Data Handling and Presentation
Turn messy lists of facts into neat tables, friendly pictures, and clear bar graphs — try the live bar-graph and pictograph builders below!
Collecting & organising data
🏏 Navya & Naresh's favourite games
Navya thinks cricket is everyone's favourite. Naresh isn't sure. So they go around and ask all 27 of their classmates and write down each answer — that's collecting data!
Q1. Just having a messy list of 27 names isn't enough — you can't tell the popular game at a glance. They should organise the list into a table, using tally marks to count how many students picked each game.
Q2. Hockey is the most popular game, with a frequency of 8!
A quick way to count while collecting data: draw one line | for each item. On the 5th one, draw it slanting across the first four ||||̄ — this makes it super fast to count in groups of 5! The count you end up with is called the frequency.
a. Most popular TV show among her classmates — ✓ needs data collection (have to ask around).
b. When did India get independence? — ✗ no data collection needed (it's a known historical fact: 1947).
c. How much water is getting wasted in her locality? — ✓ needs data collection (someone has to measure/observe it).
d. What is the capital of India? — ✗ no data collection needed (known fact: New Delhi).
🍬 Example: favourite sweets
| Sweet | Tally | Frequency |
|---|---|---|
| Jalebi | |||| | | 6 |
| Gulab jamun | |||| |||| | 9 |
| Gujiya | |||| |||| ||| | 13 |
| Barfi | ||| | 3 |
| Rasgulla | |||| || | 7 |
This table tells you HOW MANY of each sweet to buy — but not WHICH child wanted which sweet. To hand out the right sweet to the right person, you'd still need the original name-by-name list, not just the totals.
No, it isn't sufficient. The table only shows the TOTAL number of students who chose each sweet — it doesn't say which particular student wanted which sweet.
Alternative: keep the original name-by-name list (like Nilesh's roll of who-picked-what), or make a table sorted by student name showing each student's chosen sweet next to their name.
👟 Example: shoe sizes
Sushri Sandhya noted down shoe sizes for 27 students, then arranged them in ascending order to make them easier to read:
Yes! Instead of writing every single number in order, you could organise it as a frequency table (shoe size in one column, tally marks and count in the next) — that's actually the neatest way, since it groups repeats together instead of listing them one by one.
"What's the most popular TV show in my class?" — yes, you must ask around. "When did India get independence?" — no, that's a known fact (1947), not something you collect from people!
On your way from home to school, write down the name of every tree you spot and keep a running tally, like this:
| Tree | No. of trees |
|---|---|
| Peepal | ? |
| Neem | ? |
| … | ? |
Then answer: which tree did you find the most of? Which the least? Were any two trees found in equal numbers? This is a real data-collection activity — there's no single fixed answer, it depends on YOUR walk!
Paste a small news article on paper, then make this table and fill in how many times each letter appears in the article's words:
| Letter | c | e | i | r | x |
|---|---|---|---|---|---|
| Number of times found | ? | ? | ? | ? | ? |
a. The letter found the most is usually e. b. The letter found the least is usually x.
c. If you list all five letters from lowest frequency to highest, almost everyone in class gets nearly the same order: x, c, r, i, e — because in English, the letter 'x' is rare while 'e' is the most commonly used letter in the whole language, no matter which article you pick! (Also discuss: what steps did you follow, and would a different article change your process?)
Pictographs
A pictograph uses little pictures instead of numbers, so you can understand data just by counting pictures. Each picture stands for a certain amount — this is called the scale, and it must always be shown.
🚌 How students travel to school (scale: 🙂 = 1 student)
Most used: School bus (10). Least used: Cycle (3). See how fast that was to spot — just by counting faces!
If 🙂 = 10 children but you need to show 25, you can't draw 2.5 whole faces neatly! That's when we draw a half-icon (half a face = 5 children). This is one reason pictographs get tricky with bigger, messier numbers.
Nand Kishor asked children in his middle school in Berasia how often they slept at least 9 hours a night. He made a pictograph where 🌙 = 10 children:
Q1. How many children always slept 9+ hours?
Q2. How many sometimes slept 9+ hours?
Q3. How many never slept 9+ hours (i.e. always slept LESS than 9 hours)? How do you know?
Lakhanpal's friends Jarina and Sangita wanted to make a pictograph of students PRESENT in each class (bigger numbers, like 33 or 27) using one symbol = 10 students, then switched to using a half-symbol for 5. But what problems would show up if a class had exactly 33 or 27 students? At scale 1 🙂 = 10, you'd need 3.3 or 2.7 icons — and you can only draw whole or half icons, not a "third" or "tenth" of one! So numbers like 33 or 27 can't be shown exactly with this scale — you'd have to round, which makes the picture a little bit inaccurate.
🎮 Build your own pictograph
Bar graphs
A bar graph uses solid bars instead of pictures. The height of each bar shows the amount. Bar graphs are much faster to draw than pictographs when the numbers are big — one tall bar beats drawing a hundred tiny pictures!
🙋 Lakhanpal's absent-students bar graph
Lakhanpal's bar graph shows how many students were absent that day, in Classes 1–8: 3, 5, 4, 2, 0, 1, 5, 7.
