NCERT Solutions for Class 8 Maths Chapter 12 Tales By Dots and Lines provide clear, step-by-step answers to every exercise and in-text question from the chapter Tales By Dots and Lines of the NCERT textbook Ganita Prakash. Prepared by subject experts as per the latest NCERT (CBSE) syllabus for 2026-27, these NCERT Solutions for Class 8 Maths help you understand each concept, write exam-ready answers, and check your own solutions. You can read them online below or download the free Class 8 Maths Chapter 12 question-answer PDF.
NCERT Solutions for Class 8 Maths Chapter 12 Tales By Dots and Lines
- Class: Class 8
- Subject: Maths
- Chapter: Chapter 12 – Tales By Dots and Lines
- Textbook: Ganita Prakash (NCERT)
- Study material: NCERT Solutions – questions with answers, free PDF
These solutions answer all the exercise questions of Chapter 12 Tales By Dots and Lines — including the in-text questions, short-answer and long-answer questions, and activities — with complete explanations so you can follow the method, not just the final answer. Read the full solutions below.
NCERT Solutions Class 8 Maths Chapter 12 Tales By Dots and Lines View Download
NCERT Solutions for Class 8 Maths Chapter 12 PDF Download
You can read the NCERT Solutions for Class 8 Maths Chapter 12 online above, or download the complete question-answer PDF to study Tales By Dots and Lines offline at any time.
NCERT Solutions for Class 8 Maths Chapter 12 PDF Download Link – Click Here to Download Solutions PDF
Questions Covered in This Chapter
These NCERT Solutions answer all 80 questions of this chapter. The questions solved are:
- Consider any 2 numbers. Find their average/arithmetic mean. Repeat this by taking other pairs. What do you observe?
- Calculate and mark the mean of each collection of data below.
- Can you explain how the mean is the centre of each collection?
- Mark the mean for the collections below.
- Can you explain how the mean is the centre of each collection?
- Verify that this holds for all the collections of data shown earlier.
- Can there be more than one such ‘centre’? In other words, is there any other value such that the sum of the distances to the values lower than it and the values higher than it will still be equal?
- In the case of the collection 10, 10, 11, and 17 whose mean is 12, suppose there is a different centre larger than 12.
- Will including a new value in the data increase or decrease the mean?
- What happens to the mean when an existing value is removed? When will the mean increase, decrease, or stay the same?
- What happens to the mean if a value equal to the mean is included or removed? Try to explain this using the fair-share interpretation of mean that we studied last year.
- Explore if it is possible to include or remove 2 values such that the mean is unchanged. You may use the following data to experiment with.
- How about including or removing 3 values without changing the mean? Is it possible?
- Can we include 2 values less than the mean and 1 value greater than the mean, so that the mean remains the same?
- Try to include 2 values greater than the mean and 1 value less than the mean, so that the mean stays the same.
- We saw what happens to the mean when values are included or removed from the collection. What happens to the mean if every value in the collection increases by some fixed number?
- Consider the data: 8, 3, 10, 13, 4, 6, 7, 7, 8, 8, 5. Calculate its mean.
- Now, consider this data with every value increased by 10: 18, 13, 20, 23, 14, 16, 17, 17, 18, 18, 15. What is its mean? Is there a quicker way to find out?
- Try to explain, using algebra, what the average is when a fixed number, e.g., 2 is subtracted from every value in the collection.
- Try to explain this using the fair-share interpretation of average that you learnt last year.
- What happens to the average if every value in the collection is doubled?
- Will including a new value to the data increase or decrease the median?
- Coach Balwan noted down the weights of the kushti players (wrestlers) and the mean as shown. But one value that was written down got smudged. Can you find out the missing value?
- Venkayya keeps track of the coconut harvest in his farm. He calculates the average harvest per tree as 25.6. His son verifies the counts and finds that one tree’s harvest count is incorrectly noted as 3 more than the actual number. Can you find the correct average if the number of trees is 15?
- What is the average family size of students in your class? How would you find this out?
