Assertion Reason Questions For Class 10 Maths Chapter 13 Statistics

Assertion Reason Questions for Class 10 Maths Chapter 13 Statistics are provided in this article to help students build a strong understanding of important statistical concepts. These questions are highly useful for improving logical reasoning and analytical thinking while preparing for CBSE board examinations. 

In Chapter 13 Statistics, students learn important concepts such as mean, median, and mode of grouped data, cumulative frequency, and ogives. The chapter also explains different methods of finding the mean, including the Direct Method, Assumed Mean Method, and Step-Deviation Method. These concepts help students analyse and interpret data effectively in real-life situations. 

Our subject experts have prepared detailed Assertion Reason Questions with accurate explanations based on the latest CBSE syllabus and NCERT textbook. Practising these questions will help students revise formulas, understand concepts clearly, and improve their exam performance. Students can also download the free PDF for quick revision and regular practice before examinations.

Assertion and Reasoning Questions on Class 10 - Chapter 13 - Statistics

Directions: In the following questions a statement of assertion (A) is followed by a statement of reason(R). Mark the correct choice as:

Choose the correct option for the following questions:

A. Both Assertion (A) and Reason (R) are true, and Reason is the correct explanation of Assertion.

B. Both Assertion (A) and Reason (R) are true, but Reason is not the correct explanation of Assertion.

C. Assertion (A) is true, but Reason (R) is false.

D. Assertion (A) is false, but Reason (R) is true.

Q1. Assertion (A): In grouped data, the class mark is taken as the representative value of the entire class interval.

Reason (R): The class mark is the average of the upper and lower class limits.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: a)

Explanation: The class mark is calculated as the midpoint of a class interval and is assumed to represent all observations in that class while finding the mean of grouped data.

Q2. Assertion (A): The direct method for finding mean of grouped data uses the formula: Mean = Σfixi / Σfi.

Reason (R): In the direct method, xi represents the class marks of the class intervals.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: a)

Explanation: The direct method calculates the weighted average using class marks as representative values and their corresponding frequencies.

Q3. Assertion (A): The assumed mean method reduces calculation effort compared to the direct method.

Reason (R): In this method, deviations are taken from a conveniently chosen value called the assumed mean.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: a)

Explanation: By taking deviations from an assumed mean, the values become smaller and calculations become simpler.

Q4. Assertion (A): Step-deviation method is useful when all deviations have a common factor.

Reason (R): The formula ui = (xi − a)/h reduces large deviations into smaller values.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: a)

Explanation: Dividing deviations by a common factor h simplifies calculations and reduces computational work.

Q5. Assertion (A): The mean obtained by direct, assumed mean and step-deviation methods is always the same.

Reason (R): Assumed mean and step-deviation methods are simplified forms of the direct method.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: a)

Explanation: Though the methods differ in computation style, they are based on the same statistical principle and yield identical results.

Q6. Assertion (A): The modal class of grouped data is the class interval having the maximum frequency.

Reason (R): Mode always lies inside the modal class.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: b)

Explanation: Modal class is indeed the class with maximum frequency. The mode lies inside it, but that fact does not explain why it is called modal class.

Q7. Assertion (A): The formula for mode of grouped data is
Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h

Reason (R): f₁ denotes the frequency of the modal class.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: b)

Explanation: The formula is correct and f₁ represents the modal class frequency, but this alone does not explain the formula.

Q8. Assertion (A): Median class is the class whose cumulative frequency first exceeds n/2.

Reason (R): Median divides the observations into two equal parts.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: a)

Explanation: Median represents the middle value of data, so the class containing the n/2th observation becomes the median class.

Q9. Assertion (A): Cumulative frequency is obtained by adding frequencies of all previous classes including the current class.

Reason (R): Cumulative frequency helps in locating the median class.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: b)

Explanation: Both statements are true, but the definition of cumulative frequency is independent of its use in finding median.

Q10. Assertion (A): In a salary distribution with some extremely high incomes, median may be preferred over mean.

Reason (R): Extreme values affect the mean more than the median.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: a)

Explanation: Mean gets distorted by unusually large or small values, whereas median remains comparatively stable.

Q11. Assertion (A): The empirical relation among mean, median and mode is:
Mode = 3 Median − 2 Mean

Reason (R): This relation holds exactly for every grouped data distribution.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: c)

Explanation: The relation is correct, but it is empirical and only approximate; it does not hold exactly for all distributions.

Q12. Assertion (A): For constructing an ogive, class intervals should be continuous.

Reason (R): Median obtained graphically from ogives depends on cumulative frequencies of continuous intervals.

Options:
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

Answer: a)

Explanation: Continuous class intervals ensure accurate cumulative frequency representation and proper ogive construction.

Download free PDF of Assertion and Reasoning Questions for Class 10 Maths Chapter 13 - Statistics

This worksheet is designed according to the CBSE and NCERT syllabus and includes concept-based A&R questions on mean, median, mode, cumulative frequency, and grouped data. These questions help students strengthen logical thinking, improve conceptual understanding, and prepare effectively for school exams and board-level assessments. Practice with detailed solutions and boost your confidence in Statistics.

Assertion and Reasoning - Statistics - Class 10 - Practice Worksheet