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Statistics: JEE Main Previous Year Questions (2021-2026)
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JEE Main Previous Year Questions (2021-2026):
Statistics
(January 2026)
Q1: 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
(a) 7
(b) 4
(c) 5
(d) 6
Ans: (c)
Sol:
Let the missing observations be x and y.
Page 2
JEE Main Previous Year Questions (2021-2026):
Statistics
(January 2026)
Q1: 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
(a) 7
(b) 4
(c) 5
(d) 6
Ans: (c)
Sol:
Let the missing observations be x and y.
To solve the system x + y = 10 and x
2
+ y
2
= 58 by finding x - y use the formula
Now add these equations x + y = 10 & x - y = 4
2x = 14 ? x = 7
Put x = 7 in x + y = 10
7 + y = 10 ? y = 3
missing numbers are 3 and 7.
Find the Median
The 10 observations in ascending order are: 2, 3, 3, 5, 7, 10, 11, 13, 15, 21.
Since n = 10, the median is the average of the 5th and 6th terms :
Median = (7+10)/2 = 8.5
Calculate Mean Deviation about Median
Q2: Let X = {x ? N : 1 = x = 19} and for some = {ax + b : x ? 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
(a) 20
(b) 100
(c) 80
(d) 60
Ans: (d)
Sol:
Page 3
JEE Main Previous Year Questions (2021-2026):
Statistics
(January 2026)
Q1: 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
(a) 7
(b) 4
(c) 5
(d) 6
Ans: (c)
Sol:
Let the missing observations be x and y.
To solve the system x + y = 10 and x
2
+ y
2
= 58 by finding x - y use the formula
Now add these equations x + y = 10 & x - y = 4
2x = 14 ? x = 7
Put x = 7 in x + y = 10
7 + y = 10 ? y = 3
missing numbers are 3 and 7.
Find the Median
The 10 observations in ascending order are: 2, 3, 3, 5, 7, 10, 11, 13, 15, 21.
Since n = 10, the median is the average of the 5th and 6th terms :
Median = (7+10)/2 = 8.5
Calculate Mean Deviation about Median
Q2: Let X = {x ? N : 1 = x = 19} and for some = {ax + b : x ? 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
(a) 20
(b) 100
(c) 80
(d) 60
Ans: (d)
Sol:
mean for Y is 30.
Variance for Y is 750
Page 4
JEE Main Previous Year Questions (2021-2026):
Statistics
(January 2026)
Q1: 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
(a) 7
(b) 4
(c) 5
(d) 6
Ans: (c)
Sol:
Let the missing observations be x and y.
To solve the system x + y = 10 and x
2
+ y
2
= 58 by finding x - y use the formula
Now add these equations x + y = 10 & x - y = 4
2x = 14 ? x = 7
Put x = 7 in x + y = 10
7 + y = 10 ? y = 3
missing numbers are 3 and 7.
Find the Median
The 10 observations in ascending order are: 2, 3, 3, 5, 7, 10, 11, 13, 15, 21.
Since n = 10, the median is the average of the 5th and 6th terms :
Median = (7+10)/2 = 8.5
Calculate Mean Deviation about Median
Q2: Let X = {x ? N : 1 = x = 19} and for some = {ax + b : x ? 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
(a) 20
(b) 100
(c) 80
(d) 60
Ans: (d)
Sol:
mean for Y is 30.
Variance for Y is 750
Substitute value of a from (1) in equation (2)
Let roots of quadratic equation is b
1
, b
2
So sum of possible values of b = sum of roots
Q3: The mean and variance of a data of 10 observations are 10 and 2, respectively. If an
observations a in this data is replaced by ß, then the mean and variance become 10.1 and
1.99, respectively. Then a + ß equals
(a) 15
(b) 10
(c) 5
(d) 20
Ans: (d)
Sol:
Given, total observation n = 10
Initial mean
Page 5
JEE Main Previous Year Questions (2021-2026):
Statistics
(January 2026)
Q1: 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
(a) 7
(b) 4
(c) 5
(d) 6
Ans: (c)
Sol:
Let the missing observations be x and y.
