1
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1
Change Language

Let the mean of the data

$$x$$ 1 3 5 7 9
Frequency ($$f$$) 4 24 28 $$\alpha$$ 8

be 5. If $$m$$ and $$\sigma^{2}$$ are respectively the mean deviation about the mean and the variance of the data, then $$\frac{3 \alpha}{m+\sigma^{2}}$$ is equal to __________

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2
JEE Main 2023 (Online) 12th April Morning Shift
Numerical
+4
-1
Change Language

Let the positive numbers $$a_{1}, a_{2}, a_{3}, a_{4}$$ and $$a_{5}$$ be in a G.P. Let their mean and variance be $$\frac{31}{10}$$ and $$\frac{m}{n}$$ respectively, where $$m$$ and $$n$$ are co-prime. If the mean of their reciprocals is $$\frac{31}{40}$$ and $$a_{3}+a_{4}+a_{5}=14$$, then $$m+n$$ is equal to ___________.

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3
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1
Change Language

If the mean of the frequency distribution

Class : 0-10 10-20 20-30 30-40 40-50
Frequency : 2 3 $$x$$ 5 4

is 28, then its variance is __________.

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

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 _____________.

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