JEE Main · Maths · Statistics
Variance and SD: JEE Main previous year questions
72 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 21 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 72
- in 71 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.6
- model; history: 0.6 a shift on average, typically 0.4–0.9
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 71 of 108 shifts: 72 questions, #27 of 196 topics.
- 02
38% of its questions since 2020 tested an idea no earlier year had asked; 36 repeated an idea from the year before.
- 03
The most repeated idea is Finding Unknown Observations from Mean and Variance, asked 22 times in 22 shifts (2020, 2021, 2022, 2023, 2024, 2025, 2026), most often as “find unknown data from mean and variance”.
- 04
JEE Main has asked 20 of the 62 ideas in this topic; 39 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (60%); 40% need a numerical answer, 22% are easy and 6% hard.
- 06
The skill tested most is calculation (64%), then multi-step (33%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 11 in 12 shifts · 2021: 17 in 24 shifts · 2022: 10 in 24 shifts · 2023: 13 in 12 shifts · 2024: 11 in 18 shifts · 2025: 4 in 8 shifts · 2026: 6 in 9 shifts.
- Up to 2023
- 0.6
- a shift, of 25
- Since 2024
- 0.6
- 0.0
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 71/108
- 66% of analysed shifts
Recent framings
- combined variance of two sets
- mean to SD ratio from shifted square sums
- find unknown observations from mean and variance
Revise first
- Finding Unknown Observations from Mean and Variance · asked 2020, 2021, 2022, 2023, 2024, 2025, 2026
- Correcting Incorrect Variance · asked 2020, 2021, 2022, 2023, 2024, 2025
- Combined Variance of Two Sets · asked 2021, 2023, 2026
How it is asked
Difficulty, format and skill
Across all 72 questions on Variance and SD since 2017.
Difficulty
QUESTIONS- Easy16 · 22%
- Medium52 · 72%
- Hard4 · 6%
Format
SHARE- Single correct · 43 Q60%
- Numerical value · 29 Q40%
Skill tested
SHARE- Calculation · 46 Q64%
- Multi-step · 24 Q33%
- Application · 1 Q1%
- Conceptual · 1 Q1%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 20 of the 62 ideas in this topic. 39 have never been asked yet.
- Asked directly20 · 32%
- Touched inside another question3 · 5%
- Never asked39 · 63%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
19 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
20 different ideas were tested; 10 came more than once.
find unknown data from mean and variance
Single correct · 22 shifts · 7 numericalfind unknown data from mean and variance
Single correct · 10 shifts · 3 numericalfind unknown data from mean and variance
Single correct · 7 shifts · 3 numericalunknown frequency from mean of grouped data
Numerical value · 6 shifts · 4 numericalfind unknown data from mean and variance
Single correct · 4 shiftsvariance of frequency table
Single correct · 3 shifts · 1 numericalfind unknown data from mean and variance
Single correct · 3 shiftsfind unknown data from mean and variance
Numerical value · 3 shifts · 3 numericalfind unknown data from mean and variance
Numerical value · 2 shifts · 1 numericalextreme observations from mean and variance
Numerical value · 2 shifts · 1 numericalmean to sd ratio from shifted square sums
Single correct · 1 shiftfind standard deviation from sums of squares
Single correct · 1 shiftfind n from mean and variance
Single correct · 1 shiftvariance of random variable from draw
Single correct · 1 shiftfind unknown frequency then variance
Numerical value · 1 shift · 1 numericalfind unknown from mean and variance
Numerical value · 1 shift · 1 numericalvariance after removing wrong observations
Numerical value · 1 shift · 1 numericalfind unknown data from mean and variance
Numerical value · 1 shift · 1 numericalfind n from variance of first n naturals
Numerical value · 1 shift · 1 numericalcommon difference from variance of ap
Numerical value · 1 shift · 1 numerical
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Finding Unknown Observations from Mean and Variancefind unknown data from mean and variance | 22 | 22 | Single correctMulti-step | 7 | |
