JEE Main Maths · Statistics

Variance and SD in JEE Main

Name: Variance and SD: JEE Main previous year questions
Creator: Lumi

Variance and SD (Maths, Statistics) came 27 times in 26 of the 42 JEE Main shifts Lumi analysed, across 10 distinct ideas. 15 of them came in 2024–26; it was last asked in 2026.

Questions: 27; in 26 shifts
Ideas asked: 10; 6 asked more than once
Numerical answer: 7; 26% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 7Medium 20Hard 0

Format

Single correct20 Q
Numerical value7 Q

Ideas inside the topic

10 ideas

Finding Unknown Observations from Mean and Variance8 Q
Combined Variance of Two Sets4 Q
Mean of Discrete Data4 Q
Correcting Incorrect Variance3 Q
Variance of Discrete Frequency Distribution2 Q
Effect of Linear Transformations2 Q
Algebraic Expansion of Squared Deviations1 Q
Finding Number of Observations from Variance1 Q
Variance via Relative Frequencies1 Q
Calculating Sum of Squares from Variance1 Q

Where it sits

Part of Statistics, which had 32 questions in all. Variance and SD accounts for 84% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Some questions sit in other chapters too: Probability.

Every question

All 27 Variance and SD questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q8If 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 $21$ ,…MediumSingle correct
2 Apr 2026, Shift 2 · Q9The 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…EasySingle correct
4 Apr 2026, Shift 2 · Q8For 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…MediumSingle correct
6 Apr 2026, Shift 1 · Q9A 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…MediumSingle correct
6 Apr 2026, Shift 2 · Q8Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$ , $\alpha<\beta$ , be 8 and 16 respectively. Then the…MediumSingle correct
8 Apr 2026, Shift 2 · Q7A 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…EasySingle correct
2 Apr 2025, Shift 2 · Q8If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then $a+b+ab$ is equal to :MediumSingle correct
3 Apr 2025, Shift 2 · Q9Let the Mean and Variance of five observations $x_1 = 1, x_2 = 3, x_3 = a, x_4 = 7$ and $x_5 = b,\ a > b$ , be 5 and 10 respectively. Then…MediumSingle correct
4 Apr 2025, Shift 2 · Q8Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and $\sqrt{2}$ respectively. Then the mean…MediumSingle correct
7 Apr 2025, Shift 1 · Q9The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40.…EasySingle correct
9 Apr 2024, Shift 2 · Q19If the variance of the frequency distribution | $x$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ | |---|---|---|---|---|---|---| | $f$ | 2 | 1…MediumSingle correct
29 Jan 2024, Shift 1 · Q30If 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,…MediumNumerical value
30 Jan 2024, Shift 2 · Q30The variance $\sigma^2$ of the data | $x_i$ | 0 | 1 | 5 | 6 | 10 | 12 | 17 | |---|---|---|---|---|---|---|---| | $f_i$ | 3 | 2 | 3 | 2 | 6…EasyNumerical value
31 Jan 2024, Shift 1 · Q17Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in…MediumSingle correct
31 Jan 2024, Shift 2 · Q18Let the mean and the variance of 6 observations $a, b, 68, 44, 48, 60$ be 55 and 194, respectively. If $a>b$ , then $a+3b$ isMediumSingle correct
6 Apr 2023, Shift 1 · Q17The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and…MediumSingle correct
8 Apr 2023, Shift 2 · Q18Let the mean and variance of 12 observations be $\frac{9}{2}$ and $4$ respectively. Later on, it was observed that two observations were…MediumSingle correct
11 Apr 2023, Shift 1 · Q13Let $x_1, x_2, \ldots, x_{100}$ be in an arithmetic progression, with $x_1 = 2$ and their mean equal to 200. If…MediumSingle correct
11 Apr 2023, Shift 1 · Q18Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the…MediumSingle correct
13 Apr 2023, Shift 2 · Q29The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks…EasyNumerical value
29 Jun 2022, Shift 1 · Q20Let the mean and the variance of 5 observations $x_1, x_2, x_3, x_4, x_5$ be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean…MediumSingle correct
3 Aug 2021, Shift 2 · Q88The 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…MediumNumerical value
16 Mar 2021, Shift 2 · Q86Consider the statistics of two sets of observations as follows : Size Mean Variance Observation I 10 2 2 Observation II n 3 1 If the…EasyNumerical value
18 Mar 2021, Shift 1 · Q87The 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.…EasyNumerical value
8 Jan 2020, Shift 1 · Q67The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p…MediumSingle correct
2 Sep 2020, Shift 1 · Q67Let $X=\{x\in\mathbf{N} : 1\le x\le 17\}$ and $Y=\{ax+b : x\in X$ and $a, b\in\mathbf{R}, a>0\}$ . If mean and variance of elements of Y…MediumSingle correct
6 Sep 2020, Shift 2 · Q75Consider the data on $x$ taking the values $0, 2, 4, 8, \ldots, 2^n$ with frequencies ${}^nC_0, {}^nC_1, {}^nC_2, \ldots, {}^nC_n$ …MediumNumerical value