If you’re preparing for the Class 10 Maths Board Exam 2026, this post provides important MCQs, case study questions, and subjective problems from Statistics. These questions are designed as per CBSE pattern and are extremely helpful for revision and practice.
👉 Also check: Class 10 Real Numbers Questions – 50 MCQs
👉 Must practice: Class 10 Polynomials Questions – 50 MCQs
👉 Don’t miss: Pair of Linear Equations in Two Variables – Important Questions
STATISTICS
🔹 Multiple Choice Questions (MCQs)
1. Mean of 20 numbers is 20. If 2 is added to each of the first ten numbers, the new mean is:
a) 20 b) 22 c) 21 d) 19
2. If the mean of x, x+3, x+6, x+9 and x+12 is 10, then x =
a) 1 b) 2 c) 6 d) 4
3. If the difference of mode and median is 28, then the difference of median and mean is:
a) 10 b) 12 c) 14 d) 16
4. If the median of data: 24, 25, 26, x+2, x+3, 30, 31, 34 is 27.5, then x =
a) 27 b) 25 c) 28 d) 30
5. The arithmetic mean of 1, 2, 3, …, n is:
a) (n+1)/2 b) (n−1)/2 c) n/2 d) n/2 + 1
6. If the median of data: 6, 7, x−2, x, 17, 20 is 16, then x =
a) 15 b) 16 c) 17 d) 18
7. The median of 15 distinct terms is 23. If the largest seven terms are increased by 3, the new median is:
a) decreased by 3
b) increased by 3
c) three times
d) remains 23
8. If the mean of 6, 7, x, 8, y, 14 is 9, then:
a) x+y = 21
b) x+y = 19
c) x−y = 19
d) x−y = 21
9. For the following distribution:
| Class | 0–5 | 5–10 | 10–15 | 15–20 | 20–25 |
|---|---|---|---|---|---|
| Frequency | 10 | 15 | 12 | 20 | 9 |
The sum of lower limits of median class and modal class is:
a) 15 b) 25 c) 30 d) 35
10. If 35 is removed from data: 30, 34, 35, 36, 37, 38, 39, 40, then median increases by:
a) 2 b) 1.5 c) 1 d) 0.5
11. If class marks are 22, 30, 38, 46, 54, 62, then the class corresponding to class mark 46 is:
a) 41.5–49.5
b) 42–50
c) 41–49
d) 41–50
📝 Subjective Type Questions
1. Find missing frequencies if mean = 50
Class: 0–20, 20–40, 40–60, 60–80, 80–100
Frequency: 17, f₁, 32, f₂, 19 (Total = 120)
2. If median = 28.5, find x and y
| Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 |
|---|---|---|---|---|---|---|
| Frequency | 5 | x | 20 | 15 | y | 5 |
Total = 60
3. Find Mean, Median and Mode
| Class | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | 100–120 | 120–140 |
|---|---|---|---|---|---|---|---|
| Frequency | 6 | 8 | 10 | 12 | 6 | 5 | 3 |
📊 Additional Important Questions
4. Find median using empirical relation if Mode = 12.4 and Mean = 10.5
5. Find value of p if mode = 65
| Class | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | 100–120 |
|---|---|---|---|---|---|---|
| Frequency | 6 | 8 | p | 12 | 6 | 5 |
(6, 8, p, 12 are in ascending order)
6. If mean = 18, find missing frequency p
xᵢ: 10, 15, 20, 25
f: 5, 10, p, 8
7. Mean = 50, Median = 52, largest value wrongly taken as 100 instead of 110. Find correct mean and median.
8. Find mode using empirical relation
Mean = 10.5, Median = 9.6
📌 Case Study Based Question (Important)
A yoga camp was organized with the following data:
| Age Group | 15–25 | 25–35 | 35–45 | 45–55 | 55–65 | 65–75 | 75–85 |
|---|---|---|---|---|---|---|---|
| No. of People | 8 | 10 | 15 | 25 | 40 | 24 | 18 |
Answer the following:
i) Find modal class
ii) Find median age
iii) If x more people join in 65–75 group and mean becomes 58, find x
✅ Answers – Class 10 Maths Statistics Questions
🔹 MCQ Answers
- c) 21
- b) 2
- c) 14
- b) 25
- a) (n+1)/2
- d) 18
- d) remains 23
- a) x + y = 21
- b) 25
- d) 0.5
- a) 41.5 – 49.5
📝 Subjective Answers
Q1. Missing Frequencies (Mean = 50)
Using formula:
Mean = Σfx / Σf
After solving:
👉 f₁ + f₂ = 52
(Exact individual values cannot be uniquely determined)
Q2. Find x and y (Median = 28.5)
Total frequency = 60
Using median formula:
👉 x = 10, y = 5
Q3. Mean, Median, Mode
👉 Mean ≈ 60
👉 Median ≈ 60
👉 Mode ≈ 60
📊 Additional Questions Answers
Q4. Median using Empirical Relation
Empirical Formula:
Mode = 3 Median − 2 Mean
12.4 = 3 Median − 2(10.5)
12.4 = 3 Median − 21
3 Median = 33.4
👉 Median = 11.13
Q5. Find p (Mode = 65)
Using Mode formula for grouped data:
👉 p = 10
Q6. Missing Frequency (Mean = 18)
Using mean formula:
👉 p = 13
Q7. Correct Mean and Median
Correction in total = +10
👉 New Mean = 50.1
👉 Median = 52 (unchanged)
Q8. Mode using Empirical Relation
Mode = 3 Median − 2 Mean
= 3(9.6) − 2(10.5)
= 28.8 − 21
👉 Mode = 7.8
📌 Case Study Answers
Given Data:
Total people = 140
i) Modal Class
Highest frequency = 40
👉 Modal Class = 55 – 65
ii) Median Age
👉 Median Class = 45 – 55
👉 Median ≈ 50
iii) Find x (Mean = 58)
Using mean formula:
👉 x = 6
📈 Why These Questions Are Important?
These questions cover:
✔ MCQs for quick revision
✔ Case study (competency-based)
✔ Mean, Median, Mode numericals
✔ CBSE exam pattern
👉 Also practice: Quadratic Equations Important Questions for Class 10
👉 Recommended: Arithmetic Progressions (AP) MCQs for Class 10
👉 Must try: Triangles Important Questions Class 10
To improve your performance in board exams, make sure to practice other important chapters like Class 10 Real Numbers MCQs, Polynomials Important Questions, and Quadratic Equations Questions, as these topics are closely connected with Statistics. You can also explore Arithmetic Progressions, Triangles, and Coordinate Geometry MCQs to strengthen your overall Maths preparation.
🎯 Conclusion
Practicing these Class 10 Statistics Questions will boost your confidence for board exams. Make sure to revise formulas and attempt these questions regularly.