Question

Let $X=\left\{x\in N : 1\le x\le 17\right\}$ and $Y=\left\{ax+b : x\in X \mathrm{and} a, b\in R, a>0\right\}$. If mean and variance of elements of $Y$ are $17$ and $216$ respectively then $a+b$ is equal to

JEE Main 2020 (02 Sep Shift 1)

Options

• A: $7$
• B: $-7$
• C: $-27$
• D: $9$

Question

For the frequency distribution: Variate $\left(x\right):x_1, x_2, x_3,\dots ,x_{15}$
Frequency $\left(f\right):f_1, f_2, f_3,\dots ,f_{15}$ 
where $0<x_1<x_2<x_3<\dots <x_{15}=10$ and $\sum _{i=1}^{15}{f}_i>0,$ the standard deviation cannot be

JEE Main 2020 (03 Sep Shift 1)

Options

• A: $4$
• B: $1$
• C: $6$
• D: $2$

Question

Let ${\mathrm{x}}_{\mathrm{i}}\left(1\le \mathrm{i}\le 10\right)$ be ten observation of a random variable $X$. If $\sum _{i=1}^{10}\left({\mathrm{x}}_i-\mathrm{p}\right)=3$ and $\sum _{i=1}^{10}{\left({\mathrm{x}}_i-\mathrm{p}\right)}^2=9$ where $0\ne \mathrm{p}\in \mathrm{R}$, then the standard deviation of these observations is:
 

JEE Main 2020 (03 Sep Shift 2)

Options

• A: $\frac{4}{5}$
• B: $\sqrt{\frac{3}{5}}$
• C: $\frac{9}{10}$
• D: $\frac{7}{10}$

Question

Let the observation $x_i\left(1\le i\le 10\right)$ satisfy the equations  $\sum _{i=1}^{10}\left(x_i-5\right)=10$, $\sum _{i=1}^{10}{\left(x_i-5\right)}^2=40$ . If $\mu$ and $\lambda$ are the mean and the variance of the observations, $x_1-3,x_2-3,....,x_{10}-3,$ then the ordered pair $\left(\mu ,\lambda \right)$ is equal to:

JEE Main 2020 (09 Jan Shift 1)

Options

• A: $\left(\mathrm{3,3}\right)$
• B: $\left(\mathrm{6,3}\right)$
• C: $\left(\mathrm{6,6}\right)$
• D: $\left(\mathrm{3,6}\right)$

Question

If the variance of the following frequency distribution:

Class:         $10-20 20-30 30-40$
Frequency:   $2 x 2$
is $50,$ then $x$ is equal to _______ 

JEE Main 2020 (04 Sep Shift 2)

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Question

The first of the two samples in a group has $100$ items with mean $15$ and standard deviation $3.$ If the whole group has $250$ items with mean $15.6$ and standard deviation $\sqrt{13.44},$ then the standard deviation of the second sample is:

JEE Main 2021 (25 Jul Shift 2)

Options

• A: $8$
• B: $6$
• C: $4$
• D: $5$

Question

Let the mean and variance of the frequency distribution

be $6$ and $6.8$ respectively. If $x_3$ is changed from $8$ to $7,$ then the mean for the new data will be:

JEE Main 2021 (27 Jul Shift 2)

Options

• A: $4$
• B: $5$
• C: $\frac{17}{3}$
• D: $\frac{16}{3}$

Question

Consider a set of $3n$ numbers having variance $4.$ In this set, the mean of first $2n$ numbers is $6$ and the mean of the remaining $n$ numbers is $3.$ A new set is constructed by adding $1$ into each of the first $2n$ numbers, and subtracting $1$ from each of the remaining $n$ numbers. If the variance of the new set is $k,$ then $9k$ is equal to ______.