Class 2 absent: 5 students.
Maximum absent: Class 8 (7 students absent).
Full attendance (0 absent): Class 5.
🚗 India's traffic, hour by hour
Maximum traffic: 7–8 a.m., about 1200 vehicles (rush hour!). Minimum: 6–7 a.m., about 150 vehicles (too early for most people). The second-longest bar is 8–9 a.m. with about 1000 vehicles, and the two-hour total for 8–10 a.m. is about 1000 + 800 = 1800 vehicles.
Q1. Adding all six hourly bars (approx. values read off the graph):
Q2. Very little traffic 6–7 a.m. because it's too early — most people, offices, and schools haven't started their day yet.
Q3. Traffic is heaviest 7–8 a.m. because that's peak "rush hour" — people are travelling to school and work all at once.
Q4. Traffic keeps decreasing after 8 a.m. because most people have already reached school/work by then, so fewer and fewer vehicles are still on the road as the morning goes on.
🎮 Try the live bar graph
Smriti's runs in each of her 8 matches were:
Q. The smallest score is 0 and the biggest is 100. If we used a scale of 1 unit length = 1 run, what would go wrong? What scale should we use instead?
Scale chosen: 1 unit = ₹200. To find bar height, divide each amount by 200:
Q1. On which item does the family spend the most, and second-most?
Q2. Is electricity about half of education?
Q3. Is education less than one-fourth of food?
Columns, infographics & taking care
A bar graph with vertical (standing up) bars is also called a column graph — like the columns/pillars that hold up a roof! Use vertical bars for things measured upward (like mountain heights). Use horizontal bars for things measured sideways (like river lengths).
Vertical bars (a column graph) are best. Height is measured going UP from the ground, so standing columns naturally match the real-life direction of "tall" — it's easier to compare heights by comparing how tall the columns stand, just like comparing the students themselves!
Horizontal bars are best. A river's length runs sideways along the ground (not upward), so a horizontal bar matches that real-life direction — just like the tallest-mountain-vs-river example: mountains (measured up) get columns, rivers (measured sideways) get horizontal bars.
🏔️ Tallest mountain on each continent
| Continent | Mountain | Height |
|---|---|---|
| Asia | Everest | 8,848 m |
| South America | Aconcagua | 6,962 m |
| North America | Denali | 6,194 m |
| Africa | Kilimanjaro | 5,895 m |
| Europe | Elbrus | 5,642 m |
| Antarctica | Vinson Massif | 4,892 m |
| Australia | Koscuiszko | 2,228 m |
Take the same 7-mountain table and turn it into a fancy infographic — "the seven highest peaks on the seven continents", drawn as triangles instead of plain bars. If those triangles get both taller AND wider as the mountain gets bigger, it tricks your eye into thinking Everest looks about twice as tall as Elbrus — but the real ratio is only 8848 ÷ 5642 ≈ 1.57 times, not 2! A picture that looks more realistic isn't always more accurate — making a graph pretty should never make it lie.
Every question from the book
Arranging the numbers in order first (smallest to largest) makes ALL of these much easier to count!
Fewest: Thursday (0 books). Most: Saturday (8 books) — maybe more free time on a weekend!
a. Rani bought 300 kites, and the scale is 1 symbol = 100 kites, so 300 ÷ 100 = 3 symbols.
b. Maximum kites: Poonam Ben (700).
c. Jasmeet (450) vs Chaman (250): since 450 > 250, Jasmeet purchased more kites.
Since 700 > 600, yes, Rukhsana is correct! Poonam Ben bought more than double what Rani bought (and Jetha Lal, like Chaman, bought 250 kites).
🐛 Samantha's tea-garden critters
| Insect / critter | Count |
|---|---|
| Mites | 6 |
| Caterpillars | 10 |
| Beetles | 5 |
| Butterflies | 3 |
| Grasshoppers | 2 |
The biggest number is 10 (Caterpillars), and the smallest is 2 (Grasshoppers) — small enough that a simple scale of 1 unit length = 1 critter works nicely.
Vidisha: 24 ÷ 6 = 4. Jabalpur: 20 ÷ 5 = 4. Both agree, so scale = 1 unit length = 4 tickets.
So Seoni's bar is correct, but Indore's bar is wrong — it should be redrawn taller, at 7 units instead of 4.
🚦 Chinu's transport tally (9–10 a.m.)
| Means of transport | Frequency |
|---|---|
| Bike | 13 |
| Car | 6 |
| Bicycle | 8 |
| Auto rickshaw | 8 |
| Scooter | 9 |
| Bus | 4 |
| Bullock cart | 2 |
Bike was used the most (13 times). Total vehicles counted: 13+6+8+8+9+4+2 = 50.
How would you collect this data yourself? Make a 2-column table (transport type, tally marks), stand where you can see the road, and put a tally mark for each vehicle as it passes — then convert tallies to totals at the end.
