Q JEE MAIN 2026

Let the mean and the variance of seven observations $2,4, \alpha, 8, \beta, 12,14, \alpha

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Q JEE MAIN 2026

A data consists of 20 observations $x_1, x_2, \ldots, x_{20}$. If $\sum_{i=1}^{20}\left(x_i+5\right)^2=2500$ and $\sum_{i=1}^{20}\left(x_i-5\right)^2=100$, then the ratio of mean to...

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Q JEE MAIN 2026

A variable $X$ takes values $0,0,2,6,12,20, \ldots, n(n-1)$ with frequencies $...

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Q JEE MAIN 2026

For 10 observations $x_1, x_2, \ldots, x_{10}$, if $\sum_{i=1}^{10}\left(x_i+2\right)^2=180$ and $\sum_{i=1}^{10}\left(x_i-1\right)^2=90$, then their standard deviation is:

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Q JEE MAIN 2026

The mean deviation about the mean for the data

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Q Jee Main 2026

Suppose that the mean and median of the non-negative numbers $21,8,17, a, 51,103, b, 13,67,(a>b)$, are 40 and 21 ,...

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Q Jee Main 2026

The mean and variance of $n$ observations are 8 and 16 , respectively. If the sum of the first (...

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Q JEE Main 2024

If the variance of the frequency distribution is 160 , then the value of $c \in N$ is

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Q JEE MAIN 2024

Let ABC be an isosceles triangle in which A is at $(-1,0), \angle A=\frac{2 \pi}{3}, A B=A C$ and $B$...

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Q JEE MAIN 2024

The variance $\sigma^2$ of the data

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Q JEE MAIN 2024

consider 10 observation $\mathrm{x}_1, \mathrm{x}_{2, \ldots}, \mathrm{x}_{10}$. such that $\sum_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum_{i=1}^{10}\left(x_i-\beta\right)^2=40$, where $\alpha, \beta$ are positive integers. Let the...

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Q JEE-Main 2024

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was...

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Q Jee Main 2024

Let the mean and the variance of 6 observation $a, b, 68,44,48,60$ be 55 and 194 , respectively if $a>b$,...

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Q Jee Main 2024

If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of first four observations...

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Q JEE MAIN 2026

The mean and variance of 10 observations are 9 and 34.2 , respectively. If 8 of these observations are 2,3,5,10,11,13,15,21,...

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Q JEE MAIN 2026

If the mean and the variance of the data are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is

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Q JEE MAIN 2026

The mean and variance of a data of 10 observations are 10 and 2 , respectively. If an observations $\alpha$...

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Q JEE MAIN_2026_

Let the mean and variance of 8 numbers $-10,-7,-1, x, y, 9,2,16$ be $\frac{7}{2}$ and $\frac{293}{4}$, respectively. Then the mean...

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Q JEE MAIN 2026

If the mean deviation about the median of the numbers $\mathrm{k}, 2 \mathrm{k}, 3 \mathrm{k}, \ldots \ldots, 1000 \mathrm{k}$ is...

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Q JEE MAIN 2026

Let the mean and variance of 7 observations $2,4,10, x, 12,14, y, x>y$, be 8 and 16 respectively. Two numbers...

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Q Statistics_ JEE MAIN_2019_

If for some $x \in R$, the frequency distribution of the marks obtained by 20 students in a test is:

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Q JEE MAIN 2019

If the standard deviation of the numbers –1, 0, 1, k is $\sqrt{5}$ where k > 0, then k is...

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Q JEE MAIN 2020

If the variance of the terms in an increasing A.P., $b_1, b_2, b_3, \ldots, b_{11}$ is 90 , then the...

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Q JEE-MAIN 2019

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is

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Q JEE MAIN 2019

A data consists of $n$ observations $x_1, x_2 \ldots, x_n$. If $\sum_{i=1}^n\left(x_i+1\right)^2=9 n$ and $\sum_{i=1}^n\left(x_i-1\right)^2=5 n$, then the standard deviation...

