14 marksGanita Prakash Cl-8 Part 2, Section 5.2, pages 116-119 — 'Temperature'
The chapter shows the same monthly maximum temperature data for Kerala and Punjab in 2023 first as a clustered-column graph and then as a line graph. Do the two graphs carry the same information? Read the line graph using the chapter's two-step process and state what it shows.
Hint. Step 1 is describing what is on the page; step 2 is saying what it means.
Do they carry the same information? Yes. Both graphs plot exactly the same 24 numbers — the monthly maximum temperature for two states across twelve months. Nothing is added and nothing is lost by switching from columns to lines. What changes is what the eye picks up: the columns invite you to compare Kerala with Punjab within one month, while the line joins each state's own readings and makes the shape of the year jump out.
Step 1 — Identify what is given.
· The horizontal axis carries the twelve months; the vertical axis carries temperature in °C.
· Kerala's readings are blue circles joined by blue lines, Punjab's are red with a different marker shape. The markers differ in shape as well as colour so the graph still works when printed in black and white, and for readers who find colours hard to tell apart.
· Each point is a monthly maximum — the largest value recorded that month across the weather stations in that state.
Why knowing how the data was produced matters. A state has several weather stations, and the monthly maximum is the highest reading among all of them. Knowing this tells us the scope of the number: it describes the hottest spot on the hottest day, not a typical day, and if a state's stations are unevenly placed the figure may be biased towards the places that happen to be measured. Understanding this keeps us from over-claiming.
Step 2 — Infer and interpret.
· Punjab climbs steadily from about 19 °C in January to a peak of about 38 °C in June, dips to just under 35 °C in July, stays roughly flat through September, then falls continuously to about 23 °C in December. January is its coolest month.
· Kerala stays remarkably flat all year, peaking near 33 °C in April and bottoming near 29 °C in July — a swing of only about 4 °C, so its hottest months and coolest months look much alike.
· Conclusion: Punjab's temperature varies far more than Kerala's, reaching both hotter and colder extremes; Kerala is warm and steady.
Questions the graph raises. Why are the trends so different — is it latitude, or distance from the sea? Which other states behave like Punjab, and what do they have in common? What would the monthly minimum temperatures look like — would Punjab's swing be even bigger?
✦ Yes, the two graphs show the same information; the line graph simply makes the trend over time easier to follow. It shows Punjab rising to about 38 °C in June and falling to about 23 °C in December, while Kerala stays between about 29 °C and 33 °C all year — so Punjab's temperature varies much more than Kerala's.
25 marksGanita Prakash Cl-8 Part 2, Section 5.2, pages 119-120 — 'Space Jam'
A line graph shows the annual number of objects launched into space for the world, the USA, China and Russia from 2012 to 2024. Which of these are valid inferences? (a) From 2012 to 2024 the worldwide count increased every year. (b) The USA launched about three-quarters of the worldwide count in 2022–24. (c) Nepal did not launch any object in 2012–24. (d) China and Russia together launched about 400 objects in 2024. Also, identify two consecutive years where the worldwide count at least doubled, and explain why a line graph beats a clustered column graph here.
Hint. For each claim, ask whether the graph actually contains the evidence — some claims are about data that is simply not on the page.
(a) The worldwide count increased every year from 2012 to 2024 — NOT VALID. The line does rise steeply overall, but it does not rise every year: the 2024 value (about 2800) is lower than the 2023 value (about 2900). One year of decrease is enough to break a claim about every year.
(b) The USA launched about three-quarters of the worldwide count in 2022–24 — VALID. Reading the two lines in those years, the USA's count sits at roughly three-quarters of the height of the worldwide line, and the chapter's own reading confirms the USA as the dominant contributor in this period.
(c) Nepal did not launch any object in 2012–24 — NOT VALID. Nepal is not plotted at all. The graph shows only the world total and three countries, and the chapter itself points out that the three country lines do not add up to the world total, which means other countries are present but not shown. Absence from the graph is not evidence of absence in reality — this is the single most important habit to build when reading data.
(d) China and Russia together launched about 400 objects in 2024 — VALID, provided their two 2024 values are read off and added. This is exactly the kind of claim a line graph supports: read each line at 2024 and add. It is valid as long as the reading is done and not guessed.
Two consecutive years where the worldwide count at least doubled. Scanning for the steepest rise, the jump from 2020 to 2021 is the one that qualifies: the count roughly doubles, with the world line climbing from around 1250 to around 2500. The eye can find it without arithmetic — the steeper a line segment, the larger the change over that year, which is precisely the advantage of a line graph.
Why a line graph rather than 52 columns. The same data as a clustered column graph would need 13 clusters (one per year) of 4 columns each = 52 bars. That is crowded and hard to read, and worse, the eye has to hop from the first bar of one cluster to the first bar of the next to follow a single country. Joining each country's points with a line makes each trend a single continuous shape, so rises, falls and changes of steepness are read at a glance.
✦ Valid: (b) and (d). Not valid: (a) and (c). (a) fails because 2024 is below 2023; (c) fails because Nepal is not on the graph at all and the country lines do not sum to the world total, so unshown countries certainly exist. The worldwide count roughly doubled from 2020 to 2021, and a line graph is preferable here because 52 clustered bars would obscure the very trends the graph exists to show.
