1
JEE Main 2023 (Online) 8th April Morning Shift
Numerical
+4
-1

Let the mean and variance of 8 numbers $$x, y, 10,12,6,12,4,8$$ be $$9$$ and $$9.25$$ respectively. If $$x > y$$, then $$3 x-2 y$$ is equal to _____________.

2
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1

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 ___________.

3
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1

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 _____________.

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

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 ___________.