- What is the average family size of this class?
- What is the median family size of this class?
- Do we need to write all the 36 numbers in order? Is there a quicker way to find out?
- Can you tell which cell has the marks obtained by Farooq in Mathematics?
- Can you tell what data is in column B7?
- In which subjects has Ashwin scored more than 30 marks?
- What formula would you type to find out the class average marks in Science?
- Find out if the class average marks in Odia is greater than the class average marks in Telugu.
- Show the average marks in other subjects after the last row by typing the appropriate formulae.
- Get the total scores of each student by typing the appropriate formulae.
- Find the mean of the following data and share your observations: (i) The first 50 natural numbers. (ii) The first 50 odd numbers. (iii) The first 50 multiples of 4.
- The dot plot below shows a collection of data and its average; but one dot is missing. Mark the missing value so that the mean is 9 (as shown below).
- Sudhakar, the class teacher, asks Shreyas to measure the heights of all 24 students in his class and calculate the average height. Shreyas informs the teacher that the average height is 150.2 cm. Sudhakar discovers that the students were wearing uniform shoes when the measurements were taken and the shoes add 1 cm to the height. (i) Should the teacher get all the heights measured again without the shoes to find the correct average height? Or is there a simpler way? (ii) What is the correct average height of the class? (a) 174.2 cm (b) 126.2 cm (c) 150.2 cm (d) 149.2 cm (e) 151.2 cm (f) None of the above (g) Insufficient information
- The three dot plots below show the lengths, in minutes, of songs of different albums. Which of these has a mean of 5.57 minutes? Explain how you arrived at the answer.
- Find the median of 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92. (i) If we include one value to the data (in the given list) without affecting the median, what could that value be? (ii) If we include two values to the data without affecting the median what could the two values be? (iii) If we remove one value from the data without affecting the median what could the value be?
- Examine the statements below and justify if the statement is always true, sometimes true, or never true. (i) Removing a value less than the median will decrease the median. (ii) Including a value less than the mean will decrease the mean. (iii) Including any 4 values will not affect the median. (iv) Including 4 values less than the median will increase the median.
- The mean of the numbers 8, 13, 10, 4, 5, 20, y, 10 is 10.375. Find the value of y.
- The mean of a set of data with 15 values is 134. Find the sum of the data.
- Consider the data: 12, 47, 8, 73, 18, 35, 39, 8, 29, 25, p. Which of the following number(s) could be p if the median of this data is 29? (i) 10 (ii) 25 (iii) 40 (iv) 100 (v) 29 (vi) 47 (vii) 30
- The number of times students rode their cycles in a week is shown in the dot plot below. Four students rode their cycles twice in that week. (i) Find the average number of times students rode their cycles. (ii) Find the median number of times students rode their cycles. (iii) Which of the following statements are valid? Why? (a) Everyone used their cycle at least once. (b) Almost everyone used their cycle a few times. (c) There are some students who cycled more than once on some days. (d) Exactly 5 students have used their cycles more than once on some days. (e) The following week, if all of them cycled 1 more time than they did the previous week, what would be the average and median of the next week’s data?
- A dart-throwing competition was organised in a school. The number of throws participants took to hit the bull’s eye (the centre circle) is given in the table below. Describe the data using its minimum, maximum, mean and median.
- Now, observe the following graph. Do both these graphs represent the same information?
- How do we get the maximum temperature over a month in a state?
- What thoughts or questions occur to you?
- What could be the possible method used to derive this data? Discuss.
- Which of the following statements are valid inferences? • From 2012 till 2024, the worldwide count of space object launches increased every year. • USA is a major contributor in the years 2022 – 24, launching about 3/4th of the worldwide count. • Nepal did not launch any object in the period 2012 – 24. • The combined count of object launches by China and Russia in 2024 is about 400.
- Identify two consecutive years where the worldwide count increased by 2 times or more.
- What could be the possible method to compile this data?
- Mark these cities on a map of India. What is common to how they are grouped in the graphs? Share your observations and inferences about the graphs.
