Understanding numerical data becomes much easier when students learn how to organize, analyze, and interpret information mathematically, and that is exactly what students learn in Statistics. This chapter mainly focuses on mean, median, mode, grouped frequency distribution, and data interpretation techniques that help students improve calculation accuracy and analytical reasoning for CBSE board exams. Practicing Statistics Class 10 MCQs regularly helps students strengthen formula application, table interpretation, and data-handling skills for competency-based objective questions. The latest CBSE pattern now focuses more on logical interpretation and application-oriented understanding instead of direct memorization, which makes regular practice of Statistics Class 10 MCQs with Answers extremely important for improving confidence and solving speed. Students preparing for examinations can also explore MCQs, Class 10 MCQs, CBSE Board, and MCQs Class 10 Maths for chapter-wise objective practice based on the latest syllabus and board exam trends.
Why Statistics is Important in Class 10 Maths
Statistics is one of the most practical chapters in Mathematics because it teaches students how numerical information is collected, arranged, and interpreted systematically.
This chapter helps students understand:
how averages are calculated,
how data is organized,
how frequency tables work,
and how mathematical analysis helps in understanding patterns.
This chapter is important because:
- Statistics Class 10 MCQs are frequently asked in CBSE board exams
- Data interpretation skills improve significantly
- Calculation accuracy becomes stronger
- Students learn practical numerical analysis
- Competency-based questions are increasing
- Logical reasoning and observation improve naturally
- Formula application becomes easier with practice
Students who practice Statistics MCQs Class 10 regularly usually solve data-handling questions more confidently in examinations.
Important Concepts Covered in Statistics Class 10 MCQs
Before solving Statistics Class 10 MCQs with Answers, students should revise all important concepts and formulas carefully because many objective questions are directly formula and table based.
Important concepts covered in this chapter include:
- Mean
- Median
- Mode
- Grouped data
- Frequency distribution
- Cumulative frequency
- Class intervals
- Observation values
- Frequency tables
- Statistical calculations
- Empirical relationship
- Data interpretation
These concepts are extremely important for solving CBSE Statistics Class 10 MCQs accurately.
Statistics Class 10 MCQs with Answers
Practice important and exam-oriented Statistics Class 10 MCQs designed according to the latest CBSE pattern and competency-based learning approach. These objective questions help students improve data interpretation, formula understanding, statistical calculations, and board exam preparation skills effectively.
Q. The mean of the numbers 12, 18, 24, 30, and 36 is:
A) 20
B) 22
C) 24
D) 26
Answer: C
Explanation:
Mean = (12 + 18 + 24 + 30 + 36) / 5
= 120 / 5
= 24.
Q. The median of the data 8, 12, 15, 18, 20, 25, 30 is:
A) 15
B) 18
C) 20
D) 25
Answer: B
Explanation:
Since there are 7 observations, median is the middle term.
Middle term = 18.
Q. Find the mode of the data: 7, 9, 11, 9, 14, 9, 16, 11.
A) 7
B) 9
C) 11
D) 14
Answer: B
Explanation:
Mode is the observation occurring maximum times.
9 appears 3 times.
Q. The class mark of the interval 40-50 is:
A) 40
B) 45
C) 50
D) 55
Answer: B
Explanation:
Class mark = (Lower limit + Upper limit)/2
= (40 + 50)/2
= 45.
Q. If the mean of 6 observations is 18, then their total sum is:
A) 96
B) 102
C) 108
D) 120
Answer: C
Explanation:
Sum = Mean x Number of observations
= 18 x 6
= 108.
Q. The median of the first 9 odd numbers is:
A) 7
B) 9
C) 11
D) 13
Answer: B
Explanation:
First 9 odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17.
Middle term = 9.
Q. Which measure of central tendency is affected most by extreme values?
A) Mean
B) Median
C) Mode
D) None of these
Answer: A
Explanation:
Mean uses all observations, so extreme values affect it the most.
Q. If the mode of a distribution is 24 and mean is 30, then median is:
A) 26
B) 28
C) 30
D) 32
Answer: B
Explanation:
Mode = 3Median - 2Mean
24 = 3Median - 60
3Median = 84
Median = 28.
Q. The arithmetic mean of the first 10 natural numbers is:
A) 5
B) 5.5
C) 6
D) 6.5
Answer: B
Explanation:
Mean of first n natural numbers = (n + 1)/2
= (10 + 1)/2
= 5.5.
