Statistics · JEE Main previous year questions

2022 12 questions

1. Q212022 · 29 Jul 2022 · Shift 1· Numerical answer

   Let the mean and the variance of 20 observations $x_1,x_2,\dots ,x_{20}$ be 15 and 9 , respectively. For $\alpha \in \mathbf{R}$, if the mean of ${\left(x_1+\alpha \right)}^2,{\left(x_2+\alpha \right)}^2,\dots ,{\left(x_{20}+\alpha \right)}^2$ is 178 , then the square of the maximum value of $\alpha$ is equal to ____.

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   Answer: 4

2. Q282022 · 29 Jul 2022 · Shift 2· Numerical answer

   The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is ____________.

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   Answer: 96

3. Q222022 · 27 Jul 2022 · Shift 1· Numerical answer

   The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is _____________.

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   Answer: 2

4. Q172022 · 27 Jul 2022 · Shift 2

   Let $\mathrm{X}$ have a binomial distribution $\mathrm{B}(n,p)$ such that the sum and the product of the mean and variance of $\mathrm{X}$ are $24$ and $128$ respectively. If $P(X>n-3)=\frac{k}{2^n}$, then $\mathrm{k}$ is equal to :

   1. A.$528$
   2. B.$529$
   3. C.$629$
   4. D.$630$
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   Answer: B

5. Q182022 · 26 Jul 2022 · Shift 1

   The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha }{3}$ respectively. If $\mathrm{P}(X=1)=\frac{4}{243}$, then $\mathrm{P}(X=4\text{ or }5)$ is equal to :

   1. A.$\frac{5}{9}$
   2. B.$\frac{64}{81}$
   3. C.$\frac{16}{27}$
   4. D.$\frac{145}{243}$
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   Answer: C

6. Q132022 · 25 Jul 2022 · Shift 2

   If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :

   1. A.11.5
   2. B.10.5
   3. C.12
   4. D.11
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   Answer: D

7. Q222022 · 28 Jun 2022 · Shift 2· Numerical answer

   Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is _________.

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   Answer: 0

8. Q192022 · 27 Jun 2022 · Shift 1

   Let $X$ be a random variable having binomial distribution $B(7,p)$. If $P(X=3)=5P(X=4)$, then the sum of the mean and the variance of $X$ is :

   1. A.$\frac{105}{16}$
   2. B.$\frac{7}{16}$
   3. C.$\frac{77}{36}$
   4. D.$\frac{49}{16}$
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   Answer: C

9. Q112022 · 27 Jun 2022 · Shift 2

   The mean and variance of the data $4,5,6,6,7,8,x,y$, where $x<y$, are $6$ and $\frac{9}{4}$ respectively. Then $x^4+y^2$ is equal to :

   1. A.$162$
   2. B.$320$
   3. C.$674$
   4. D.$420$
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   Answer: B

10. Q112022 · 26 Jun 2022 · Shift 1

    The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to :

    1. A.60
    2. B.55
    3. C.50
    4. D.45
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    Answer: A

11. Q122022 · 26 Jun 2022 · Shift 2

    The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

    1. A.10
    2. B.36
    3. C.43
    4. D.60
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    Answer: C

12. Q252022 · 25 Jun 2022 · Shift 2· Numerical answer

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

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    Answer: 21