Statistics · JEE Main previous year questions

2021 11 questions

1. Q212021 · 1 Sept 2021 · Shift 2· Numerical answer

   Let X be a random variable with distribution. | x | -2 | -1 | 3 | 4 | 6 | | :--- | :--- | :--- | :--- | :--- | :--- | | $\mathrm{P}(\mathrm{X}=\mathrm{x})$ | $\frac{1}{5}$ | a | $\frac{1}{3}$ | $\frac{1}{5}$ | b | If the mean of X is 2.3 and variance of X is ${\sigma }^2$, then $100{\sigma }^2$ is equal to :

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   Answer: 781

2. Q262021 · 26 Aug 2021 · Shift 2· Numerical answer

   Let the mean and variance of four numbers $3,7,x$ and $y$ ($x>y$) be $5$ and $10$ respectively. Then the mean of four numbers $3+2x$, $7+2y$, $x+y$ and $x-y$ is ________.

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   Answer: 12

3. Q62021 · 27 Jul 2021 · Shift 2

   Let the mean and variance of the frequency distribution $$\begin{array}{lcccc}x:& x_1=2& x_2=6& x_3=8& x_4=9\\ f:& 4& 4& \alpha & \beta \end{array}$$ be 6 and 6.8 respectively. If $x_3$ is changed from 8 to 7, then the mean for the new data will be :

   1. A.4
   2. B.5
   3. C.$\frac{17}{3}$
   4. D.$\frac{16}{3}$
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   Answer: C

4. Q222021 · 25 Jul 2021 · Shift 1· Numerical answer

   Consider the following frequency distribution : $$\begin{array}{lccccc}\text{Class :}& 10\text{-}20& 20\text{-}30& 30\text{-}40& 40\text{-}50& 50\text{-}60\\ \text{Frequency :}& \alpha & 110& 54& 30& \beta \end{array}$$ If the sum of all frequencies is 584 and median is 45, then $|\alpha -\beta |$ is equal to ____.

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   Answer: 164

5. Q22021 · 25 Jul 2021 · Shift 2

   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 :

   1. A.8
   2. B.6
   3. C.4
   4. D.5
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   Answer: C

6. Q242021 · 22 Jul 2021 · Shift 2· Numerical answer

   Consider the following frequency distribution : | Class : | 0-6 | 6-12 | 12-18 | 18-24 | 24-30 | |---|---|---|---|---|---| | Frequency : | a | b | 12 | 9 | 5 | If $\text{mean}=\frac{309}{22}$ and $\text{median}=14$, then the value $(a-b{)}^2$ is equal to ________.

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   Answer: 4

7. Q22021 · 20 Jul 2021 · Shift 1

   The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are :

   1. A.10, 11
   2. B.3, 18
   3. C.8, 13
   4. D.1, 20
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   Answer: A

8. Q252021 · 18 Mar 2021 · Shift 1· Numerical answer

   The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is _________.

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   Answer: 35

9. Q92021 · 18 Mar 2021 · Shift 2

   Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $-a$. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of $a^2+b^2$ is equal to :

   1. A.425
   2. B.250
   3. C.925
   4. D.650
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   Answer: A

10. Q102021 · 16 Mar 2021 · Shift 1

    Consider three observations a, b, and c such that $b=a+c$. If the standard deviation of $a+2,b+2,c+2$ is d, then which of the following is true?

    1. A.$b^2=3(a^2+c^2)+9d^2$
    2. B.$b^2=3(a^2+c^2)-9d^2$
    3. C.$b^2=3(a^2+c^2+d^2)$
    4. D.$b^2=a^2+c^2+3d^2$
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    Answer: B

11. Q272021 · 26 Feb 2021 · Shift 2· Numerical answer

    Let $X_1,X_2,\dots \dots ,X_{18}$ be eighteen observations such that ${\sum }_{i=1}^{18}(X_i-\alpha )=36$ and ${\sum }_{i=1}^{18}(X_i-\beta {)}^2=90$, where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of $|\alpha -\beta |$ is _________.

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    Answer: 4