If the mean and variance of the frequency distribution
$$x_i$$ | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 |
---|---|---|---|---|---|---|---|---|
$$f_i$$ | 4 | 4 | $$\alpha$$ | 15 | 8 | $$\beta$$ | 4 | 5 |
are 9 and 15.08 respectively, then the value of $$\alpha^2+\beta^2-\alpha\beta$$ is ___________.
If the variance of the frequency distribution
$$x_i$$ | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|
Frequency $$f_i$$ | 3 | 6 | 16 | $$\alpha$$ | 9 | 5 | 6 |
is 3, then $$\alpha$$ is equal to _____________.
The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of remaining 6 observation, then $$\mathrm{a+3 b-5}$$ is equal to ___________.
Let $$X=\{11,12,13,....,40,41\}$$ and $$Y=\{61,62,63,....,90,91\}$$ be the two sets of observations. If $$\overline x $$ and $$\overline y $$ are their respective means and $$\sigma^2$$ is the variance of all the observations in $$\mathrm{X\cup Y}$$, then $$\left| {\overline x + \overline y - {\sigma ^2}} \right|$$ is equal to ____________.