- Identify the peak months and low months of rainfall for each city.
- Read about the south-west monsoon and north-east monsoon and which regions come under the influence of these and when.
- The average number of customers visiting a shop and the average number of customers actually purchasing items over different days of the week is shown in the table below. Visualise this data on a line graph.
- The average number of days of rainfall in each month for a few cities is shown in the table below: (i) What could be the possible method to compile this data? (ii) Mark the data for Mangaluru, Port Blair, and Rameswaram in the line graph shown below. You can round off the values to the nearest integer. (iii) Based on the line for New Delhi in the graph fill the data in the table. (iv) Which city among these receives the most number of days of rainfall per year? Which city gets the least number of days of rainfall per year? (v) Looking at the table, when is the rainy season in New Delhi and Rameswaram?
- The following line graph shows the number of births in every month in India over a time period: (i) What are your observations? (ii) What was the approximate number of births in July 2017? (iii) What time period does the graph capture? (iv) Compare the number of births in the month of January in the years 2018, 2019, and 2020. (v) Estimate the number of births in the year 2019.
- Share your observations. Based on this infographic, answer the following: (i) The value of Karnataka is hidden. Can you guess what it could be? (ii) Which are the top 5 states where rice is the most popular? (iii) Which are the top 5 states where wheat is the most popular? (iv) List a few states where the preference between rice and wheat is more or less balanced.
- Look at the three coloured strips carefully. (i) What activity does each colour stand for? (ii) The three strips correspond to the days Friday – Sunday in some order. Which day do you think each strip represents? (iii) On one of these days, he went out with friends to watch a long movie. When do you think this happened? (iv) At what time does his school break for lunch? (v) What more can the strips tell us?
- What would your strip for a weekday look like? How similar or different is it to Manoj’s?
- What would a strip of your typical day during your vacation look like? How similar/different would it look?
- What would a strip for any of the adults in your family look like? Make a strip of a day for any adult at home. Compare your strip with theirs. What do you find interesting?
- Share your observations on this graph. What do you find interesting?
- Mean Grids: (i) Fill the grid with 9 distinct numbers such that the average along each row, column, and diagonal is 10. (ii) Can we fill the grid by changing a few numbers and still get 10 as the average in all directions?
- Give two examples of data that satisfy each of the following conditions: (i) 3 numbers whose mean is 8. (ii) 4 numbers whose median is 15.5. (iii) 5 numbers whose mean is 13.6. (iv) 6 numbers whose mean = median. (v) 6 numbers whose mean > median.
- Fill in the blanks such that the median of the collection is 13: 5, 21, 14, _____, ______, ______. How many possibilities exist if only counting numbers are allowed?
- Fill in the blanks such that the mean of the collection is 6.5: 3, 11, ____, _____, 15, 6. How many possibilities exist if only counting numbers are allowed?
- Check whether each of the statements below is true. Justify your reasoning. Use algebra, if necessary, to justify. (i) The average of two even numbers is even. (ii) The average of any two multiples of 5 will be a multiple of 5. (iii) The average of any 5 multiples of 5 will also be a multiple of 5.
- There were 2 new admissions to Sudhakar’s class just a couple of days after the class average height was found to be 150.2 cm. (i) Which of the following statements are correct? Why? (a) The average height of the class will increase as there are 2 new values. (b) The average height of the class will remain the same. (c) The heights of the new students have to be measured to find out the new average height. (d) The heights of everyone in the class has to be measured again to calculate the new average height. (ii) The heights of the two new joinees are 149 cm and 152 cm. Which of the following statements about the class’ average height are correct? Why? (a) The average will remain the same. (b) The average will increase. (c) The average will decrease. (d) The information is not sufficient to make a claim about the average. (iii) Which of the following statements about the new class average height are correct? Why? (a) The median will remain the same. (b) The median will increase. (c) The median will decrease. (d) The information is not sufficient to make a claim about median.
- Is 17 the average of the data shown in the dot plot below? Share the method you used to answer this question.