| Correcting Incorrect Variancefind unknown data from mean and variance | 10 | 10 | Single correctCalculation | 3 | |
| Combined Variance of Two Setsfind unknown data from mean and variance | 7 | 7 | Single correctCalculation | 3 | |
| Mean of Discrete Dataunknown frequency from mean of grouped data | 6 | 6 | Numerical valueCalculation | 4 | |
| Effect of Linear Transformationsfind unknown data from mean and variance | 4 | 4 | Single correctCalculation | – | |
| Variance of Discrete Frequency Distributionvariance of frequency table | 3 | 3 | Single correctCalculation | 1 | |
| Variance via Arbitrary Point Deviationsfind unknown data from mean and variance | 3 | 3 | Single correctCalculation | – | |
| Finding Unknown Frequency via Variancefind unknown data from mean and variance | 3 | 3 | Numerical valueCalculation | 3 | |
| Variance Formula Calculationfind unknown data from mean and variance | 2 | 2 | Numerical valueCalculation | 1 | |
| Maximum Variance of Bounded Dataextreme observations from mean and variance | 2 | 2 | Numerical valueConceptual | 1 | |
| Algebraic Expansion of Squared Deviationsmean to sd ratio from shifted square sums | 1 | 1 | Single correctCalculation | – | |
| Calculating Sum of Squares from Variancefind standard deviation from sums of squares | 1 | 1 | Single correctCalculation | – | |
| Finding Number of Observations from Variancefind n from mean and variance | 1 | 1 | Single correctCalculation | – | |
| Variance via Relative Frequenciesvariance of random variable from draw | 1 | 1 | Single correctMulti-step | – | |
| Variance of Continuous Grouped Datafind unknown frequency then variance | 1 | 1 | Numerical valueCalculation | 1 | |
| Relationship Between RMS, Mean, and Variancefind unknown from mean and variance | 1 | 1 | Numerical valueCalculation | 1 | |
| Updating Variance After Removing an Observationvariance after removing wrong observations | 1 | 1 | Numerical valueCalculation | 1 | |
| Minimum Sum of Squared Deviationsfind unknown data from mean and variance | 1 | 1 | Numerical valueMulti-step | 1 | |
| Variance of First n Naturalsfind n from variance of first n naturals | 1 | 1 | Numerical valueCalculation | 1 | |
| Variance of an Arithmetic Progressioncommon difference from variance of ap | 1 | 1 | Numerical valueCalculation | 1 |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Variance and SD questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20266 questions in 6 shifts
- 2 Apr, Shift 1Q8If the mean of the data | Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | | Frequency | 2 | | 28 | 54 | | 5 | is ,…
Idea: Mean of Discrete Data
MediumSingle correct - 2 Apr, Shift 2Q9The mean and variance of observations are 8 and 16, respectively. If the sum of the first observations is 48 and the sum of…
Idea: Finding Number of Observations from Variance
New ideaEasySingle correct - 4 Apr, Shift 2Q8For 10 observations , if and , then their standard…
Idea: Calculating Sum of Squares from Variance
New ideaMediumSingle correct - 6 Apr, Shift 1Q9A data consists of 20 observations . If and , then…
Idea: Algebraic Expansion of Squared Deviations
New ideaMediumSingle correct - 6 Apr, Shift 2Q8Let the mean and the variance of seven observations , , be 8 and 16 respectively. Then the…
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct - 8 Apr, Shift 2Q7A 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…
Idea: Combined Variance of Two Sets
EasySingle correct
JEE Main 20254 questions in 4 shifts
- 2 Apr, Shift 2Q8If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then is equal to :
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct - 3 Apr, Shift 2Q9Let the Mean and Variance of five observations and , be 5 and 10 respectively. Then…
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct - 4 Apr, Shift 2Q8Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and respectively. Then the mean…
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct - 7 Apr, Shift 1Q9The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40.…
