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Figure it Out

🎓 Class 8 Mathematics CBSE Theory Ch 5 — Making Sense of Data ⏱ ~30 min
🌐 Language: [gtranslate]

This MCQ module is based on: Figure it Out

This mathematics assessment will be based on: Figure it Out
Targeting Class 8 level in General Mathematics, with Basic difficulty.

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Figure it Out — Chapter 5 End-of-Chapter Exercises

These exercises? pull together everything the chapter explored — mean?, median?, line graphs? and infographics?. Work through them carefully and use the "Show Answer" button to check your reasoning.

Q1. The table below shows the average number of customers visiting a shop and the average number of customers actually purchasing items over different days of the week. Visualise this data in a line graph.
DayMonTueWedThuFriSatSun
Visiting16191014202235
Purchasing108711121626
Plot both series on the same axes (days on x-axis, number of customers on y-axis). Each point is joined by a line.
010203040 MonTueWedThuFriSatSun VisitingPurchasing
Two line graphs on the same axes — the "visit" and "purchase" curves both peak on Sunday.
Observations: both curves rise towards the weekend; the Sunday gap (35 vs 26) is the largest difference.
Q2. The average number of days of rainfall in each month for a few cities is shown below.
JanFebMarAprMayJunJulAugSepOctNovDec
Mangaluru0.100.11.86.224.127.724.5146.83.90.9
New Delhi221123884101
Port Blair2.31.50.93.315.518.717.316.814.814.111.35.4
Rameswaram2.61.31.93.42.50.4111.36.510.47.8
(i) Which is the possible method to compile this data? (ii) Mark the data for Mangaluru, Port Blair and Rameswaram in a line graph (shown below). (iii) Based on the line for New Delhi, 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?
(i) Collect rainy-day counts for each city from meteorological records over several years and take their average month by month.
(ii) Plot month on x-axis and "Number of days" on y-axis; join the monthly points for each city with a smooth line.
(iii) Reading the New-Delhi curve matches the row: 2, 2, 1, 1, 2, 3, 8, 8, 4, 1, 0, 1.
(iv) Most: Port Blair (annual total ≈ 121.9 days). Least: New Delhi (≈ 33 days).
(v) New Delhi — July–August (monsoon peak). Rameswaram — October–December (north-east monsoon).
Q3. The following line graph shows the number of births in every month in India over a three-year 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 January in the years 2018, 2019 and 2020. (v) Estimate the number of births in the year 2019.
(i) Births peak every year around August–September and dip around April; a clear seasonal variation repeats each year.
(ii) ≈ 1.9 million.
(iii) Jul 2017 – Jan 2020, about 30 months.
(iv) Jan 2018 ≈ 1.4 M, Jan 2019 ≈ 1.5 M, Jan 2020 ≈ 1.5 M — roughly similar with a gentle rise.
(v) Sum of the 12 monthly values in 2019 ≈ \(12 \times 1.6\text{ M} \approx 19.2\) million births (rough estimate).

Infographic — Wheat vs Rice

Wheat preference +41 +93 +30 Rice preference +86 +99 +80
Simplified infographic — warm bubbles (wheat-leaning states) on the left, cool bubbles (rice-leaning states) on the right. National index ≈ +13.48 leans towards rice.
Q4. Study the infographic "Wheat vs Rice" and answer: (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 wheat and rice is more or less balanced.
(i) Karnataka's neighbours (Kerala +99, Tamil Nadu +100, Andhra +97) are strongly rice-leaning, so Karnataka would likely be near +80.
(ii) Most rice-leaning: Kerala (+99), Tamil Nadu (+100), Andhra Pradesh (+97), West Bengal (+91), Assam (+86).
(iii) Most wheat-leaning: Punjab (−100), Haryana (−93), Rajasthan (−78), Himachal Pradesh (−86), Gujarat (−60).
(iv) Balanced (small index): Maharashtra (−15), Odisha (+30), Jharkhand — wheat and rice consumption are comparable.
Q5. Manoj colours a vertical strip of paper with 48 boxes, marking his 30-minute intervals from midnight to midnight. He uses six colours for six activities: (i) Sleeping (ii) Eating (iii) Meeting friends / media-time with family (iv) Attending classes, studying, homework (v) Showering and getting dressed, yoga / exercise (vi) Travelling. Answer each sub-part in full.
(i) The colour areas represent the proportion of the 24-hour day spent on each activity.
(ii) If the Friday–Sunday strip has very little "classes/study" colour and more "meeting friends" or "travelling", that strip represents the weekend.
(iii) On days marked by long "travelling" strips or by many "meeting friends / family" blocks, he probably went out with friends/relatives.
(iv) School break = days where the "attending classes/homework" colour is missing — look for strips without the study colour.
(v) A classmate's strip can be compared to see similar routines (all school-goers sleep at night, study in the afternoon) or differences (travel time depends on where a child lives).
Q6. (Try This) Make a strip of your typical day during the vacation. How similar or different is it to Manoj's? Also make a strip for any adult at home and compare.
Typically, vacation strips show more sleep, more play, less study — the study colour shrinks and new colours (reading, games) grow. An adult's strip shows a longer work block, shorter play, and different travel pattern (commute to office). Exact values will vary per family.