Q. The cumulative frequency of a class is obtained by:
A) Adding all frequencies
B) Multiplying frequencies
C) Adding frequencies up to that class
D) Dividing frequencies
Answer: C
Explanation:
Cumulative frequency is the running total of frequencies.
Q. Find the mean of: 15, 20, 25, 30, 35.
A) 20
B) 25
C) 30
D) 35
Answer: B
Explanation:
Mean = (15 + 20 + 25 + 30 + 35)/5
= 125/5
= 25.
Q. The mode of the data 18, 22, 22, 25, 30, 30, 30, 35 is:
A) 22
B) 25
C) 30
D) 35
Answer: C
Explanation:
30 appears maximum 3 times.
Q. If the mean of x, x+2, x+4, x+6, x+8 is 14, then x is:
A) 8
B) 10
C) 12
D) 14
Answer: B
Explanation:
Sum = 5x + 20
(5x + 20)/5 = 14
x + 4 = 14
x = 10.
Q. The median of 5, 8, 12, 15, 18, 21 is:
A) 12
B) 13.5
C) 15
D) 16
Answer: B
Explanation:
Median = average of middle two terms
= (12 + 15)/2
= 13.5.
Q. The modal class is the class having:
A) Least frequency
B) Highest frequency
C) Zero frequency
D) Equal frequency
Answer: B
Explanation:
Modal class is the class interval with maximum frequency.
Q. The mean of 4 observations is 16. If one observation is removed, the mean becomes 14. The removed observation is:
A) 18
B) 20
C) 22
D) 24
Answer: C
Explanation:
Original sum = 4 x 16 = 64
New sum = 3 x 14 = 42
Removed observation = 64 - 42 = 22.
Q. The class size of interval 25-35 is:
A) 5
B) 10
C) 15
D) 20
Answer: B
Explanation:
Class size = 35 - 25 = 10.
Q. If all observations in a data increase by 5, then mean will:
A) Increase by 5
B) Decrease by 5
C) Remain same
D) Double
Answer: A
Explanation:
Mean changes by the same amount added to each observation.
Q. The median class is determined by:
A) Highest frequency
B) Lowest frequency
C) N/2
D) Mean value
Answer: C
Explanation:
Median class contains the cumulative frequency just greater than N/2.
Q. Find the mean of first 5 multiples of 7.
A) 14
B) 18
C) 21
D) 28
Answer: C
Explanation:
Multiples are 7, 14, 21, 28, 35
Mean = 105/5 = 21.
Q. The empirical relation between mean, median, and mode is:
A) Mode = Mean + Median
B) Mode = 2Median - Mean
C) Mode = 3Median - 2Mean
D) Mode = Mean - Median
Answer: C
Explanation:
This is the standard empirical formula used in statistics.
Q. The mean of the data 9, 11, 13, 15, 17 is:
A) 11
B) 12
C) 13
D) 14
Answer: C
Explanation:
Mean = (9 + 11 + 13 + 15 + 17)/5
= 65/5
= 13.
Q. Which of the following is not a measure of central tendency?
A) Mean
B) Median
C) Mode
D) Range
Answer: D
Explanation:
Range measures dispersion, not central tendency.
Q. If the mean of 8 observations is 25, then total sum of observations is:
A) 150
B) 175
C) 200
D) 225
Answer: C
Explanation:
Sum = Mean x Number of observations
= 25 x 8
= 200.
Q. The median of the first 11 natural numbers is:
A) 5
B) 5.5
C) 6
D) 7
Answer: C
Explanation:
First 11 natural numbers are 1 to 11.
Middle term = 6.
Q. If the mode of data is 18 and median is 20, then mean is:
A) 19
B) 20
C) 21
D) 22
Answer: C
Explanation:
Mode = 3Median - 2Mean
18 = 60 - 2Mean
2Mean = 42
Mean = 21.
Q. Which graph is commonly used to determine median graphically?
A) Histogram
B) Pie chart
C) Ogive
D) Bar graph
Answer: C
Explanation:
Median is graphically determined using an ogive curve.
Q. Find the mode of the data: 4, 5, 6, 7, 8.
A) 4
B) 5
C) 6
D) No mode
Answer: D
Explanation:
No observation repeats, so there is no mode.
Q. If each observation is multiplied by 3, then the mean becomes:
A) One-third
B) Triple
C) Double
D) Same
Answer: B
Explanation:
Mean changes in the same ratio as the observations.