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Q JEE MAIN 2020

Let the observations $x_i(1 \leq i \leq 10)$ satisfy the equations, $\sum_{\mathrm{i}=1}^{10}\left(\mathrm{x}_{\mathrm{i}}-5\right)=10$ and $\sum_{\mathrm{i}=1}^{10}\left(\mathrm{x}_{\mathrm{i}}-5\right)^2=40$. If $\mu$ and $\lambda$ are the...

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Q JEE MAIN 2020

Consider the data on $x$ taking the values $0,2,4,8$, $\ldots, 2^n$ with frequencies $...

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Q JEE MAIN 2019

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3,...

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Q JEE MAIN 2019

A data consists of $n$ observations $x_1, x_2, \ldots ., x n$. If $\sum_{i=1}^n\left(x_i+1\right)^2=9 n$ and $\sum_{i=1}^n\left(x_i-1\right)^2=5 n$, then the...

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Q JEE MAIN 2020

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations...

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Q JEE MAIN 2019

The outcome of each of 30 items was observed; 10 items gave an outcome $\frac{1}{2}$-d each, 10 items gave outcome...

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Q JEE-MAIN 2020

If the mean and the standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively,...

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Q JEE MAIN 2019

If both the mean and the standard deviation of 50 observations $x_1, x_2, \ldots x_{50}$ are equal to 16 ,...

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Q JEE Main 2019

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are...

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Q JEE MAIN 2020

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7,...

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Q JEE MAIN 2019

A bag contains 30 white ball and 10 red balls. 16 balls are drawn one by one randomly from the...

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Q JEE-MAIN 2020

Let $x i(1 \leq i \leq 10)$ be ten observations of a random variable $X$. If $\sum_{i=1}^{10}\left(x_i-p\right)=3$ and $\sum_{i=1}^{10}\left(x_i-p\right)^2=9$ where...

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Q JEE MAIN 2020

The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found...

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Q JEE MAIN 2020

If the variance of the first n natural numbers is 10 and the variance of the first m even natural...

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Q JEE MAIN 2019

The mean and the median of the following ten numbers in increasing order $10,22,26,29,34, x, 42,67,70, y$ are 42 and...

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Q JEE MAIN 2021

The mean of 10 numbers $$ 7 \times 8,10 \times 10,13 \times 12,16 \times 14, \ldots . \text { is...

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Q JEE Main 2021

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then...

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Q JEE MAIN 2019

If mean and standard deviation of 5 observations $x_1, x_2, x_3, x_4, x_5$ are 10 and 3 , respectively, then...

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Q JEE MAIN 2021

Let the mean and variance of four numbers $3,7, x$ and $y(x>y)$ be 5 and 10 respectively. Then the mean...

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Q JEE MAIN_2021_

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys...

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Q JEE Main 2021

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by...

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Q JEE MAIN 2019

The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4,...

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Q JEE Main 2019

5 students of a class have an average height 150 cm and variance $18 \mathrm{~cm}^2$. A new student, whose height...

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Q JEE MAIN_2021

Consider the following frequency distribution

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Q JEE MAIN 2021

Let $X_1, X_2, \ldots \ldots X_{18}$ be eighteen observations such that $\sum_{i=1}^{18}\left(x_i-\alpha\right)=36$ and $\sum_{i=1}^{18}\left(x_i-\beta\right)^2=90$, where $\alpha$ and $\beta$ are distinct...

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Q JEE MAIN 2019

A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known...

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Q JEE MAIN 2021

the first of the two samples in a group has 100 items with mean 15 and standard deviation 3 ....

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Q JEE MAIN 2021

If the mean and variance of the following data : $6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively,...

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Q JEE-MAIN 2021

Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6...

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Q JEE MAIN 2021

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are...

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Q JEE MAIN 2021

Let in a series of $2 n$ observations, half of them are equal to a and remaining half are equal...

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Q JEE MAIN 2021

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Q JEE MAIN 2021

-If the mean and variance of six observations $7,10,11,15, a, b$ are 10 and $\frac{20}{3}$, respectively, then the value of...

