14 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 122, Q1
The average number of customers visiting a shop and the average number actually purchasing on each day of the week is: Visiting — Mon 16, Tue 19, Wed 10, Thu 14, Fri 20, Sat 22, Sun 35; Purchasing — Mon 10, Tue 8, Wed 7, Thu 11, Fri 12, Sat 16, Sun 26. Visualise this data on a line graph and describe what it shows.
Hint. Both series share one pair of axes; choose a vertical scale that comfortably fits the largest value.
Drawing the graph.
· Horizontal axis: the seven days, Mon to Sun, evenly spaced.
· Vertical axis: number of customers, from 0 to 35. A scale of 1 cm = 5 customers works well, with gridlines at 0, 5, 10, 15, 20, 25, 30, 35.
· Plot the seven 'Visiting' points and join them; plot the seven 'Purchasing' points and join them with a different colour and a different marker shape, so the graph still reads in black and white.
· Add a legend and label both axes.
The two series in a table:
| Mon | Tue | Wed | Thu | Fri | Sat | Sun |
|---|
| Visiting | 16 | 19 | 10 | 14 | 20 | 22 | 35 |
| Purchasing | 10 | 8 | 7 | 11 | 12 | 16 | 26 |
| Not purchasing | 6 | 11 | 3 | 3 | 8 | 6 | 9 |
| Purchasing as % of visiting | 63% | 42% | 70% | 79% | 60% | 73% | 74% |
What the graph shows.
· Both lines climb towards the weekend and peak sharply on Sunday (35 visiting, 26 purchasing) — Sunday brings more than half again as many visitors as any weekday.
· Wednesday is the quietest day on both counts, with only 10 visitors.
· The purchasing line stays below the visiting line throughout, as it must, since every purchaser is also a visitor. The vertical gap between the lines is the number of people who came and bought nothing.
· The gap is widest on Tuesday — 19 visitors but only 8 buyers, a conversion of just 42%, the poorest of the week even though Tuesday is the third-busiest day. Thursday is the best converter at 79%, despite being a quiet day.
A caution about the numbers. These are averages over many weeks, not a single week's counts, which is why they need not be whole numbers in general and why one unusual Sunday would not distort the picture.
✦ The line graph has days on the horizontal axis and customers on the vertical axis, with two labelled lines. Both peak on Sunday (35 visiting, 26 purchasing) and are lowest on Wednesday (10 and 7). The purchasing line always lies below the visiting line, and the gap is widest on Tuesday, where only 8 of 19 visitors bought anything — the worst conversion of the week.
26 marksGanita Prakash Cl-8 Part 2, Figure it Out, pages 122-123, Q2
The average number of rainy days per month is tabulated for Mangaluru, New Delhi (blank), Port Blair and Rameswaram, and a line graph shows New Delhi's line. (i) How could this data be compiled? (ii) Plot Mangaluru, Port Blair and Rameswaram on the graph. (iii) Fill in the New Delhi row from the graph. (iv) Which city gets the most rainy days per year and which the least? (v) When is the rainy season in New Delhi and in Rameswaram?
Hint. For (iii) read the printed New Delhi line month by month; for (iv) add up each row.
(i) How the data is compiled. For each city, the number of days on which rain fell in a given month is counted, and this is repeated over many years; the counts for that month are then averaged. That is why the entries are decimals — 27.7 rainy days in July does not describe one particular July but the average across several. Averaging over years removes the effect of one freak wet or dry year.
(ii) Plotting the three cities. Use the same axes as the printed New Delhi line: months along the bottom, number of days (0 to 30) up the side. Round to whole days as the question allows, and give each city a distinct colour and marker:
| Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|
| Mangaluru | 0 | 0 | 0 | 2 | 6 | 24 | 28 | 25 | 14 | 9 | 4 | 1 |
| Port Blair | 2 | 1 | 1 | 3 | 16 | 19 | 17 | 19 | 17 | 14 | 11 | 5 |
| Rameswaram | 3 | 1 | 2 | 3 | 3 | 0 | 1 | 1 | 2 | 8 | 10 | 8 |
(iii) Reading New Delhi off the printed line. Taking each month's height against the gridlines:
| Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|
| New Delhi | 1.3 | 1.5 | 1.5 | 1.1 | 1.5 | 3.8 | 9.7 | 9.7 | 4.0 | 1.0 | 0.4 | 1.0 |
The line is almost flat at 1 to 1.5 days for most of the year, rises through June, sits on a twin peak of nearly 10 days in July and August, then drops steeply through September.
(iv) Yearly totals.