Data Story — Sleepy-Deepy

0481216 020406080 Sleep hours across age (years)
Typical sleep-hour curve: long sleep at infancy (12+ h) → about 7 h for working adults → slight rise after 60.
Q7. Share your observations on the sleep graph. (a) What age group sleeps the longest? (b) Is sleep duration more similar among people of the same age, or quite variable? (c) What advice does the data suggest for babies and for teenagers?
(a) Babies (0–2 years) sleep around 12–14 hours a day — the longest of any age group.
(b) Within an age group the range is wide (2 hours or more between the lightest and heaviest sleepers).
(c) Babies need long naps to support rapid growth. Teenagers (13–17) need about 8–10 hours — less than a baby but more than most adults.
Q8. Mean Grids. (i) Fill the \(3 \times 3\) grid with 9 distinct numbers such that the average along each row, each column, and the main diagonal is also 5. (ii) Can we fill the grid by changing a few numbers and still get 10 as the average in all directions?
(i) A classic magic square with mean 5 works because its total is \(9 \times 5 = 45\) and every row/column/diagonal sums to 15 — for example:
2 9 4 7 5 3 6 1 8
(ii) Yes — add 5 to every cell: the average of every row/column/diagonal also rises by 5, giving 10. Many other grids are possible.
Q9. Give two examples of data that satisfy each of the conditions: (i) mean is 8 (ii) 4 numbers whose mean is 15.5 (iii) 5 numbers whose mean is 13.6 (iv) 6 numbers whose mean = median (v) 6 numbers whose mean > median.
(i) 6, 8, 10 and 7, 9 mean = 8.
(ii) 10, 14, 18, 20 (sum 62, mean 15.5) and 12, 15, 16, 19.
(iii) 10, 12, 14, 15, 17 (sum 68, mean 13.6) and 11, 12, 13, 14, 18.
(iv) Symmetric data like 2, 4, 6, 8, 10, 12 — mean = median = 7. Also 3, 5, 7, 9, 11, 13.
(v) Right-skewed data like 1, 2, 3, 4, 5, 25 (mean = 40/6 ≈ 6.67, median = 3.5) or 2, 3, 4, 5, 6, 30.
Q10. Fill the blanks such that the median of the collection 13, 5, 21, 14, ___, 15, 4 is 8. How many possibilities exist if only counting numbers are allowed?
Sort the six known values: 4, 5, 13, 14, 15, 21. For the median of 7 values to be 8, the 4th value (after sorting) must equal 8. So the missing number must sit between 5 and 13 and be the middle value — i.e. the blank = 8 is forced. No other counting number satisfies this. Only 1 possibility.
Q11. Fill in the blanks such that the mean of 6.5, 3, 11, ___, ___, 15, 6 is 8. How many possibilities exist if only counting numbers are allowed?
Total needed = \(7 \times 8 = 56\). Known sum = \(6.5 + 3 + 11 + 15 + 6 = 41.5\). So the two blanks must sum to \(56 - 41.5 = 14.5\). With only counting numbers (positive integers), we need \(a + b = 14.5\) — not possible because two integers sum to an integer. 0 possibilities with counting numbers; many with decimals (e.g. 7, 7.5).
Q12. Check whether each of the following statements is true. Justify your reasoning. (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.
(i) Not always. E.g. (2 + 4)/2 = 3 (odd). Sometimes even, e.g. (2 + 6)/2 = 4.
(ii) Not always. (5 + 10)/2 = 7.5 — not a multiple of 5.
(iii) Always true. If the 5 numbers are 5a, 5b, 5c, 5d, 5e then the mean is \(5(a+b+c+d+e)/5 = a+b+c+d+e\) — a whole number, and when we note each was a multiple of 5 the mean is \(5\times\) (that integer)/5 which equals a multiple of 5 divided by 5 — i.e. the mean is itself a multiple of 5 only because dividing a sum of five multiples of 5 by 5 cancels exactly.
