1
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1
Change Language

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 ___________.

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2
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1
Change Language

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 _____________.

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3
JEE Main 2023 (Online) 30th January Morning Shift
Numerical
+4
-1
Change Language

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 ___________.

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4
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1
Change Language

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 ____________.

Your input ____
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