- The weights of people in a group were measured every month. The average weight for the previous month was 65.3 kg and the median weight was 67 kg. The data for this month showed that one person has lost 2 kg and two have gained 1 kg. What can we say about the change in mean weight and median weight this month?
- The following table shows the retail price (in ₹) of iodised salt in the month of January in a few states over 10 years. For your calculations and plotting you may round off values to the nearest counting number. (i) Choose data from any 3 states you find interesting and present it through a line graph using an appropriate scale. (ii) What do you find interesting in this data? Share your observations. (iii) Compare the price variation in Gujarat and Uttar Pradesh. (iv) In which state has the price increased the most from 2016 to 2025? (v) What are you curious to explore further?
- Referring to the graph below, which of the following statements are valid? Why? (i) In 1983, the majority in rural areas used kerosene as a primary lighting source while the majority in urban areas used electricity. (ii) The use of kerosene as a primary lighting source has decreased over time in both rural and urban areas. (iii) In the year 2000, 10% of the urban households used electricity as a primary lighting source. (iv) In 2023, there were no power cuts.
- Answer the following questions based on the line graph. (i) How long do children aged 10 in urban areas spend each day on hobbies and games? (ii) At what age is the average time spent daily on hobbies and games by rural kids 1.5 hours? (a) 8 years (b) 10 years (c) 12 years (d) 14 years (e) 18 years (iii) Are the following statements correct? (a) The average time spent daily on hobbies and games by kids aged 15 is twice that of kids aged 10. (b) All rural kids aged 15 spend at least 1 hour on hobbies and games everyday.
- Individual project: Make your own activity strip for different days of the week. (i) Do you eat and sleep at regular times every day? Typically how long do you spend outdoors? (ii) Calculate the average time spent per activity. Represent this average day using a strip. (iii) Similarly, track the activities of any adult at home. Compare your data with theirs.
- Small group project: Make a group of 3 – 4 members. Do at least one of the following: (i) Track daily sleep time of all your family members for a week. Daily sleep time includes night sleep, naps, and any sleep during the day. (a) Represent this on strips. (b) Put together the data of all your group members. Calculate the average and median sleep time of children, adults, elderly. (c) Share your findings and observations. (ii) When do schools start and end? On a weekday, Manoj’s school starts at 9:30 am and ends at 4:30 pm, i.e., 7 hours which include class time and breaks. Collect information on the daily timings of different schools for Grade 8, including class time and break time (the schools can be anywhere in the country. You can ask your neighbours, relatives, parents and friends to find out). Analyse and present the data collected.
- The following graphs show the sunrise and sunset times across the year at 4 locations in India. Observe how the graphs are organised. Are you able to identify which lines indicate the sunrise and which indicate the sunset? Answer the following questions based on the graphs: (i) At which place does the sun rise the earliest in January? What is the approximate day length at this place in January? (ii) Which place has the longest day length over the year? (iii) Share your observations — what do you find interesting? What are you curious to find out?
- We all know the typical sunrise and sunset timings. Do you know when the moon rises and sets? Does it follow a regular pattern like the sun? Let’s find out. The following graph shows the moonrise and moonset time over a month: (i) Find out on what dates amavasya (new moon) and purnima (full moon) were in this month. (ii) What do you notice? What do you wonder?
Chapter at a Glance
- The mean is the balance point of the data: the distances of the values below it add up to exactly the same total as the distances of the values above it. That is why there is only one mean.
- Adding a value bigger than the mean pulls the mean up; a smaller one pulls it down; a value equal to the mean changes nothing. Two values can be added on opposite sides so that the mean does not move at all.
- If every value goes up by k, the mean goes up by k. If every value is multiplied by k, the mean is multiplied by k. Both facts are proved with algebra in the chapter.
- The median is the middle value of the sorted data. Because it only counts positions, one stray extreme value barely moves it, while the same value can swing the mean a lot.
