Maths Statistics

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5,7,10,12,14,15, then the absolute difference of the remaining two observations is:

Let xᵢ (1 ≤ i ≤ 10) be ten observations of a random variable x. If Σ(from i=1 to 10)(xᵢ – p) = 3 and Σ(from i=1 to 10)(xᵢ – p)² = 9 where 0 ≠ p ∈ R, then the standard deviation of these observations is:

For the frequency distribution:
Variate (x): x₁, x₂, x₃.x₁₅
Frequency (f): f₁, f₂, f₃ . f₁₅
Where 0 < x < x < x < < x = 10 and
Σ(i=1 to 15) fᵢ > 0, the standard deviation cannot be:

If the variance of the terms in an increasing A.P. b?,b?,b?,.,b? is 90, then the common difference of this A.P. is 

Let X={x∈N: 1≤x≤17} and Y={ax+b: x∈X and a,b∈R, a>0}. If mean and variance of elements of Y are 17 and 216 respectively then a+b is equal to

Consider the following frequency distribution:
| Class: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
|---|---|---|---|---|---|
| Frequency: | α | 110 | 54 | 30 | β |
If the sum of all frequencies is 584 and median is 45, then |α - β| is equal to…….

If the mean and variance of eight numbers $\mathrm{3,7},\mathrm{9,12,13,20}$ , $x$ and $y$ be 10 and 25 respectively, then $xy$  is equal to