JEE Main 2021 (17 Mar Shift 2)

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Question

Consider the following frequency distribution:

If mean $=\frac{309}{22}$ and median $=14,$ then the value $(a-b{)}^2$ is equal to

JEE Main 2021 (22 Jul Shift 1)

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Question

Consider the following frequency distribution :

If the sum of all frequencies is $584$ and median is $45$, then $|\alpha -\beta |$ is equal to            .

JEE Main 2021 (25 Jul Shift 1)

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Question

An online exam is attempted by $50$ candidates out of which $20$ are boys. The average marks obtained by boys is $12$ with a variance $2.$ The variance of marks obtained by $30$ girls is also $2.$ The average marks of all $50$ candidates is $15.$ If $\mu$ is the average marks of girls and ${\sigma }^2$ is the variance of marks of $50$ candidates, then $\mu +{\sigma }^2$ is equal to

JEE Main 2021 (27 Aug Shift 2)

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Question

Let the mean and the variance of $5$ observations $x_1,x_2,x_3,x_4,x_5$ be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean and variance of the first $4$ observation are $\frac{7}{2}$ and $a$ respectively, then $\left(4a+x_5\right)$ is equal to

JEE Main 2022 (29 Jun Shift 1)

Options

• A: $13$
• B: $15$
• C: $17$
• D: $18$

Question

The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38{\sigma }^2$ is equal to _______.

JEE Main 2022 (26 Jul Shift 2)

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Question

Let $\mu$  be the mean and $\sigma$ be the standard deviation of the distribution

where $\Sigma f_i=62$. If $\left[x\right]$ denotes the greatest integer $\le x$, then$\left[{\mu }^2 + {\sigma }^2\right]$  is equal to

JEE Main 2023 (10 Apr Shift 2)

Options

• A: $9$
• B: $8$
• C: $7$
• D: $6$

Question

The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted, $a$ and $b$ are respectively mean and variance of remaining $6$ observation, then $a+3 b-5$ is equal to ________

JEE Main 2023 (30 Jan Shift 1)

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Question

If the mean of the following probability distribution of a random variable $\mathrm{X}$ : $\begin{array}{|c|c|c|c|c|c|} \hline \mathrm{X} & 0 & 2 & 4 & 6 & 8 \\ \hline \mathrm{P}(\mathrm{X}) & a & 2 a & a+b & 2 b & 3 b \\ \hline \end{array}$ is $\frac{46}{9}$, then the variance of the distribution is

JEE Main 2024 (04 Apr Shift 2)

Options

• A: $\frac{173}{27}$
• B: $\frac{566}{81}$
• C: $\frac{151}{27}$
• D: $\frac{581}{81}$

Question

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable $\mathrm{X}$ denote the number of defective items in the sample. If the variance of $\mathrm{X}$ is $\sigma^2$, then $96 \sigma^2$ is equal to ______

JEE Main 2024 (05 Apr Shift 1)

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Question

Let $\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{N}$ and $\mathrm{a} < \mathrm{b} < \mathrm{c}$. Let the mean, the mean deviation about the mean and the variance of the 5 observations $9,25, \mathrm{a}, \mathrm{b}, \mathrm{c}$ be 18,4 and $\frac{136}{5}$, respectively. Then $2 \mathrm{a}+\mathrm{b}-\mathrm{c}$ is equal to__________

JEE Main 2024 (08 Apr Shift 2)

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Question

The mean and standard deviation of $15$ observations were found to be $12$ and $3$ respectively. On rechecking it was found that an observation was read as $10$ in place of $12.$ If $\mu$ and ${\sigma }^2$ denote the mean and variance of the correct observations respectively, then $15\left(\mu +{\mu }^2+{\sigma }^2\right)$ is equal to _________.

JEE Main 2024 (27 Jan Shift 2)

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Question

Let the median and the mean deviation about the median of $7$ observation $170,125,230,190,210,a,b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is:

JEE Main 2024 (01 Feb Shift 1)

Options

• A: $31$
• B: $28$
• C: $30$
• D: $32$