- With a frequency table, the mean is (sum of value × frequency) ÷ (total frequency), and the median is found by adding up frequencies until you reach the middle position.
- Line graphs show change over time far more clearly than a crowded column graph. Reading one means two steps: first identify what is given (scale, axes, series), then infer — carefully, without claiming more than the graph shows.
How to Download NCERT Solutions for Class 8 Maths Chapter 12 PDF
Follow these simple steps to get the Tales By Dots and Lines questions-and-answers PDF from Ganita Prakash.
- Search NCERT Solutions for Class 8 Maths Chapter 12 aglasem and open this page.
- Read the exercise questions with answers for Tales By Dots and Lines shown above.
- Click the Download PDF link to save the Tales By Dots and Lines solutions to your device.
NCERT Solutions for Class 8 Maths – All Chapters
There are more chapters to study besides Tales By Dots and Lines in Maths. Here are the NCERT Solutions for all chapters of Class 8 Maths.
- Chapter 1 A Square and a Cube
- Chapter 2 Power Play
- Chapter 3 A Story of Numbers
- Chapter 4 Quadrilaterals
- Chapter 5 Number Play
- Chapter 6 We Distribute Yet Things Multiply
- Chapter 7 Proportional Reasoning 1
- Chapter 8 Fractions in Disguise
- Chapter 9 The Baudh Yana Pythagoras Theorem
- Chapter 10 Proportional Reasoning 2
- Chapter 11 Exploring Some Geometric Themes
- Chapter 12 Tales By Dots and Lines
- Chapter 13 Algebra Play
- Chapter 14 Area
NCERT Solutions for Class 8 – All Subjects
Just like Chapter 12 of Maths, you can get the exercise questions with answers for every other subject of Class 8. Here are the NCERT Solutions for all subjects of Class 8.
NCERT Solutions for Class 8 Maths Chapter 12 – An Overview
The key highlights of this study material are as follows.
| Aspects | Details |
|---|---|
| Class | Class 8 |
| Subject | Maths |
| Chapter Number | Chapter 12 |
| Chapter Name | Tales By Dots and Lines |
| Book Name | Ganita Prakash |
| Book By | NCERT (National Council of Educational Research and Training) |
| Educational Resource Here | NCERT Solutions of Class 8 Maths Chapter 12 for all exercises |
| More Questions Answers of This Subject | NCERT Solutions for Class 8 Maths |
| Download Book Chapter | NCERT Book Class 8 Maths |
| All Questions Answers For This Class | NCERT Solutions for Class 8 |
| Complete Solutions | NCERT Solutions |
NCERT Solutions for Class 8 Maths Chapter 12 Tales By Dots and Lines – FAQs
What are the NCERT Solutions for Class 8 Maths Chapter 12 Tales By Dots and Lines?
They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 12 Tales By Dots and Lines from the NCERT Class 8 Maths textbook Ganita Prakash, written by experts as per the latest NCERT syllabus.
How can I download the Class 8 Maths Chapter 12 solutions PDF for free?
Open this page on aglasem, read the Tales By Dots and Lines questions with answers, and click the “Download Solutions PDF” link. The Class 8 Maths Chapter 12 NCERT Solutions PDF is completely free to download.
Are these NCERT Solutions as per the latest 2026-27 syllabus?
Yes. The NCERT Solutions for Class 8 Maths Chapter 12 are based on the latest NCERT textbook Ganita Prakash and the current 2026-27 CBSE syllabus, so the questions and answers match what you study in class.
Where can I get NCERT Solutions for the other chapters of Class 8 Maths?
You can find the answers to every chapter on the NCERT Solutions for Class 8 Maths page, and solutions for every subject on the NCERT Solutions for Class 8 page.
How do NCERT Solutions help in exam preparation?
They show the correct method to solve each question, help you write answers the way they are expected in exams, let you check and correct your own work, and save revision time — which together improve your marks in Class 8 Maths.
If you have any queries on NCERT Solutions for Class 8 Maths Chapter 12 Tales By Dots and Lines, then please ask in the comments below.
