n
∑x
2
Mean=\frac{\frac{n(n+1)(2n+1)}{6}}{n}Mean=
n
6
n(n+1)(2n+1)
Mean=\frac{n(n+1)(2n+1)}{6n}Mean=
6n
n(n+1)(2n+1)
Cancel out the common factors.
Mean=\frac{(n+1)(2n+1)}{6}Mean=
6
(n+1)(2n+1)
Therefore, the mean of the squares of the numbers 0,1,2,3,........,n is \frac{(n+1)(2n+1)}{6}
6
(n+1)(2n+1)