Statistics · JEE Main previous year questions

2024 15 questions

1. Q92024 · 9 Apr 2024 · Shift 1

   The frequency distribution of the age of students in a class of 40 students is given below. | Age | 15 | 16 | 17 | 18 | 19 | 20 | |---|---|---|---|---|---|---| | No of Students | 5 | 8 | 5 | 12 | $x$ | $y$ | If the mean deviation about the median is 1.25, then $4x+5y$ is equal to :

   1. A.43
   2. B.46
   3. C.44
   4. D.47
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   Answer: C

2. Q132024 · 9 Apr 2024 · Shift 2

   If the variance of the frequency distribution $$\begin{array}{ccccccc}x& c& 2c& 3c& 4c& 5c& 6c\\ f& 2& 1& 1& 1& 1& 1\end{array}$$ is $160$, then the value of $c\in N$ is

   1. A.$5$
   2. B.$8$
   3. C.$6$
   4. D.$7$
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   Answer: D

3. Q212024 · 8 Apr 2024 · Shift 2· Numerical answer

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

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   Answer: 33

4. Q222024 · 5 Apr 2024 · Shift 2· Numerical answer

   Let the mean and the standard deviation of the probability distribution \begin{tabular}{|l|l|l|l|l|} \hline X & $\alpha$ & 1 & 0 & $-3$ \\ \hline P(X) & $\frac{1}{3}$ & K & $\frac{1}{6}$ & $\frac{1}{4}$ \\ \hline \end{tabular} be $\mu$ and $\sigma$, respectively. If $\sigma -\mu =2$, then $\sigma +\mu$ is equal to _________.

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   Answer: 5

5. Q62024 · 4 Apr 2024 · Shift 1

   Let $\alpha ,\beta \in \mathbf{R}$. Let the mean and the variance of 6 observations $-3,4,7,-6,\alpha ,\beta$ be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is :

   1. A.$\frac{16}{3}$
   2. B.$\frac{11}{3}$
   3. C.$\frac{14}{3}$
   4. D.$\frac{13}{3}$
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   Answer: D

6. Q122024 · 4 Apr 2024 · Shift 2

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

   1. A.$\frac{581}{81}$
   2. B.$\frac{566}{81}$
   3. C.$\frac{151}{27}$
   4. D.$\frac{173}{27}$
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   Answer: B

7. Q72024 · 1 Feb 2024 · Shift 1

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

   1. A.31
   2. B.28
   3. C.30
   4. D.32
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   Answer: C

8. Q102024 · 1 Feb 2024 · Shift 2

   Consider 10 observations $x_1,x_2,\dots ,x_{10}$ such that ${\sum }_{i=1}^{10}(x_i-\alpha )=2$ and ${\sum }_{i=1}^{10}(x_i-\beta {)}^2=40$, where $\alpha ,\beta$ are positive integers. Let the mean and the variance of the observations be $\frac{6}{5}$ and $\frac{84}{25}$ respectively. Then $\frac{\beta }{\alpha }$ is equal to :

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

9. Q82024 · 31 Jan 2024 · Shift 1

   Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in a draw of two apples, the variance of $x$ is

   1. A.$\frac{57}{153}$
   2. B.$\frac{40}{153}$
   3. C.$\frac{37}{153}$
   4. D.$\frac{47}{153}$
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   Answer: B

10. Q202024 · 31 Jan 2024 · Shift 2

    Let the mean and the variance of 6 observations $a,b,68,44,48,60$ be $55$ and $194$, respectively. If $a>b$, then $a+3b$ is

    1. A.180
    2. B.210
    3. C.190
    4. D.200
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    Answer: A

11. Q122024 · 30 Jan 2024 · Shift 1

    Let M denote the median of the following frequency distribution | Class | 0 - 4 | 4 - 8 | 8 - 12 | 12 - 16 | 16 - 20 | |---|---|---|---|---|---| | Frequency | 3 | 9 | 10 | 8 | 6 | Then 20M is equal to :

    1. A.104
    2. B.52
    3. C.208
    4. D.416
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    Answer: C

12. Q222024 · 29 Jan 2024 · Shift 1· Numerical answer

    If the mean and variance of the data $65,68,58,44,48,45,60,\alpha ,\beta ,60$ where $\alpha >\beta$, are 56 and 66.2 respectively, then ${\alpha }^2+{\beta }^2$ is equal to _______.

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    Answer: 6344

13. Q82024 · 29 Jan 2024 · Shift 2

    If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of the first four observations is $\frac{7}{2}$, then the variance of the first four observations is equal to

    1. A.$\frac{5}{4}$
    2. B.$\frac{4}{5}$
    3. C.$\frac{105}{4}$
    4. D.$\frac{77}{12}$
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    Answer: A

14. Q172024 · 27 Jan 2024 · Shift 1

    Let ${\mathrm{a}}_1,{\mathrm{a}}_2,\dots {\mathrm{a}}_{10}$ be 10 observations such that $\sum _{\mathrm{k}=1}^{10}{\mathrm{a}}_{\mathrm{k}}=50$ and $\sum _{\forall \mathrm{k}<\mathrm{j}}{\mathrm{a}}_{\mathrm{k}}\cdot {\mathrm{a}}_{\mathrm{j}}=1100$. Then the standard deviation of ${\mathrm{a}}_1,{\mathrm{a}}_2,\dots ,{\mathrm{a}}_{10}$ is equal to :

    1. A.5
    2. B.$\sqrt{115}$
    3. C.10
    4. D.$\sqrt{5}$
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    Answer: D

15. Q212024 · 27 Jan 2024 · Shift 2· Numerical answer

    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 _______.

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    Answer: 2521