MHT CET 2024 3rd May Morning Shift | Statistics Question 16 | Mathematics

The mean of $n$ observations is $\bar{x}$. If three observations $\mathrm{n}+1, \mathrm{n}-1,2 \mathrm{n}-1$ are added such that mean remains same, then value of $n$ is

$\frac{2 \bar{x}+1}{3}$

$\frac{3 \bar{x}-1}{4}$

$\frac{3 \bar{x}+1}{4}$

$\frac{\bar{x}+1}{4}$

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

Consider three observations $\mathrm{a}, \mathrm{b}$ and c such that $b=a+c$. If the standard deviation of $\mathrm{a}+2, \mathrm{~b}+2, \mathrm{c}+2$ is d , then ............ holds.

$\mathrm{b}^2=3\left(\mathrm{a}^2+\mathrm{c}^2+\mathrm{d}^2\right)$

$\mathrm{b}^2=\mathrm{a}^2+\mathrm{c}^2+3 \mathrm{~d}^2$

$b^2=3\left(a^2+c^2\right)-9 d^2$

$\mathrm{b}^2=3\left(\mathrm{a}^2+\mathrm{c}^2\right)+9 \mathrm{~d}^2$

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

A random variable $X$ has the following probability distribution

$\mathrm{X=}x_i$:	1	2	3	4
$\mathrm{P(X=}x_i)$ :	0.2	0.4	0.3	0.1

The mean and variance of X are respectively

2.3 and 6.1

2.3 and 0.1

2.3 and 0.81

2.3 and 0.9

MHT CET 2024 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

The mean of 100 observations is 50 and their standard deviation is 5 , then the sum of all squares of all the observations is

252500

250500

250000

255000

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