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Q JEE MAIN 2021

If the variance of 10 natural numbers 1, 1, 1,...., 1, k is less than 10, then the maximum possible...

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Q JEE MAIN 2021

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60...

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Q JEE MAIN 2021

Consider three observations a, b and c such that b = a + c. If the standard deviation of a...

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Q JEE MAIN 2022

The mean and variance of the data $4,5,6,6,7,8, x, y$ where $x

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Q JEE MAIN 2022

Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their...

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Q JEE MAIN 2022

The number of values of $a \in \mathbb{N}$ such that the variance of $3,7,12 a, 43-a$ is a natural number...

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Q JEE MAIN 2022

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation...

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Q JEE MAIN 2022

If the mean deviation about the mean of the numbers $1,2,3$, $\_\_\_\_$ $n$, where $n$ is odd, is $\frac{5(n+1)}{n}$, then...

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Q JEE MAIN 2022

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...

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Q JEE MAIN 2022

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was...

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Q JEE MAIN 2022

The mean of the numbers $a, b, 8,5,10$ is 6 and their variance is 6.8 . If $M$ is the...

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Q JEE MAIN 2023

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Q JEE MAIN 2023

Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is reciprocal to that of the hyperbola $2 x^2-2 y^2=1$. If the ellipse...

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Q JEE MAIN 2023

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later,...

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Q JEE-Main 2023

Let the mean and variance of 12 observations be $\frac{9}{2}$ and 4 respectively. Later on, it was observed that two...

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Q JEE MAIN 2025

Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=b, a>b$, be 5 and 10 respectively....

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Q JEE MAIN 2025

Let the mean and the standard deviation of the observation $2,3,3,4,5,7, a, b$ be 4 and $\sqrt{2}$ respectively. Then the...

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Q JEE MAIN 2025

If the mean and the variance of 6, 4, a, 8, b, 12,10,13 are 9 and 9.25 respectively, then a...

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Q JEE MAIN 2023

Let the mean of the data \begin{tabular}{|l|l|l|l|l|l|} \hline$x$ & 1 & 3 & 5 & 7 & 9 \\ \hline...

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Q JEE-Main 2023

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of...

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Q JEE MAIN 2023

The number of ordered triplets of the truth values of $p, q$ and $r$ such that the truth value of...

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Q JEE MAIN 2023

Let the mean and variance of 8 numbers x, y, 10, 12, 6, 12, 4, 8, be 9 and 9.25...

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Q JEE MAIN 2023

If the mean of the frequency distribution then its variance is ______.

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Q JEE-Main 2023

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of...

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Q JEE MAIN

The frequency distribution of the age of students in a class of 40 students is given below. If the mean...

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Q JEE MAIN 2024

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random....

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Q JEE-Main

Let a variable line of slope m > 0 passing through the point (4,-9) intersect the coordinate axes at the...

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Q JEE MAIN 2024

Let a,b∈R. Let the mean and the variance of 6 observations -3,4,7,-6,a,b be 2 and 23 , respectively. The mean...

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Q JEE-Main 2024

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was...

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Q JEE MAIN

If the mean and variance of the data 65,68,58,44, 48, 45, 60, α,β,60 where α>β are 56 and 66.2 respectively,...

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Q JEE MAIN 2024

Let M denote the median of the following frequency distribution. Then 20 M is equal to :

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Q JEE MAIN 2024

Let $a_1, a_2, \ldots . . a_{10}$ be 10 observations such that $\sum_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50$ and $\sum_{\forall \mathrm{k}

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Q JEE MAIN 2025

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as...

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Q JEE MAIN 2025

Let ${x_1},{x_2}, \ldots .,{x_{10}}$ be ten observations such that $...

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Q JEE MAIN 2025

Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to...

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Q JEE MAIN 2025

For a statistical data ${{\rm{x}}_1},{{\rm{x}}_2}, \ldots ,{{\rm{x}}_{10}}$ of 10 values, a student obtained the mean as 5.5 and $...

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Q JEE MAIN 2025

Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width....

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