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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 101-150 of 169

  1. The mean of a data set consisting of $20$ observations is $40$. If one observation $53$ was wrongly recorded as $33$, then the correct mean will be :
  2. The mean and the median of the following ten numbers in increasing order $10,22,26,29,34,x,42,67,70,y$ are $42$ and $35$ respectively, then $\frac yx$ is equal to :
  3. If the mean of the data: $7,8,9,7,8,7,\lambda,8$ is $8$, then the variance of this data is
  4. If the mean and standard deviation of $5$ observations $x_1,x_2,x_3,x_4,x_5$ are $10$ and $3$, respectively, then the variance of $6$ observations $x_1,x_2,\ldots,x_5$ …
  5. In a set of $2n$ observations, half of them are equal to $a$ and the remaining half are equal to $-a$. If the standard deviation of all the observations is $2$; then the …
  6. Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a_1,a_2,a_3,\ldots,a_{100}$ is $25$. Then …
  7. If the standard deviation of the numbers $-1,0,1,k$ is $\sqrt5$ where $k>0$, then $k$ is equal to
  8. The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1,3$ and $8$, then a ratio of other two observations is
  9. In an experiment with $15$ observations on $x$, the following results were available: $\sum x^{2}=2830$, $\sum x=170$. One observation that was $20$ was found to be …
  10. If in a frequency distribution, the mean and median are $21$ and $22$ respectively, then its mode is approximately :
  11. If the standard deviation of the numbers $2,3,a$ and $11$ is $3.5$, then which of the following is true?
  12. The mean of $5$ observations is $5$ and their variance is $12.4$. If three of the observations are $1,2$ and $6$; then the value of the remaining two is :
  13. Statement - 1: The variance of first $n$ even natural numbers is $\frac{n^{2}-1}{4}$. Statement - 2: The sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$ and the …
  14. If the mean deviation of numbers $1,1+d,1+2d,\ldots,1+100d$ from their mean is $255$, then $d$ is equal to
  15. In a series of $2n$ observations, half of them equal $a$ and remaining half equal $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals
  16. In a set of $2n$ distinct observations, each of the observation below the median of all the observations is increased by $5$ and each of the remaining observations is …
  17. 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 …
  18. If the data $x_1,x_2,\ldots,x_{10}$ is such that the mean of first four of these is $11$, the mean of the remaining six is $16$ and the sum of squares of all of these is …
  19. The mean and variance for seven observations are $8$ and $16$ respectively. If $5$ of the observations are $2,4,10,12,14$, then the product of the remaining two …
  20. Let $9=x_1<x_2<\ldots<x_7$ be in an A.P. with common difference $d$. If the standard deviation of $x_1,x_2,\ldots,x_7$ is $4$ and the mean is $\overline x$, then …
  21. Let $x_1,x_2,\ldots,x_{10}$ be ten observations such that $\sum_{i=1}^{10}(x_i-2)=30$, $\sum_{i=1}^{10}(x_i-\beta)^2=98$, $\beta>2$, and their variance is $\frac45$. If …
  22. Let the mean and standard deviation of marks of class $A$ of $100$ students be respectively $40$ and $\alpha(>0)$, and the mean and standard deviation of marks of class …
  23. The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is
  24. If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of first four observations is $\frac72$, then the …
  25. For a statistical data $x_1,x_2,\ldots,x_{10}$ of $10$ values, a student obtained the mean as $5.5$ and $\sum_{i=1}^{10}x_i^{2}=371$. He later found that he had noted …
