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Yukti Vault

Statistics & Probability

Statistics: JEE Main & Advanced PYQs

169 previous year questions on Statistics from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

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Questions 51-100 of 169

  1. For the frequency distribution : Variate $(x)$: $x_1,x_2,x_3,\ldots,x_{15}$, Frequency $(f)$: $f_1,f_2,f_3,\ldots,f_{15}$ where $0 0$, the standard deviation cannot be :
  2. If the mean deviation about the mean of the numbers $1,2,3,\ldots,n$, where $n$ is odd, is $\frac{5(n+1)}{n}$, then $n$ is equal to $\_\_\_\_\_\_$ .
  3. An online exam is attempted by $50$ candidates out of which $20$ are boys. The average marks obtained by boys is $12$ with a variance $2$. The variance of marks obtained …
  4. The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If …
  5. 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 …
  6. Let the mean of the data $x$ : $1,3,5,7,9$ Frequency $(f)$ : $4,24,28,\alpha,8$ be $5$. If $m$ and $\sigma^{2}$ are respectively the mean deviation about the mean and …
  7. 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 $25M$ is equal to :
  8. If the variance of $10$ natural numbers $1,1,1,\ldots,1,k$ is less than $10$, then the maximum possible value of $k$ is $\_\_\_\_\_\_$ .
  9. Let $n$ be an odd natural number such that the variance of $1,2,3,4,\ldots,n$ is $14$. Then $n$ is equal to $\_\_\_\_\_\_$ .
  10. 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 …
  11. 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 …
  12. The probability distribution of $X$ is : $X$ : $0,1,2,3$ $P(X)$ : $\frac{1-d}{4},\ \frac{1+2d}{4},\ \frac{1-4d}{4},\ \frac{1+3d}{4}$ For the minimum possible value of …
  13. The mean and variance of $8$ observations are $10$ and $13.5$, respectively. If $6$ of these observations are $5,7,10,12,14,15$, then the absolute difference of the …
  14. 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
  15. If the mean and median of the data $x$: $0$-$10$, $10$-$20$, $20$-$30$, $30$-$40$, $40$-$50$ with frequencies $f$: $3,6,2,x,y$ and $\sum f=20$ are equal, then $xy^2$ is …
  16. If the variance of the following frequency distribution : Class: $10$-$20$, $20$-$30$, $30$-$40$; Frequency: $2$, $x$, $2$ is $50$, then $x$ is equal to ________.
  17. The mean and variance of $7$ observations are $7$ and $18$ respectively. If $5$ of the observations are $2,4,10,11,13$ and the remaining observations are $x$ and $y$ …
  18. If the mean and variance of the following data : $6,10,7,13,a,12,b,12$ are $9$ and $\frac{37}{4}$ respectively, then $(a-b)^2$ is equal to :
  19. 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 …
  20. Let $x_1,x_2,x_3,\ldots,x_{20}$ be in geometric progression with $x_1=3$ and the common ratio $\frac12$. A new data is constructed replacing each $x_i$ by $(x_i-i)^2$. …
  21. The number of values of $a\in\mathbf{N}$ such that the variance of $3,7,12,a,43-a$ is a natural number is:
  22. The mean and variance of $7$ observations are $8$ and $16$, respectively. If five observations are $2,4,10,12,14$, then the absolute difference of the remaining two …
  23. Consider a set of $3n$ numbers having variance $4$. In this set, the mean of first $2n$ numbers is $6$ and the mean of the remaining $n$ numbers is $3$. A new set is …
  24. Consider the data on $x$ taking the values $0,2,4,8,\ldots,2^n$ with frequencies ${}^nC_0,{}^nC_1,{}^nC_2,\ldots,{}^nC_n$ respectively. If the mean of this data is …
  25. The mean and standard deviation of $15$ observations are found to be $8$ and $3$ respectively. On rechecking it was found that, in the observations, $20$ was misread as …
  26. 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 …
  27. Let the observations $x_i$ ($1\le i\le10$) 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 …
  28. 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 …
  29. The variance $\sigma^{2}$ of the data $x_i$ : $0,1,5,6,10,12,17$ $f_i$ : $3,2,3,2,6,3,3$ is $\_\_\_\_\_\_$ .
  30. Let the mean and variance of the frequency distribution $x$: $x_1=2,x_2=6,x_3=8,x_4=9$ with $f$: $4,4,\alpha,\beta$ be $6$ and $6.8$ respectively. If $x_3$ is changed …
  31. 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 …
  32. The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to …
  33. If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observations is :
  34. $5$ students of a class have an average height $150$ cm and variance $18$ cm$^2$. A new student, whose height is $156$ cm, joined them. The variance in cm$^2$ of the …
  35. A data consists of $n$ observations: $x_1,x_2,\ldots,x_n$. If $\sum_{i=1}^{n}(x_i+1)^{2}=9n$ and $\sum_{i=1}^{n}(x_i-1)^{2}=5n$, then the standard deviation of this data …
  36. If the mean deviation of the numbers $1,\ 1+d,\ \ldots,\ 1+100d$ from their mean is $255$, then a value of $d$ is :
  37. The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac12-d$ each, $10$ items gave outcome $\frac12$ each and the remaining $10$ items gave …
  38. If the median and the range of four numbers $\{x,y,2x+y,x-y\}$, where $0<y<x<2y$, are $10$ and $28$ respectively, then the mean of the numbers is :
  39. 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 $21$, respectively. If the mean deviation about the median …
  40. The mean and the variance of five observations are $4$ and $5.20$, respectively. If three of the observations are $3$, $4$ and $4$; then the absolute value of the …
  41. A student scores the following marks in five tests: $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is $48$ in the six tests, then the …
  42. Let the six numbers $a_1,a_2,\ldots,a_6$ be in A.P. and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^{2}$, then …
  43. If for some $x\in\mathbb R$, the frequency distribution of the marks obtained by $20$ students in a test is: Marks $2,3,5,7$ with frequencies $(x+1)^{2}$, $(2x-5)$ …
  44. If both the mean and the standard deviation of $50$ observations $x_1,x_2,\ldots,x_{50}$ are equal to $16$, then the mean of …
  45. The mean and the standard deviation (S.D.) of five observations are $9$ and $0$, respectively. If one of the observation is increased such that the mean of the new set …
  46. In a class of $100$ students there are $70$ boys whose average marks in a subject are $75$. If the average marks of the complete class is $72$, then what is the average …
  47. 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 …
  48. The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observations $3$, $4$ and $5$ were found to be incorrect. …
  49. Let $x_1,x_2,\ldots,x_n$ be $n$ observations such that $\sum x_i^{2}=400$ and $\sum x_i=80$. Then a possible value of $n$ among the following is
  50. Suppose a population $A$ has $100$ observations $101,102,\ldots,200$, and another population $B$ has $100$ observations $151,152,\ldots,250$. If $V_A$ and $V_B$ …

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