To solve the system x + y = 10 and x
2
+ y
2
= 58 by finding x - y use the formula
Now add these equations x + y = 10 & x - y = 4
2x = 14 ? x = 7
Put x = 7 in x + y = 10
7 + y = 10 ? y = 3
missing numbers are 3 and 7.
Find the Median
The 10 observations in ascending order are: 2, 3, 3, 5, 7, 10, 11, 13, 15, 21.
Since n = 10, the median is the average of the 5th and 6th terms :
Median = (7+10)/2 = 8.5
Calculate Mean Deviation about Median
Q2: Let X = {x ? N : 1 = x = 19} and for some = {ax + b : x ? 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
(a) 20
(b) 100
(c) 80
(d) 60
Ans: (d)
Sol:
mean for Y is 30.
Variance for Y is 750
Substitute value of a from (1) in equation (2)
Let roots of quadratic equation is b
1
, b
2
So sum of possible values of b = sum of roots
Q3: The mean and variance of a data of 10 observations are 10 and 2, respectively. If an
observations a in this data is replaced by ß, then the mean and variance become 10.1 and
1.99, respectively. Then a + ß equals
(a) 15
(b) 10
(c) 5
(d) 20
Ans: (d)
Sol:
Given, total observation n = 10
Initial mean
Sum of 10 observation
Initial variance
It is given that if a is replace by ß
Also new variance
? 1020 - a² + ß² = 10[1.99 + 102.01] = 10 × 104 = 1040
? ß² - a² = 20
? (ß + a)(ß - a) = 20
? (ß + a)(1) = 20 (substitute ß - a = 1)
? a + ß = 20
Read MoreFAQs on Statistics: JEE Main Previous Year Questions (2021-2026)
| 1. What are the most important statistics formulas asked in JEE Main exams? |  |
Ans. Mean, median, mode, standard deviation, and variance are the core formulas tested repeatedly in JEE Main statistics questions. Standard deviation measures data spread as σ = √[Σ(xi - mean)²/n], while variance equals σ². Coefficient of variation, skewness, and kurtosis also appear frequently. Students should master grouped and ungrouped data calculations, as previous year questions heavily emphasize these computational techniques for securing marks.
| 2. How do I solve mean deviation problems that keep appearing in JEE Main previous year papers? | |
Ans. Mean deviation calculates average distance of data points from central tendency: MD = Σ|xi - A|/n, where A is mean or median. For grouped data, use class midpoints and frequencies. JEE Main typically tests mean deviation around mean rather than median. Practice identifying whether questions require absolute deviations or squared deviations, as this distinction determines whether you're calculating mean deviation or standard deviation in exam scenarios.
| 3. Why do variance and standard deviation questions confuse me in statistics exams? | |
Ans. Variance (σ²) and standard deviation (σ) measure data dispersion differently-variance squares deviations while standard deviation doesn't. Students confuse them because both quantify spread, but standard deviation uses original units, making it more interpretable. In JEE Main problems, variance often appears in combined dataset questions requiring the formula: Combined variance = [n₁σ₁² + n₂σ₂² + n₁d₁² + n₂d₂²]/(n₁+n₂), where d represents deviation from combined mean.
| 4. What's the difference between coefficient of variation and standard deviation in JEE problems? | |
Ans. Coefficient of variation (CV) is a relative measure: CV = (σ/mean) × 100%, comparing variability across datasets with different means or units, while standard deviation is absolute. JEE Main uses CV when comparing two datasets' consistency-higher CV indicates greater relative variability. Standard deviation alone can't compare datasets meaningfully if their means differ significantly, making CV essential for comparative statistics questions testing data interpretation skills.
| 5. Which statistics topics from JEE Main 2021-2026 papers appear most frequently in exams? | |
Ans. Combined mean and variance of two or more datasets dominate JEE Main statistics questions consistently across 2021-2026 papers. Frequency distribution, grouped data calculations, and deviation methods rank second. Problems testing understanding of correlation and regression appear increasingly. Students should focus on mastering shortcut methods for combined statistics, practicing with authentic previous year questions, and referring to mind maps and flashcards on EduRev for quick concept revision before exams.
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