  26. If the variance of the frequency distribution $x_i: 2,3,4,5,6,7,8$ with frequencies $f_i: 3,6,16,\alpha,9,5,6$ respectively is $3$, then $\alpha$ is equal to
  27. If the variance of the first $n$ natural numbers is $10$ and the variance of the first $m$ even natural numbers is $16$, then the value of $m+n$ is equal to
  28. If $\sum_{i=1}^{9}(x_i-5)=9$ and $\sum_{i=1}^{9}(x_i-5)^2=45$, then the standard deviation of the $9$ items $x_1,x_2,\ldots,x_9$ is
  29. Let $X$ be a random variable with distribution $x$: $-2,\ -1,\ 3,\ 4,\ 6$ $P(X=x)$: $\frac15,\ a,\ \frac13,\ \frac15,\ b$ If the mean of $X$ is $2.3$ and variance of $X$ …
  30. Let $X=\{11,12,13,\ldots,40,41\}$ and $Y=\{61,62,63,\ldots,90,91\}$ be the two sets of observations. If $\bar x$ and $\bar y$ are their respective means and $\sigma^{2}$ …
  31. Consider the given data with frequency distribution $$\begin{array}{c|cccccc} x_i & 3 & 8 & 11 & 10 & 5 & 4\\ \hline f_i & 5 & 2 & 3 & 2 & 4 & 4\end{array}$$ Match each …
  32. Consider the following frequency distribution:\\ …
  33. Consider a data consisting of 10 observations $x_1,x_2,\ldots,x_{10}$, whose mean is $5$ and variance is $7$. If the mean and the variance of the first $8$ observations …
  34. The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted, $a$ and $b$ are respectively mean and variance of remaining …
  35. 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 …
  36. A factory is operating in two shifts, day and night, with $70$ and $30$ workers, respectively. If per day mean wage of the day shift workers is Rs. $54$ and per day mean …
  37. Let the mean and variance of $8$ numbers $-10,-7,-1,x,y,9,2,16$ be $\frac72$ and $\frac{293}{4}$, respectively. Then the mean of $4$ numbers $x,y,x+y+1,|x-y|$ is :
  38. The mean deviation about the mean for the data $\begin{array}{|c|c|c|c|c|c|c|}\hline x_i&5&7&9&10&12&15\\\hline f_i&8&6&2&2&2&6\\\hline\end{array}$ is equal to :
  39. If the mean of the data …
  40. A data consists of $20$ observations $x_1,x_2,\ldots,x_{20}$. If $\sum_{i=1}^{20}(x_i+5)^{2}=2500$ and $\sum_{i=1}^{20}(x_i-5)^{2}=100$, then the ratio of mean to …
  41. Let the mean and variance of $7$ observations $2, 4, 10, x, 12, 14, y$, $x>y$, be $8$ and $16$ respectively. Two numbers are chosen from $\{1, 2, 3, x-4, y, 5\}$ one …
  42. If the mean deviation about the median of the numbers $k,2k,3k,\ldots,1000k$ is $500$, then $k^2$ is equal to :
  43. If the mean and the variance of the data …
  44. Let $X=\{x\in\mathbf{N}:1\le x\le19\}$ and for some $a,b\in\mathbf{R}$ define $Y=\{ax+b:x\in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$ …
  45. The mean and variance of $10$ observations are $9$ and $34.2$, respectively. If $8$ of these observations are $2,3,5,10,11,13,15,21$, then the mean deviation about the …
  46. Let $\bar X$ and $M.D.$ be the mean and the mean deviation about $\bar X$ of $n$ observations $x_i$, $i=1,2,\ldots,n$. If each of the observations is increased by $5$ …
  47. The median of a set of $9$ distinct observations is $20.5$. If each of the largest $4$ observations of the set is increased by $2$, then the median of the new set :
  48. If the mean and variance of eight numbers $3,7,9,12,13,20,x$ and $y$ be $10$ and $25$ respectively, then $x\cdot y$ is equal to
  49. Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of scale (c) Variance is independent of change of …
  50. Let $\overline{x}$, $M$ and $\sigma^{2}$ be respectively the mean, mode and variance of $n$ observations $x_1,x_2,\ldots,x_n$ and $d_i=-x_i-a$, $i=1,2,\ldots,n$, where …

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