Make a table with rows for 1, 2, 3, 4, 5, 6. Roll the die 30 times, and for each roll put a tally mark next to the number you got. When you're done, count up the tallies for each number — they should add up to 30 in total.
| Number rolled | Tally marks | Frequency |
|---|---|---|
| 1 | — | ? |
| 2 | — | ? |
| 3 | — | ? |
| 4 | — | ? |
| 5 | — | ? |
| 6 | — | ? |
There's no single "correct" answer here since it depends on your own 30 rolls — but a fair die should land on each number roughly 30 ÷ 6 = 5 times, though real rolls will vary a bit! Find your minimum, maximum, and any numbers that tied.
🏏 Bumrah's wickets, in detail
| Wickets taken | No. of matches |
|---|---|
| 0 | 2 |
| 1 | 4 |
| 2 | 6 |
| 3 | 8 |
| 4 | 3 |
| 5 | 5 |
| 6 | 1 |
| 7 | 1 |
a. It shows, over Bumrah's last 30 matches, how many matches he took each possible number of wickets (0 through 7) in.
b. A good title: "Wickets Taken by Jaspreet Bumrah in his Last 30 Matches".
c. Something that stands out: he took 7 wickets in only 1 match out of 30 — a really rare, impressive feat! (Also notice he most often took exactly 3 wickets, in 8 matches.)
d. He took 4 wickets in 3 matches (read straight from the table).
No, Mayank is wrong! Just adding the wicket numbers ignores how many matches had each count. You must MULTIPLY each wicket count by its number of matches, then add:
Smallest: Village D (3). Most: Village C (8).
Village C minus Village B: 8 − 5 = 3 — Village C has 3 more tractors than Village B.
Half of Village E's tractors: 6 ÷ 2 = 3. Village D has exactly 3.
Yes, Komal is correct!
All six numbers divide evenly by 6, so scale = 1 icon = 6 dogs works perfectly (18÷6=3, 36÷6=6, 12÷6=2, 48÷6=8, 18÷6=3, 24÷6=4).
Since 84 > 72, Kamini is correct!
🎨 120 students' free-time survey (scale: 1 unit = 5 students)
| Preferred activity | No. of students |
|---|---|
| Playing | 45 |
| Reading story books | 30 |
| Watching TV | 20 |
| Listening to music | 10 |
| Painting | 15 |
Other than playing, reading story books is preferred by the most students (30 of them).
🌱 Tree-sapling planting, day by day
a. Wednesday + Thursday: 30 + 40 = 70 saplings.
c. Greatest number planted on Saturday (60), least on Wednesday (30). Possibly more people are free to help plant on a weekend (Saturday), while a mid-week rainy day or a busy school day could explain fewer saplings on Wednesday — you could check this by comparing with the week's weather or school schedule!
🐅 Tigers in India — find the graph's mistakes
| Year | Number of tigers (approx.) |
|---|---|
| 2006 | 1,400 |
| 2010 | 1,700 |
| 2014 | 2,200 |
| 2018 | 3,000 |
| 2022 | 3,700 |
Comparing each drawn bar to the table:
Only the 2022 bar is drawn correctly. The bars for 2006, 2010, 2014, and 2018 all need to be redrawn to the right length so they match the frequency table.
Everest would need to be 11,284 m to be truly double Elbrus — but it's only 8,848 m. The picture exaggerates the difference. Never let a "pretty" graph lie about the numbers!
Increase over the full 50 years (1951 to 2001):
Increase in each individual decade:
Notice the amount added each decade kept growing too (8, 10, 14, 16, 18) — population wasn't just increasing, it was increasing faster and faster each decade!
👧 Girls per class (8 classes, scale: 1 icon = 4 girls)
A school's pictograph shows the number of girl students in each of its 8 classes, using one girl-icon to represent 4 girls (with half-icons for 2 more).
a. Class 8 has the least number of girl students (fewest icons drawn).
b. Reading the icons for Class 5 and Class 6, the difference between them works out to 6 girls.
c. If 2 more girls join Class 2, that's exactly enough to turn Class 2's half-icon into a full icon (since scale = 1 icon = 4 girls, a half-icon = 2 girls, and 2 more girls completes it).
d. Class 7 has 12 girls — that's 3 full icons, since 3 × 4 = 12.
Practice like the real exam
Section A · MCQ (1 mark each)
(b) scale
(b) column graph
Section B · short answer (2 marks each)
Section C · longer answer (3 marks each)
If the scale doesn't start at zero, bar lengths stop being truly proportional to the real values — a small difference can be made to LOOK huge, or a big difference can be hidden. This is exactly the kind of mistake the mountain infographic made (adding width as well as height), which made Everest look twice as tall as Elbrus when it's really only about 1.57 times taller. Starting from zero keeps the picture honest.
Section D · 4 marks each
Section E · case study (4 marks)
(a) Vidisha: 24÷6=4. Jabalpur: 20÷5=4. Both give the same answer, so the scale is 1 unit = 4 tickets.
(b) Sagar (16 tickets): 16 ÷ 4 = 4 unit-lengths — the same height as Seoni's bar (also 16 tickets).
You did it! 🎉
🏁 Chapter 4 of 5 · Term 1 Maths · Niyati, Class 6