The chapter, Statistics, introduces students to understand how to organize, analyze, and interpret numerical data. It covers important concepts such as mean, median, mode, and grouped frequency distribution. Students also learn how to calculate measures of central tendency and interpret data accurately using mathematical methods.
The chapter also focuses on conceptual understanding and application-based problem-solving, helping students improve their accuracy and confidence. Practicing chapter-wise MCQs and preparing through CBSE Board resources and MCQs Class 10 Maths can help students revise important concepts and prepare according to the latest syllabus.
Topics Covered
Before solving Probability Class 10 MCQs with Answers, students should revise all important concepts carefully because many objective questions are directly concept and logic based. Important concepts covered in this chapter :
- Mean
- Median
- Mode
- Grouped data
- Frequency distribution
- Cumulative frequency
- Class intervals
- Observation values
- Frequency tables
- Statistical calculations
- Empirical relationship
- Data interpretation
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MCQs for Class 10 Maths Chapter 13 Statistics with Answers and Explanations
Practice important and exam-oriented Statistics Class 10 MCQs designed according to the latest CBSE Board pattern and competency-based learning approach. These objective questions help students improve data interpretation, formula understanding, statistical calculations, and board exam preparation skills effectively.
Q1. 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.
Q2. 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.
Q3. 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.
Q4. 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.
Q5. 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.
Q6. 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.
Q7. 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.
Q8. 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.
Q9. 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.
Q10. 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.
Q11. 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.
Q12. 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.
Q13. 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.
Q14. 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.
Q15. 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.
Q16. 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.
Q17. The class size of interval 25-35 is:
A) 5
B) 10
C) 15
D) 20
Answer: B
Explanation:
Class size = 35 - 25 = 10.
Q18. 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.
Q19. 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.
Q20. 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.
Q21. 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.
Q22. 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.
Q23. 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.
Q24. 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.
Q25. 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.
Q26. 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.
Q27. 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.
Q28. 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.
Q29. 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.
Q30. 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. Common mistakes are :
- Incorrect frequency addition
- Wrong median class identification
- Formula substitution mistakes
- Cumulative frequency confusion
- Calculation errors during simplification
- Observation arrangement mistakes
- Incorrect class interval interpretation