Idea: Correcting Incorrect Variance
Asked the year beforeEasySingle correct
JEE Main 202411 questions in 11 shifts
- 4 Apr, Shift 1Q20Let . Let the mean and the variance of 6 observations be 2 and 23,…
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct - 5 Apr, Shift 2Q29Let the mean and the standard deviation of the probability distribution | X | | 1 | 0 | | |---|---|---|---|---| | P(X) |…
Idea: Variance Formula Calculation
New ideaMediumNumerical value · figure - 6 Apr, Shift 1Q18The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation…
Idea: Correcting Incorrect Variance
Asked the year beforeEasySingle correct - 8 Apr, Shift 2Q30Let and . Let the mean, the mean deviation about the mean and the variance of the 5 observations…
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeHardNumerical value - 9 Apr, Shift 2Q19If the variance of the frequency distribution | | | | | | | | |---|---|---|---|---|---|---| | | 2 | 1…
Idea: Variance of Discrete Frequency Distribution
Asked the year beforeMediumSingle correct - 1 Feb, Shift 2Q19Consider observations such that and ,…
Idea: Variance via Arbitrary Point Deviations
MediumSingle correct - 27 Jan, Shift 1Q20Let be 10 observations such that and . Then the…
Idea: Variance Formula Calculation
New ideaMediumSingle correct - 29 Jan, Shift 1Q30If the mean and variance of the data where , are 56 and 66.2 respectively,…
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumNumerical value - 30 Jan, Shift 2Q30The variance of the data | | 0 | 1 | 5 | 6 | 10 | 12 | 17 | |---|---|---|---|---|---|---|---| | | 3 | 2 | 3 | 2 | 6…
Idea: Variance of Discrete Frequency Distribution
Asked the year beforeEasyNumerical value - 31 Jan, Shift 1Q17Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable to be the number of rotten apples in…
Idea: Variance via Relative Frequencies
New ideaMediumSingle correct - 31 Jan, Shift 2Q18Let the mean and the variance of 6 observations be 55 and 194, respectively. If , then is
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct
JEE Main 202313 questions in 12 shifts
- 6 Apr, Shift 1Q17The 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…
Idea: Combined Variance of Two Sets
MediumSingle correct - 6 Apr, Shift 2Q29If the mean and variance of the frequency distribution : 2, 4, 6, 8, 10, 12, 14, 16 : 4, 4, , 15, 8, , 4, 5 are 9…
Idea: Finding Unknown Frequency via Variance
MediumNumerical value · figure - 8 Apr, Shift 1Q30Let the mean and variance of 8 numbers be 9 and 9.25 respectively. If , then is equal to __________.
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumNumerical value - 8 Apr, Shift 2Q18Let the mean and variance of 12 observations be and respectively. Later on, it was observed that two observations were…
Idea: Correcting Incorrect Variance
Asked the year beforeMediumSingle correct - 10 Apr, Shift 1Q30If the mean of the frequency distribution | Class : | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | Frequency : | 2 | 3 | | 5 | 4 | is 28,…
Idea: Variance of Continuous Grouped Data
New ideaMediumNumerical value · figure - 10 Apr, Shift 2Q19Let be the mean and be the standard deviation of the distribution : , , , , , : , ,…
Idea: Variance of Discrete Frequency Distribution
New ideaMediumSingle correct · figure - 11 Apr, Shift 1Q13Let be in an arithmetic progression, with and their mean equal to 200. If…
Idea: Mean of Discrete Data
MediumSingle correct - 11 Apr, Shift 1Q18Let 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…
Idea: Combined Variance of Two Sets
MediumSingle correct - 11 Apr, Shift 2Q18Let the mean of observations and be and their variance be . Then their mean deviation about the mean is…
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct - 12 Apr, Shift 1Q24Let the positive numbers and be in a G.P. Let their mean and variance be and …
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeHardNumerical value - 13 Apr, Shift 1Q29Let the mean of the data | | 1 | 3 | 5 | 7 | 9 | | Frequency () | 4 | 24 | 28 | | 8 | be 5. If and are…
Idea: Finding Unknown Frequency via Variance