Q. The cumulative frequency just before the median class is called:
A) Frequency
B) Class size
C) cf
D) xi
Answer: C
Explanation:
In median formula, cumulative frequency before median class is represented by cf.
Important Instructions Before Solving Statistics MCQs
- Read the frequency table carefully before applying any formula because small observation mistakes can affect the entire calculation.
- Check class intervals properly before identifying median and modal class.
- Arrange data carefully whenever required because median calculations depend on correct ordering.
- Use formulas step-by-step instead of solving mentally because grouped data calculations require proper substitution.
- Calculate cumulative frequencies carefully because students often make addition mistakes in tables.
- Practice competency-based and application-oriented Statistics Class 10 MCQs regularly because the latest CBSE pattern focuses heavily on analytical understanding.
- Avoid rushing calculations because statistical questions require accuracy and proper interpretation.
- Revise all formulas regularly to improve solving speed and confidence during examinations.
Common Mistakes Students Make in Statistics Questions
Many students lose marks in Statistics Class 10 MCQs because of formula confusion and incorrect table interpretation.
Some common mistakes include:
- Incorrect frequency addition
- Wrong median class identification
- Formula substitution mistakes
- Cumulative frequency confusion
- Calculation errors during simplification
- Observation arrangement mistakes
- Incorrect class interval interpretation
Students should solve statistical calculations carefully instead of depending only on shortcuts.
Understanding Mean, Median, and Mode in Simple Language
Statistics mainly helps students understand large sets of numerical data in an organized mathematical form.
The three most important measures in this chapter are:
- mean,
- median,
- and mode.
Mean represents the average value of observations.
Median represents the middle value when observations are arranged properly.
Mode represents the value that occurs most frequently in a dataset.
For grouped data:
information is arranged into class intervals,
frequencies are recorded,
and formulas are used to calculate statistical values accurately.
This chapter becomes easier when students understand the logic behind data organization instead of memorizing formulas only.
Important Formulas Used in Statistics Class 10 MCQs
The following formulas are extremely important for solving Statistics MCQs Class 10 and board exam questions.
| Concept | Formula |
|---|---|
| Mean | Σfx / Σf |
| Median | l + [(n/2 – cf) / f] × h |
| Mode | l + [(f1 – f0) / (2f1 – f0 – f2)] × h |
| Empirical Relationship | Mode = 3 Median – 2 Mean |
Students should revise these formulas regularly because many Statistics Class 10 objective questions are directly calculation based.
Important Terms Students Must Understand
The following terms are very important for solving Statistics Class 10 MCQs with Answers correctly.
| Term | Meaning |
|---|---|
| Frequency | Number of times an observation occurs |
| Class Interval | Range used to group data |
| Cumulative Frequency | Running total of frequencies |
| Mean | Average value of observations |
| Median | Middle value of arranged data |
| Mode | Most repeated observation |
| Observation | Individual data value |
Understanding these terms properly improves conceptual clarity and solving speed.
Understanding Frequency Tables and Data Analysis
One of the most important skills in this chapter is understanding how large numerical data is organized systematically.
Students can improve statistical understanding by:
- Observing tables carefully
- Practicing grouped data questions regularly
- Understanding frequency relationships
- Comparing mean, median, and mode values
- Interpreting numerical patterns logically
Once students become comfortable with data analysis and formula application, solving Statistics Class 10 MCQs with Answers becomes much easier.
Revision Notes for Statistics Class 10 MCQs
Students should revise these important points regularly before exams:
- Mean represents average value
- Median represents middle observation
- Mode represents highest frequency value
- Grouped data uses class intervals
- Frequency tables organize information
- Formula substitution requires accuracy
- Cumulative frequency calculation is important
- Data interpretation improves problem-solving accuracy
Short revision sessions help improve retention and board exam confidence significantly.
Final Summary
Practicing Statistics Class 10 MCQs with Answers is one of the best ways to improve data interpretation, analytical reasoning, and calculation accuracy for Class 10 Maths. This chapter is highly practical because students must understand grouped data, frequency distribution, and statistical relationships together instead of focusing only on direct formulas. Students preparing for CBSE board exams should focus on formula clarity, table interpretation, and regular objective practice to improve confidence and solving speed naturally. Consistent practice of Statistics Class 10 MCQs helps students strengthen logical reasoning, numerical analysis, mathematical accuracy, and overall board exam performance effectively.