CBSE Class 8 Maths Chapter 12: Tales by Dots and Lines — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 12: Tales by Dots and Lines from the NCERT Class 8 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(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.
(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.
Assertion & Reason Questions
1
Assertion (A): The arithmetic mean equals the sum of the data values divided by their number.
Reason (R): It can be interpreted as the fair-share or balancing value of the data.
Reason (R): It can be interpreted as the fair-share or balancing value of the data.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Redistributing the total equally gives the mean.
2
Assertion (A): For two numbers, their mean lies halfway between them.
Reason (R): The median is found after arranging the data in order.
Reason (R): The median is found after arranging the data in order.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the median procedure does not explain the two-number mean.
3
Assertion (A): The mean of 3, 7 and 8 is 6.
Reason (R): The sum of the three values is 15.
Reason (R): The sum of the three values is 15.
Answer: (c)
A is true, but R is false. Their sum is 18, and 18 divided by 3 is 6.
4
Assertion (A): The mean of a data set must always equal one of its observed values.
Reason (R): A mean can lie between data values.
Reason (R): A mean can lie between data values.
Answer: (d)
A is false, but R is true. For example, the mean of 2 and 3 is 2.5.
5
Assertion (A): Adding a value greater than the current mean increases the mean.
Reason (R): The new value contributes more than the old average contribution.
Reason (R): The new value contributes more than the old average contribution.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The total rises by more than is needed to preserve the previous average.
6
Assertion (A): Adding a value equal to the current mean leaves the mean unchanged.
Reason (R): Removing a value equal to the mean also leaves the mean unchanged when data remain.
Reason (R): Removing a value equal to the mean also leaves the mean unchanged when data remain.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true balance properties, but removal does not explain the addition case.
7
Assertion (A): Adding a value below the current mean decreases the mean.
Reason (R): An added below-average value increases the balance point.
Reason (R): An added below-average value increases the balance point.
Answer: (c)
A is true, but R is false. The new observation pulls the balance point downward.
8
Assertion (A): Removing a value greater than the mean always increases the mean.
Reason (R): Removing an above-average value tends to lower the remaining mean.
Reason (R): Removing an above-average value tends to lower the remaining mean.
Answer: (d)
A is false, but R is true. The assertion has the direction reversed.
9
Assertion (A): Adding the same constant k to every data value adds k to the mean.
Reason (R): The total increases by nk for n values, so the average increases by k.
Reason (R): The total increases by nk for n values, so the average increases by k.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Dividing the added total nk by n yields k.
10
Assertion (A): Multiplying every value by 2 multiplies the mean by 2.
Reason (R): The median depends on the ordered middle position.
Reason (R): The median depends on the ordered middle position.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the median definition does not explain scaling of the mean.
11
Assertion (A): The median of an odd number of ordered values is the middle value.
Reason (R): For 1, 4, 9, the median is (1 + 9)/2.
Reason (R): For 1, 4, 9, the median is (1 + 9)/2.
Answer: (c)
A is true, but R is false. The middle value is 4; averaging endpoints is not the median rule.
12
Assertion (A): The median of 2, 5, 7 and 10 is 7.
Reason (R): For an even number of values, the median is the mean of the two middle values.
Reason (R): For an even number of values, the median is the mean of the two middle values.
Answer: (d)
A is false, but R is true. The median is (5 + 7)/2 = 6.
13
Assertion (A): A frequency table records how often each value occurs.
Reason (R): Frequencies allow repeated observations to be represented compactly.
Reason (R): Frequencies allow repeated observations to be represented compactly.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The table replaces repeated listing with counts.
14
Assertion (A): The total frequency equals the number of observations.
Reason (R): Cumulative frequency gives running totals across ordered values.
Reason (R): Cumulative frequency gives running totals across ordered values.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but cumulative frequency does not explain the basic total.
15
Assertion (A): An extreme value can strongly affect the mean.
Reason (R): The median always changes by the same large amount as the extreme value.
Reason (R): The median always changes by the same large amount as the extreme value.
Answer: (c)
A is true, but R is false. The median is generally more resistant to an extreme observation.
16
Assertion (A): A graph can be interpreted correctly without reading its scale or labels.
Reason (R): Scale, axes, units and source are essential for understanding displayed data.
Reason (R): Scale, axes, units and source are essential for understanding displayed data.
Answer: (d)
A is false, but R is true. Ignoring them can produce false conclusions.
17
Assertion (A): A line graph is useful for showing change across an ordered variable such as time.
Reason (R): Connecting plotted points helps reveal trends between successive observations.
Reason (R): Connecting plotted points helps reveal trends between successive observations.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The ordered sequence makes rises and falls visible.
18
Assertion (A): A dot plot shows the distribution of individual data values.
Reason (R): Two data sets can share a mean but have different spreads.
Reason (R): Two data sets can share a mean but have different spreads.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but equal means with different spreads do not define a dot plot.
19
Assertion (A): If every value in a data set is 8, its mean is 8.
Reason (R): Its median must be 0 because there is no variation.
Reason (R): Its median must be 0 because there is no variation.
Answer: (c)
A is true, but R is false. The middle value is also 8.
20
Assertion (A): The mean alone always gives a complete description of a data set.
Reason (R): Data sets with the same mean can differ in median, spread and shape.
Reason (R): Data sets with the same mean can differ in median, spread and shape.
Answer: (d)
A is false, but R is true. Several summaries and the full distribution may be needed.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 12 Tales by Dots and Lines?
This chapter covers all key topics from Tales by Dots and Lines as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Tales by Dots and Lines online for free?
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