· Mangaluru: 0.1 + 0 + 0.1 + 1.8 + 6.2 + 24.1 + 27.7 + 24.5 + 14 + 8.8 + 3.9 + 0.9 = 112.1 days
· Port Blair: 2.4 + 1.3 + 0.9 + 3.3 + 15.5 + 18.7 + 17.3 + 18.8 + 16.8 + 14.1 + 11.3 + 5.4 = 125.8 days
· Rameswaram: 2.6 + 1.3 + 1.9 + 3.4 + 2.5 + 0.4 + 1 + 1 + 1.9 + 8.1 + 10.4 + 7.8 = 42.3 days
· New Delhi (from the graph): ≈ 1.3 + 1.5 + 1.5 + 1.1 + 1.5 + 3.8 + 9.7 + 9.7 + 4.0 + 1.0 + 0.4 + 1.0 = ≈ 37 days
Most: Port Blair (about 126 days — rain on more than a third of all days). Least: New Delhi (about 37 days), just below Rameswaram's 42.
Port Blair's total is worth a second look: it never has a month as wet as Mangaluru's July, yet it beats Mangaluru over the year because its rain is spread across eight months instead of concentrated in three.
(v) The rainy seasons.
· New Delhi: July – September, peaking in July and August. This is the south-west monsoon, which reaches the north of India by late June.
· Rameswaram: October – December, peaking in November. This is the north-east monsoon, which brings rain across the Bay of Bengal to the south-east coast. Rameswaram is almost dry from January to September — the south-west monsoon largely passes it by.
✦ (iii) New Delhi ≈ 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. (iv) Port Blair gets the most (≈ 126 days/year) and New Delhi the least (≈ 37 days/year). (v) New Delhi's rainy season is July – September (south-west monsoon) and Rameswaram's is October – December (north-east monsoon).
36 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 123, Q2 (the second question numbered 2)
A line graph shows the number of live births each month in India. (i) What are your observations? (ii) Approximately how many births were there in July 2017? (iii) What time period does the graph capture? (iv) Compare January births in 2018, 2019 and 2020. (v) Estimate the number of births in 2019.
Hint. Look for a shape that repeats — and remember that the graph shows months, while (v) asks for a year.
(The book numbers this question 2 as well; it is the second Q2 in this Figure it Out, and it follows the rainfall question.)
(iii) The time period — take this first, since everything else depends on it. The labelled gridlines are Jul 2017, Jan 2018, Jul 2018, Jan 2019, Jul 2019 and Jan 2020, spaced six months apart. The first plotted point sits three months to the left of Jul 2017 and the last sits two months to the right of Jan 2020, so the graph runs from April 2017 to March 2020 — 36 monthly points, exactly three years.
(ii) July 2017. Reading the point above the Jul 2017 gridline against the vertical scale gives about 1.77 million live births — a little under halfway between the 1.5M and 2M gridlines.
(i) Observations. The striking feature is a strong seasonal pattern that repeats almost identically every year:
· Births peak in August – October each year, reaching close to 2 million a month.
· They dip in February and again in April – June, falling to about 1.45 – 1.6 million.
· The whole three-year record stays inside a band of roughly 1.4M to 2.0M, so the seasonal swing is about half a million births a month — a variation of nearly a third from trough to peak.
· The pattern is so regular that the 2018 curve, the 2019 curve and the 2017 curve almost lie on top of one another. This is what makes a line graph the right choice: the repetition is visible instantly, whereas 36 separate bars would hide it.
A natural follow-up question: births peaking in August – October means conceptions peaking around November – January. Why?
(iv) January births.
· Jan 2018 ≈ 1.67 million
· Jan 2019 ≈ 1.75 million
· Jan 2020 ≈ 1.77 million
January rises slightly from year to year, by roughly 80,000 then 20,000. January is always a mid-range month, well below the autumn peak and above the spring trough.
(v) Births in 2019. Read all twelve 2019 points and add them:
Jan 1.75, Feb 1.56, Mar 1.78, Apr 1.49, May 1.63, Jun 1.63, Jul 1.81, Aug 1.99, Sep 1.96, Oct 1.99, Nov 1.93, Dec 1.86 (all in millions)
Total ≈ 21.4 million births in 2019.
A quicker estimate: the monthly values hover around 1.78 million on average, and 12 × 1.78 ≈ 21.4 million — the same answer. Since each reading is only accurate to about ±0.03 million, the honest statement is 'roughly 21 million'.
✦ (i) A strongly repeating seasonal pattern — a peak of nearly 2 million in August – October and troughs near 1.5 million in February and April – June, almost identical in all three years. (ii) About 1.77 million in July 2017. (iii) April 2017 to March 2020, 36 monthly points. (iv) January births rise slightly: 1.67M (2018), 1.75M (2019), 1.77M (2020). (v) About 21.4 million births in 2019.
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.
