Statistics JEE Main PYQs PDF, 2020–2026

Statistics questions per year

Topic-wise weightage by year

How many Statistics questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 15 JEE Main 2026 Statistics questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Variance and Standard Deviation

   A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1 . Then, the variance of all these 10 observations is equal to :

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2. JEE Main 2026 · 6 Apr · Shift 1 · Variance and Standard Deviation

   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 standard deviation of this data is :

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3. JEE Main 2026 · 6 Apr · Shift 2 · Variance and Standard Deviation

   Let the mean and the variance of seven observations $2,4,\alpha,8,\beta,12,14,\alpha<\beta$, be 8 and 16 respectively. Then the quadratic equation whose roots are $3\alpha+2$ and $2\beta+1$ is :

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4. JEE Main 2026 · 5 Apr · Shift 2 · Variance and Standard Deviation

   A variable $X$ takes values $0,0,2,6,12,20,\ldots,n(n-1)$ with frequencies ${}^{n}C_{0},{}^{n}C_{1},{}^{n}C_{2},{}^{n}C_{3},{}^{n}C_{4},{}^{n}C_{5},\ldots,{}^{n}C_{n}$, respectively. If the mean of this data is 60 , then its median is :

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5. JEE Main 2026 · 5 Apr · Shift 1 · Variance and Standard Deviation

   The mean deviation about the mean for the data

   $\begin{array}{ccccccc}x_{i} & 5 & 7 & 9 & 10 & 12 & 15 \\ f_{i} & 8 & 6 & 2 & 2 & 2 & 6\end{array}$

   $\text{ is equal to:}$

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6. JEE Main 2026 · 4 Apr · Shift 2 · Variance and Standard Deviation

   For 10 observations $x_{1},x_{2},\ldots,x_{{10}}$, if $\sum_{{i=1}}^{{10}}{(x_{i}+2)}^{2}=180$ and $\sum_{{i=1}}^{{10}}{(x_{i}-1)}^{2}=90$, then their standard deviation is :

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7. JEE Main 2026 · 4 Apr · Shift 1 · Variance and Standard Deviation

   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 is 26 , then $2a$ is equal to :

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8. JEE Main 2026 · 2 Apr · Shift 2 · Variance and Standard Deviation

   The mean and variance of n observations are 8 and 16, respectively. If the sum of the first (n − 1) observations is 48 and the sum of squares of the first (n − 1) observations is 496, then the value of n is :

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9. JEE Main 2026 · 2 Apr · Shift 1 · Measures of Central Tendency

   If the mean of the data

   Class	5-10	10-15	15-20	20-25	25-30	30-35
   Frequency	2	k	28	54	k + 1	5

   is 21, then $k$ is one of the roots of the equation:

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10. JEE Main 2026 · 28 Jan · Shift 1 · Variance and Standard Deviation

    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 median of all the 10 observations is

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11. JEE Main 2026 · 24 Jan · Shift 1 · Variance and Standard Deviation

    The mean and variance of a data of 10 observations are 10 and 2 , respectively. If an observations $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99 , respectively. Then $\alpha+\beta$ equals

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12. JEE Main 2026 · 24 Jan · Shift 2 · Variance and Standard Deviation

    Let ${\mathrm{X}}=\{x\in {\ \mathrm{N}}:1\leq x\leq 19\}$ and for some $a,b\in {\mathbb{R}},{\mathrm{Y}}=\{ax+b:x\in {\mathrm{X}}\}$. If the mean and variance of the elements of Y are 30 and 750 , respectively, then the sum of all possible values of $b$ is

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Sample questions from recent papers

The free PDF above has all 104 questions grouped by topic, with an answer key.

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