Q13. Two new admissions in Sudhakar's class raised the average height of the class to 150.2 cm. (i) Which of the statements are correct? (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 have 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's average height are correct? Why? (a) Average will remain the same. (b) Average will increase. (c) Average will decrease. (d) Information is insufficient. (iii) If 17 of the data were above the median, which statements about the new median are correct? (a) Median remains same. (b) Median increases. (c) Median decreases. (d) Information insufficient.
(i) Only (c) is correct — you need to measure the two new students and recompute, not re-measure everyone.
(ii) Whether the average changes depends on where 149 and 152 sit relative to the current mean of 150.2. Since their own average is (149 + 152)/2 = 150.5, the class mean will rise slightly — answer (b).
(iii) With only a count of "17 are above the median", we cannot predict the new median — answer (d) Information insufficient.
Q14. (Math Talk) Is 17 the average of the data shown in the dot plot below (values 14, 15, 16 … 22)? Share the method used to answer this.
141516171819202122
Count dots per value: 14:2, 15:1, 16:3, 17:2, 18:3, 19:1, 20:2, 21:1, 22:1. Total points = 16. Sum = \(28+15+48+34+54+19+40+21+22 = 281\). Mean = \(281/16 ≈ 17.6\), not 17. So 17 is not the average; the actual mean is close to 17.6.
Q15. 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?
Net change in total weight = \(-2 + 1 + 1 = 0\) kg. So the mean is unchanged at 65.3 kg. The median depends on who changed weight — if the "middle" persons did not change, the median is still 67 kg; otherwise it may shift slightly. Without knowing who changed, we say mean is definitely unchanged and median may or may not change.
Q16. The following table shows retail price (in ₹) of rice (in ₹ per kg) for the month of January in a few states over years 2016–2025. (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? (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?
(i) Pick, say, Andaman, Mizoram and West Bengal; plot the year on x-axis and price on y-axis, joining each state's points with a coloured line.
(ii) Prices rise steadily almost everywhere; jumps are sharpest between 2020 and 2022.
(iii) Gujarat is flat around ₹12–14 for most of the decade. Uttar Pradesh rises from ₹16 to ≈ ₹25, a much larger increase.
(iv) Mizoram jumped from ≈ ₹20 to ≈ ₹29 — the largest percentage increase.
(v) You might ask: how does this compare to wheat? Did government minimum support price policy match the rise? Are these prices adjusted for inflation?
Q17. Referring to the graph on primary sources of energy used for household lighting (rural vs urban, 1983–2023), decide which of the following are valid. Justify. (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.
(i) Valid — the 1983 curves show >60% rural on kerosene and >80% urban on electricity.
(ii) Valid — both kerosene curves fall steadily.
(iii) Invalid — in 2000 the urban electricity share was already >80%, not 10% (the 10% belongs to kerosene, not electricity).
(iv) Invalid — the graph only shows primary lighting source, not outage data. No claim about power cuts can be drawn.
Q18. Using the line graph "Average Daily Time Spent on Hobbies and Games" (urban vs rural kids, ages 10–18): At what age is the average time spent daily on hobbies and games by rural kids 1.5 hours? Options: 8, 10, 12, 14, 18 years. Also: which of the following are correct? (a) Average time spent daily on hobbies and games by kids aged 15 is twice that of kids aged 8. (b) At the age of 16, kids from both urban and rural areas spend each day the same time on hobbies and games.
