Statistics

16 JEE Main questions · Maths

MathsJEE Main 21 Jan 2026, Shift 1·Q13·MCQ·Moderate
Open
Mean and variance
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 after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is:
1. (1) $\dfrac35$
2. (2) $\dfrac45$
3. (3) $\dfrac25$
4. (4) $\dfrac13$
MathsJEE Main 22 Jan 2026, Shift 2·Q2·MCQ·Moderate
Open
Mean deviation about median
If the mean deviation about the median of the numbers $k, 2k, 3k, \ldots, 1000k$ is 500, then $k^2$ is equal to:
1. (1)16
2. (2)4
3. (3)1
4. (4)9
MathsJEE Main 23 Jan 2026, Shift 1·Q13·MCQ·Easy–moderate
Open
Mean and variance
Let the mean and variance of 8 numbers $-10$ , $-7$ , $-1$ , $x$ , $y$ , 9, 2, 16 be $\dfrac72$ and $\dfrac{293}{4}$ , respectively. Then the mean of 4 numbers $x$ , $y$ , $x + y + 1$ , $\lvert x - y\rvert$ is:
1. (1)11
2. (2)9
3. (3)10
4. (4)12
MathsJEE Main 23 Jan 2026, Shift 2·Q18·MCQ·Moderate
Open
Mean and variance of grouped data
If the mean and the variance of the data
Class 4–8 8–12 12–16 16–20
Frequency 3 $\lambda$ 4 7
are $\mu$ and 19 respectively, then the value of $\lambda + \mu$ is
1. (1)18
2. (2)21
3. (3)20
4. (4)19
MathsJEE Main 24 Jan 2026, Shift 1·Q18·MCQ·Moderate
Open
Mean and variance
The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$ , then the mean and variance become 10.1 and 1.99, respectively. Then $\alpha + \beta$ equals.
1. (1)10
2. (2)15
3. (3)5
4. (4)20
We corrected a printing error in the original paper
Source printed “If an observations $\alpha$ ”.
MathsJEE Main 24 Jan 2026, Shift 2·Q14·MCQ·Moderate
Open
Mean and variance of transformed data
Let $X = \{x \in \mathbb{N} : 1 \le x \le 19\}$ and for some $a, b \in \mathbb{R}$ , $Y = \{ax + b : x \in X\}$ . 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
1. (1)20
2. (2)80
3. (3)100
4. (4)60
MathsJEE Main 28 Jan 2026, Shift 1·Q15·MCQ·Moderate
Open
Mean deviation about median
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
1. (1)5
2. (2)4
3. (3)6
4. (4)7
MathsJEE Main 2 Apr 2026, Shift 1·Q8·MCQ·Easy–moderate
Open
Mean of grouped data
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:
1. (1) $2x^2 - 23x - 10 = 0$
2. (2) $4x^2 - 35x + 24 = 0$
3. (3) $2x^2 - 19x - 10 = 0$
4. (4) $2x^2 - 35x + 98 = 0$
MathsJEE Main 2 Apr 2026, Shift 2·Q9·MCQ·Moderate
Open
Mean and variance
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:
1. (1)21
2. (2)16
3. (3)13
4. (4)7
MathsJEE Main 4 Apr 2026, Shift 1·Q10·MCQ·Moderate
Open
Mean median and mean 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:
1. (1)109
2. (2)117
3. (3)161
4. (4)131
MathsJEE Main 4 Apr 2026, Shift 2·Q8·MCQ·Easy–moderate
Open
Variance and standard deviation
For 10 observations $x_1, x_2, \ldots, x_{10}$ , if $\displaystyle\sum_{i=1}^{10}(x_i + 2)^2 = 180$ and $\displaystyle\sum_{i=1}^{10}(x_i - 1)^2 = 90$ , then their standard deviation is:
1. (1)2
2. (2) $\sqrt3$
3. (3) $2\sqrt2$
4. (4)3
MathsJEE Main 5 Apr 2026, Shift 1·Q8·MCQ·Easy–moderate
Open
Mean deviation about mean
The mean deviation about the mean for the data
$x_i$ 5 7 9 10 12 15
$f_i$ 8 6 2 2 2 6
is equal to:
1. (1) $\dfrac{40}{13}$
2. (2) $\dfrac{42}{13}$
3. (3) $\dfrac{44}{13}$
4. (4) $\dfrac{46}{13}$
MathsJEE Main 5 Apr 2026, Shift 2·Q10·MCQ·Tough
Open
Median of a frequency distribution
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:
1. (1)56
2. (2)42
3. (3)72
4. (4)90
MathsJEE Main 6 Apr 2026, Shift 1·Q9·MCQ·Easy–moderate
Open
Mean and standard deviation
A data consists of 20 observations $x_1, x_2, \ldots, x_{20}$ . If $\displaystyle\sum_{i=1}^{20}(x_i + 5)^2 = 2500$ and $\displaystyle\sum_{i=1}^{20}(x_i - 5)^2 = 100$ , then the ratio of mean to standard deviation of this data is:
1. (1) $2:1$
2. (2) $3:1$
3. (3) $3:2$
4. (4) $4:1$
MathsJEE Main 6 Apr 2026, Shift 2·Q8·MCQ·Easy–moderate
Open
Mean and variance
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:
1. (1) $x^2 - 35x + 306 = 0$
2. (2) $x^2 - 41x + 420 = 0$
3. (3) $x^2 - 45x + 506 = 0$
4. (4) $x^2 - 37x + 342 = 0$
MathsJEE Main 8 Apr 2026, Shift 2·Q7·MCQ·Easy–moderate
Open
Combined variance of two groups
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:
1. (1)5.96
2. (2)6.14
3. (3)6.04
4. (4)6.24

Class	4–8	8–12	12–16	16–20
Frequency	3	$\lambda$	4	7

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

$x_i$	5	7	9	10	12	15
$f_i$	8	6	2	2	2	6