Let xi(1≤i≤10) be ten observations of a random variable X. If ∑i=110(xi-p)=3and∑i=110(xi-p)2=9 where 0≠p∈R, then the standard deviation of these observations is
710
910
35
45
Explanation for the correct option
It is given that n=10
We know that
S.D.=variance=∑(xi-x¯)2n-1
On solving, we get:
∴S.D.=∑(xi-p)2n-∑(xi-p)n2=910-3102∵(xi-p)=3and(xi-p)2=9=81100⇒S.D=910
Hence, the correct answer is option B.
Let X1,X2.....X18 be eighteen observations such that ∑i=118Xi-α=36 and ∑i=118Xi-β2=90, where αandβ are distinct real numbers.
If the standard deviation of these observations is 1, then the value of α-β is