Reading the rural curve, 1.5 h corresponds to about age 14. For the other statements: (a) likely false — the ratio at age 15 vs age 8 is not exactly 2. (b) may be true or false — check the graph at age 16; if the two curves cross there, it is true; if they are still apart, it is false.
Q19. Individual project: Make a strip chart of your own daily activities for different days of the week. For how long do you spend studying? How long on play? (Compare to friends.)
Answers will vary. Typical Class 8 breakdown: sleep 8 h, school 6 h, study at home 2 h, play 2 h, meals 1.5 h, travel 0.5 h, screen/media 2 h, other 2 h. Compare colour lengths with a friend to find large gaps.
Q20. Small group project: Do the following in groups of 3–4 members. (i) Track daily sleep time of all members of your family for a week. Daily sleep times include night sleep, naps and any sleep during the day. (a) Represent this on a strip chart. (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.
Collect 7 days × 3–4 families = 21–28 rows of data. Typical medians you might find: children 9 h, adults 7 h, elderly 6.5 h. Mean values will be similar unless a family has an unusual member (e.g. new-born baby would skew the child mean up). Findings could include "teenagers who use phones at night sleep about 1 hour less".
Q21. When do schools start and end at 4:30 p.m.? Data would include class time, breaks, etc. 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 — relatives, friends). Analyse and present the data collected.
A simple presentation: make a line chart with "school name" on x-axis and "school duration in hours" on y-axis. Most Indian Grade 8 schools run 6–7 hours with 30–60 minutes of break. Note the spread — some schools end at 2 p.m., others at 4:30 p.m.
Q22. The following graphs show the sunrise and sunset times over a year at 4 locations (Kibithu, Ghuar Moti, Srinagar, Kanyakumari). Answer: (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?
(i) Kibithu (eastern-most India) — sun rises around 5:30 a.m. in January and the day length is about 10.5 hours.
(ii) All four places have roughly 12 hours average, but Kanyakumari (near equator) has the most uniform, longest average day length ≈ 12 h.
(iii) Interesting: Srinagar's day length varies the most (14 h in summer, 9 h in winter) because it is far north. Curious: why does sunrise/sunset vary more in northern India than southern?
Q23. The graph shows the moonrise and moonset over a month. (i) What do you notice? What do you wonder?
Moonrise shifts by about 50 minutes later each day through the month. On full-moon night, the moon rises when the sun sets and is visible all night. On new-moon days, the moon rises with the sun and cannot be seen. Curious: why is the daily shift exactly 50 minutes? (Because the moon orbits Earth roughly every 27.3 days, so it appears to fall behind the Sun by 360°/27.3 ≈ 13° per day ≈ 52 minutes.)
Activity: My Classroom's Sleep Survey
L4 Analyse
Materials: Paper, pencil, a ruler, participation of 20 classmates
Predict first: Do you think the average (mean) or the median is a better single number to represent your class's sleep pattern?
  1. Ask 20 classmates the number of hours they slept last night. Tally the answers in a table.
  2. Compute the mean sleep time and the median sleep time.
  3. Draw a dot plot on a number line from 4 h to 12 h.
  4. If the distribution is skewed (one or two very high or very low values), compare: does the mean move more than the median?
  5. Present the class's "typical" sleep time using whichever measure you think represents the class best, and justify.

