Statistics · JEE Main previous year questions

2020 11 questions

1. Q132020 · 6 Sept 2020 · Shift 1

   If ${\sum }_{i=1}^n(x_i-a)=n$ and ${\sum }_{i=1}^n(x_i-a{)}^2=na$ $(n,a>1)$ then the standard deviation of $n$ observations $x_1,x_2,\dots ,x_n$ is :

   1. A.$a-1$
   2. B.$n\sqrt{a-1}$
   3. C.$\sqrt{n(a-1)}$
   4. D.$\sqrt{a-1}$
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   Answer: D

2. Q252020 · 6 Sept 2020 · Shift 2· Numerical answer

   Consider the data on x taking the values $0,2,4,8,\dots ,2^n$ with frequencies ${}^n{C}_0,{}^n{C}_1,{}^n{C}_2,\dots ,{}^n{C}_n$ respectively. If the mean of this data is $\frac{728}{2^n}$, then n is equal to ______ .

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   Answer: 6

3. Q72020 · 3 Sept 2020 · Shift 1

   For the frequency distribution : Variate ($x$) : $x_1{x}_2{x}_3\dots x_{15}$ Frequency ($f$) : $f_1{f}_2{f}_3\dots f_{15}$ where $0<x_1<x_2<x_3<\cdots <x_{15}=10$ and ${\sum }_{i=1}^{15}{f}_i>0$, the standard deviation cannot be :

   1. A.6
   2. B.1
   3. C.4
   4. D.2
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   Answer: A

4. Q112020 · 3 Sept 2020 · Shift 2

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

   1. A.$\frac{7}{10}$
   2. B.$\frac{9}{10}$
   3. C.$\frac{4}{5}$
   4. D.$\sqrt{\frac{3}{5}}$
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   Answer: B

5. Q82020 · 2 Sept 2020 · Shift 1

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

   1. A.7
   2. B.9
   3. C.-7
   4. D.-27
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   Answer: C

6. Q212020 · 2 Sept 2020 · Shift 2· Numerical answer

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

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   Answer: 3

7. Q82020 · 9 Jan 2020 · Shift 1

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

   1. A.$(6,6)$
   2. B.$(3,3)$
   3. C.$(3,6)$
   4. D.$(6,3)$
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   Answer: B

8. Q62020 · 8 Jan 2020 · Shift 1

   The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where $p\ne 0$ and $q\ne 0$. If the new mean and new s.d. become half of their original values, then q is equal to

   1. A.10
   2. B.-20
   3. C.-10
   4. D.-5
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   Answer: B

9. Q112020 · 8 Jan 2020 · Shift 2

   The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is

   1. A.3.98
   2. B.3.99
   3. C.4.01
   4. D.4.02
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   Answer: B

10. Q232020 · 7 Jan 2020 · Shift 1· Numerical answer

    If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m + n is equal to_____.

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    Answer: 18

11. Q242020 · 7 Jan 2020 · Shift 2· Numerical answer

    If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to _______.

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    Answer: 54