MediumNumerical value - 13 Apr, Shift 2Q29The 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…
Idea: Correcting Incorrect Variance
Asked the year beforeEasyNumerical value - 15 Apr, Shift 1Q19The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded…
Idea: Correcting Incorrect Variance
Asked the year beforeEasySingle correct
JEE Main 202210 questions in 10 shifts
- 26 Jul, Shift 2Q26The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were…
Idea: Updating Variance After Removing an Observation
New ideaMediumNumerical value - 27 Jul, Shift 1Q22The 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…
Idea: Correcting Incorrect Variance
Asked the year beforeEasyNumerical value - 29 Jul, Shift 1Q22Let the mean and the variance of 20 observations be 15 and 9, respectively. For , if the…
Idea: Relationship Between RMS, Mean, and Variance
New ideaMediumNumerical value - 26 Jun, Shift 1Q18The 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 25 M…
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct - 26 Jun, Shift 2Q17The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such…
Idea: Correcting Incorrect Variance
Asked the year beforeMediumSingle correct - 27 Jun, Shift 2Q16The mean and variance of the data , where , are and respectively. Then is equal to
Idea: Finding Unknown Observations from Mean and Variance
Asked the year beforeMediumSingle correct - 28 Jun, Shift 1 · Q23Correcting Incorrect VarianceAsked the year beforeEasy
- 28 Jun, Shift 2 · Q22Maximum Variance of Bounded DataMedium
- 29 Jun, Shift 1 · Q20Finding Unknown Observations from Mean and VarianceAsked the year beforeMedium
- 29 Jun, Shift 2 · Q17Finding Unknown Observations from Mean and VarianceAsked the year beforeMedium
JEE Main 202117 questions in 17 shifts
- 3 Aug, Shift 1 · Q77Variance via Arbitrary Point DeviationsAsked the year beforeEasy
- 3 Aug, Shift 2 · Q88Finding Unknown Observations from Mean and VarianceAsked the year beforeMedium
- 4 Aug, Shift 2 · Q77Finding Unknown Observations from Mean and VarianceAsked the year beforeMedium
- 26 Aug, Shift 1 · Q80Correcting Incorrect VarianceAsked the year beforeMedium
- 26 Aug, Shift 2 · Q86Finding Unknown Observations from Mean and VarianceAsked the year beforeMedium
- 27 Aug, Shift 1 · Q88Variance of First n NaturalsNew ideaEasy
- 27 Aug, Shift 2 · Q90Combined Variance of Two SetsNew ideaMedium
- 31 Aug, Shift 1 · Q90Mean of Discrete DataAsked the year beforeMedium
- 31 Aug, Shift 2 · Q77Finding Unknown Observations from Mean and VarianceAsked the year beforeMedium
- 24 Feb, Shift 2 · Q81Finding Unknown Observations from Mean and VarianceAsked the year beforeMedium
- 26 Feb, Shift 2 · Q85Minimum Sum of Squared DeviationsNew ideaMedium
- 22 Jul, Shift 2 · Q89Mean of Discrete DataAsked the year beforeMedium
- 25 Jul, Shift 2 · Q68Combined Variance of Two SetsNew ideaMedium
- 16 Mar, Shift 2 · Q86Combined Variance of Two SetsNew ideaEasy
- 17 Mar, Shift 2 · Q84Combined Variance of Two SetsNew ideaHard
- 18 Mar, Shift 1 · Q87Mean of Discrete DataAsked the year beforeEasy
- 18 Mar, Shift 2 · Q64Effect of Linear TransformationsAsked the year beforeMedium
JEE Main 202011 questions in 11 shifts
- 8 Jan, Shift 1 · Q67Effect of Linear TransformationsNew ideaMedium
- 8 Jan, Shift 2 · Q68Correcting Incorrect VarianceNew ideaEasy
- 9 Jan, Shift 1 · Q68Effect of Linear TransformationsNew ideaMedium
- 2 Sep, Shift 1 · Q67Effect of Linear TransformationsNew ideaMedium
- 2 Sep, Shift 2 · Q75Variance of an Arithmetic ProgressionNew ideaMedium
- 3 Sep, Shift 1 · Q67Maximum Variance of Bounded DataNew ideaHard
- 3 Sep, Shift 2 · Q67Variance via Arbitrary Point DeviationsNew ideaEasy
- 4 Sep, Shift 1 · Q68Finding Unknown Observations from Mean and VarianceNew ideaMedium
- 4 Sep, Shift 2 · Q71Finding Unknown Frequency via VarianceNew ideaEasy
- 5 Sep, Shift 1 · Q68Finding Unknown Observations from Mean and VarianceNew ideaMedium
- 6 Sep, Shift 2 · Q75Mean of Discrete DataNew ideaMedium
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.
More topics in Statistics
This is the only topic tagged in this chapter.