34 marksGanita Prakash Cl-8 Part 2, Section 5.2, pages 120-121 — 'Catch the (Pattern in) Rain'
Monthly average rainfall graphs are shown for Kovalam, Udupi, Mumbai, Rameswaram, Chennai and Puri. How is this data compiled? What is common to the way the cities are grouped, and what are the peak and low rainfall months for each?
Hint. Mark the six cities on a map of India before looking at the graphs again.
How the data is compiled. 'Monthly average rainfall' means rainfall was measured in each city over several years, and then all the June figures (say) were averaged to give the average June rainfall for that city. This smooths out freak years — one exceptionally dry June will not decide the shape of the curve — so the graph shows the city's typical rainfall pattern rather than the story of any single year.
How the cities are grouped. Marking them on a map makes the grouping obvious:
· Kovalam, Udupi and Mumbai lie along the west coast
· Rameswaram, Chennai and Puri lie along the east coast
The graphs are grouped by coast, and the west-coast cities plainly receive more rain overall.
Peak and low months.
· Udupi, Mumbai and Kovalam (west coast): peak rainfall during June – August, driven by the south-west monsoon striking the west coast first.
· Rameswaram (south-east coast): most of its rain arrives October – December, and it receives very little from January right through to September.
· Chennai: rain begins around June, peaks in November and continues into December.
· Puri: although on the east coast, its peak is July – September, which makes it the interesting exception in the group.
· All six cities: January – March are dry months with low rainfall.
What lies behind this. India receives two monsoons. The south-west monsoon (roughly June – September) sweeps in from the Arabian Sea and hits the west coast first, which is why Kovalam, Udupi and Mumbai peak in mid-year. The north-east monsoon (roughly October – December) brings moisture across the Bay of Bengal to the south-east coast, which is why Rameswaram and Chennai peak late in the year. Puri, further north on the east coast, still sits within the reach of the south-west monsoon, which explains its July – September peak and makes it the exception that proves the rule.
✦ The data averages several years of monthly rainfall for each city. The six cities split by coast — Kovalam, Udupi and Mumbai on the west, Rameswaram, Chennai and Puri on the east — with the west coast receiving more rain. West-coast cities peak in June – August (south-west monsoon), Rameswaram in October – December and Chennai in November (north-east monsoon), while Puri peaks in July – September; January – March are dry everywhere.
Solutions written by the tuition.in editorial team and checked against NCERT Ganita Prakash Grade 8 Part 2 (hegp205.pdf), Chapter 5 'Tales by Dots and Lines', pages 103-133. HAND-WRITTEN throughout. Part 2 books carry NO printed answer key, so every numeric answer was derived from first principles and independently recomputed in Python. MEASURED OFF THE PRINTED FIGURES at 300-1200 dpi: the page-113 dot plot reads 4, 7, 8, 8, 9, 9, 9, 9, 9, 11 (ten dots, so the missing eleventh is 16); the three page-114 album dot plots read A = 5, 5, 5.25, 5.5, 5.75, 6, 6.5 (mean 39/7 = 5.5714), B = 0.5, 0.75, 1.5, 1.5, 2, 3.75, 4.25, 5 (mean 2.406) and C = 3.5, 3.5, 3.5, 4, 4, 4, 4.25, 4.5 (mean 3.906), so A is the 5.57 album; the page-115 cycle dot plot reads 0:3, 1:1, 2:4, 3:7, 4:7, 5:5, 6:4, 7:6, 8:3, 9:0, 10:2 (N = 42, sum 193, mean 4.595, median 4 — and the book's own hint that four students rode twice confirms the reading); the page-128 dot plot reads 14:2, 15:2, 16:3, 17:5, 18:4, 19:4, 20:3, 21:1, 22:0, 23:1 (N = 25, sum 443, mean 17.72); the page-122 New Delhi rainfall line reads 1.3, 1.5, 1.5, 1.1, 1.5, 3.8, 9.7, 9.7, 4.0, 1.0, 0.4, 1.0 days, total about 37, which makes New Delhi the least-rainy of the four cities and Port Blair the most at 125.8; the page-123 births line graph was found to span April 2017 to March 2020 (36 monthly points) with July 2017 about 1.77 M, January 1.67/1.75/1.77 M in 2018/19/20 and a 2019 total of about 21.4 M; the page-124 Wheat-vs-Rice infographic was read state by state and Karnataka's hidden shade was matched against the colour bar (calibrated exactly on Kerala +79 and Chhattisgarh +80) to about +68; the page-125 activity strips were decoded box by box across all 48 boxes of all three strips, giving Friday/Saturday/Sunday and an identical 10.5 hours of sleep and 1.5 hours of eating on each day; the page-130 hobbies line graph gives urban age 10 about 2 h 06 min and rural 1.5 h at age about 14.3, so option (d); the page-132 sunrise/sunset charts give Kibithu the earliest January sunrise (05:57, day length 10 h 31 min) and Srinagar the longest day of the year (14 h 25 min in June); and the page-132 moon chart gives purnima about the 14th and amavasya about the 28th-29th with a measured daily lag of 49 minutes. TWO SLIPS IN THE PRINTED BOOK ARE FLAGGED: page 125 says Manoj recorded 'five types of activities' and then lists six (the strips do use six colours), and the page-122 Figure it Out numbers two different questions as '2'.. Questions are referenced from the NCERT textbook for identification.