Expected: Most Grade-8 students will report 6–9 hours. If even one student is a heavy sleeper (12 hours) or a sleep-deprived gamer (3 hours), the mean shifts noticeably but the median barely moves. The median is usually the better "typical" measure for small skewed samples.

Competency-Based Questions

Scenario: A health department monitors the average monthly rainfall in two cities, A and B, to plan water resources. In City A the monthly averages (in mm) for one year are: 10, 12, 15, 20, 60, 180, 240, 210, 160, 40, 15, 8. In City B they are: 45, 48, 52, 55, 70, 80, 90, 92, 88, 75, 60, 50.
Q1. For each city, compute the mean monthly rainfall and decide which city has more rainfall per year.
L3 Apply
City A total = 10+12+15+20+60+180+240+210+160+40+15+8 = 970. Mean = 970/12 ≈ 80.8 mm.
City B total = 45+48+52+55+70+80+90+92+88+75+60+50 = 805. Mean = 805/12 ≈ 67.1 mm.
City A has more total/mean rainfall despite having a dry stretch.
Q2. Analyse: which city has a more variable (less predictable) rainfall pattern? Justify using the shape of the line graph.
L4 Analyse
City A is far more variable: its line graph shoots from 10 mm in winter to 240 mm in the monsoon — a range of 230 mm. City B's range is only about 50 mm (45–92). A is clearly monsoon-driven; B is more uniform.
Q3. Evaluate: A water engineer plans storage tanks. Should she size the tanks using the mean monthly rainfall or the peak monthly rainfall? Why?
L5 Evaluate
She should plan around the peak (240 mm for City A), not the mean. Using only the mean would cause overflow in July/August. Storage tanks are designed for the worst-case inflow so that heavy rain does not flood out.
Q4. Create: design a simple infographic that communicates "City A is monsoon-dependent, City B is evenly watered" to a Class 5 student who has never seen a line graph.
L6 Create
One design: a blue cloud with 4 raindrops for City A during Jun–Sep and tiny 1-drop icons in other months; for City B, a consistent 2-drop cloud every month. Labels: "City A: Dry most months, flooded for 3" and "City B: A steady shower all year". A Class 5 child understands pictures before axes.

Assertion–Reason Questions

Assertion (A): Adding a very large outlier to a data set changes the mean more than the median.
Reason (R): The mean is affected by every value, while the median is only affected by the position of the middle value.
(a) Both true, R explains A.
(b) Both true, R doesn't explain A.
(c) A true, R false.
(d) A false, R true.
Answer: (a) — Adding a single huge value adds a large amount to the total and changes the mean, but the middle position in the sorted list changes only slightly or not at all.
Assertion (A): A line graph is the best way to visualise the distribution of a one-time survey of student heights.
Reason (R): Line graphs show how a quantity changes over time.
(a) Both true, R explains A.
(b) Both true, R doesn't explain A.
(c) A true, R false.
(d) A false, R true.
Answer: (d) — R is true (line graphs track change over time), but A is false — a line graph is not suited for a single moment's survey; a dot plot, bar graph or histogram is better.
Assertion (A): Infographics can reveal patterns in data that are hard to see from a table alone.
Reason (R): Human visual system recognises shapes and colours much faster than it reads numbers in rows.
(a) Both true, R explains A.
(b) Both true, R doesn't explain A.
(c) A true, R false.
(d) A false, R true.
Answer: (a) — Both true, and R directly explains why infographics work so well.

Summary

Key Ideas — Tales by Dots and Lines
  • Last year we looked at the mean as a fair-share. Here we learnt that the sum of the distances of the values to its left and right are the same — the mean is a "balancing point".
  • We saw that when values greater than the mean are inserted, the mean increases. When values less than the mean are inserted, the mean decreases. Similar phenomena can be observed with the median.
  • Line graphs can be used to visualise change over time — rising curves mean growth, dips mean decreases, and parallel curves mean a stable gap.
  • We saw that examining data can lead to new questions and directions to probe further — infographics such as bubble maps, strip charts and colour gradients help us compare and communicate.

Frequently Asked Questions — Chapter 5

What is Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool in NCERT Class 8 Mathematics?

Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool is a key concept covered in NCERT Class 8 Mathematics, Chapter 5: Chapter 5. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.

How do I solve problems on Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool step by step?

To solve problems on Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 8 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.

What are the most important formulas for Chapter 5: Chapter 5?

The essential formulas of Chapter 5 (Chapter 5) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.

Is Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool important for the Class 8 board exam?

Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool is part of the NCERT Class 8 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.

What mistakes should students avoid in Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool?

Common mistakes in Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.

Where can I find more NCERT practice questions on Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool?

End-of-chapter NCERT exercises for Part 4 — Figure it Out Exercises & Summary | Class 8 Maths Ch 5 Tales by Dots and Lines | MyAiSchool cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 5, and solve at least one previous-year board paper to consolidate your understanding.

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