Collecting data in a table
Samaira and Kabir played TV reporters and asked 35 friends how long they watch TV. To keep the answers tidy they wrote them in a table with tally marks.
Data is information we collect. A table lists each group and how many fall in it. Tally marks help count: four upright lines and a fifth line across them make a bundle of 5. The total of all groups equals the number of people asked.
Formula: Bundle of 5 = 5 tally marks. Total = sum of all groups. Difference = bigger group − smaller group.
In the figure: Tally marks: 7 + 12 + 9 + 7 = 35 children. 12 is two bundles of 5 and 2 more.
Rule 1: Reading a table — Find the group, read its number. For "more than" or "less than" add the groups that fit.
- Easy: Fruit survey: mango 12, banana 8, apple 6, orange 9; total 35.
- Medium: Most popular: mango (12). Least: apple (6). Difference 12 − 6 = 6.
- Exam-type: Watching more than 1 hour: add the "2 hours" and "more" groups.
Rule 2: Counting with tally — Count the bundles in 5s, then add the extra lines.
- Easy: 3 bundles and 2 lines: 15 + 2 = 17.
- Medium: 4 bundles and 1 line: 21.
- Exam-type: Two bundles: 10.
Always check that the groups add up to the number of people you asked.
Counting the fifth crossing line as an extra number instead of part of the bundle of 5.
Count in 5s: 5, 10, 15 … then add the loose lines. Memory clue: "Four lines, one cross: a bundle of five."
Spot the difference
| Group | Children |
|---|---|
| Half hour | 7 |
| 1 hour | 12 |
| 2 hours | 9 |
| More | 7 |
Practice questions
- 1In the table above how many children watch TV for 1 hour?
- 2How many children watch for more than 1 hour?
- 3How many watch for 1 hour or less?
- 4A tally shows 4 bundles and 3 lines. What number?
- 5Votes: cricket 14, kabaddi 9, football 11, hockey 6. How many children voted?
- 6In that vote, which game is the most popular and by how many votes does it lead the next?
- 7Ask 20 friends their favourite colour and make a table with tally marks. Do the groups add to 20?
- 8In a survey of 30 children, 18 chose tea-time snacks A and 7 chose B; the rest chose C. How many chose C?
Show answers (try them yourself first)
- 112
- 29 + 7 = 16
- 37 + 12 = 19
- 423
- 540
- 6Cricket, by 3 votes
- 7It should; if not, recount
- 85
Pictographs and the scale of an icon
Joseph Uncle has hundreds of toys, board games and sports items. Drawing one picture for each is too slow. Dipesh suggests one picture for every 5 items.
A pictograph shows data with pictures (icons). The scale tells how many items one icon stands for, for example 1 icon = 5 items. Number of items = number of icons × scale. A half icon shows half of the scale.
Formula: Items = icons × scale. Icons = items ÷ scale. Half icon = scale ÷ 2.
In the figure: Toys 4 icons = 20, board games 7 icons = 35, sports items 3 icons = 15. A bigger scale needs fewer icons.
Rule 1: Icons to items — Multiply the number of icons by the scale; add a half scale for a half icon.
Pictographs and the scale of an icon
In the app you can move this figure with your finger.
Open in the app- Easy: 7 icons, 1 icon = 5: 35 items.
- Medium: 3 icons and a half, 1 icon = 10: 35.
- Exam-type: 9 icons, 1 icon = 2: 18.
Rule 2: Items to icons — Divide the items by the scale. Choose a scale that divides all the numbers neatly.
- Easy: 30 items, 1 icon = 5: 6 icons.
- Medium: Data 20, 35, 15: scale 5 works (4, 7, 3 icons).
- Exam-type: Data 12, 18, 24: scale 6 works (2, 3, 4 icons).
Always write the scale next to the pictograph; without it nobody can read the numbers.
Counting each icon as 1 and forgetting to multiply by the scale.
Look at the scale first, then count icons. Memory clue: "Icons × scale = items."
Spot the difference
| Icons | Scale | Items |
|---|---|---|
| 7 | 5 | 35 |
| 3½ | 10 | 35 |
| 9 | 2 | 18 |
| 6 | 4 | 24 |
Practice questions
- 11 icon = 5. There are 6 icons. How many items?
- 21 icon = 3. There are 8 icons. How many items?
- 31 icon = 10. How many icons for 40?
- 41 icon = 10. How would you show 25?
- 5Dipesh uses 1 icon = 5 toys for 25 toys. A friend uses 1 icon = 1. How many icons does each use?
- 6Which scale is neat for 12, 18 and 30: 4, 6 or 7?
- 7Show 15, 20 and 35 books with another scale than 5 (for example 1 icon = 1)?
- 8A pictograph uses 1 icon = 4 and has 9 icons for apples and 6 for oranges. How many fruits in all?
Show answers (try them yourself first)
- 130
- 224
- 34
- 42 icons and a half icon
- 55 icons and 25 icons
- 66 (2, 3 and 5 icons)
- 7Scale 1: 15, 20, 35 icons; scale 10: 1½, 2, 3½ icons
- 8(9 + 6) × 4 = 60
Reading a pictograph
Deepti counted two-wheelers passing her house for an hour on three days and drew a pictograph with 1 icon = 3 two-wheelers. Which day was the busiest?
To read a pictograph: (1) read the scale; (2) count icons in each row; (3) multiply by the scale; (4) then compare, add or subtract.
Formula: Row value = icons × scale. Total = sum of rows. More/fewer = difference of rows.
In the figure: Monday 4 icons = 12, Wednesday 3 icons = 9, Friday 5 icons = 15 two-wheelers. Total 36; Friday is the busiest.
Rule 1: Compare rows — The longest row is the biggest; subtract the numbers to find how many more or fewer.
Reading a pictograph
In the app you can move this figure with your finger.
Open in the app- Easy: Mon 12, Wed 9: Wednesday had 3 fewer.
- Medium: Fri 15, Wed 9: Friday had 6 more.
- Exam-type: Most: Friday (15). Least: Wednesday (9).
Rule 2: Total and re-drawing — Add the row values for the total. To redraw with a new scale divide each value by it.
- Easy: 12 + 9 + 15 = 36 two-wheelers.
- Medium: New scale 1 icon = 6: 2, 1½ and 2½ icons.
- Exam-type: New scale 1 icon = 1: 12, 9 and 15 icons.
A half icon is half of the scale, not 1.
Comparing the number of icons when rows use different scales.
Write the row values next to each row first. Memory clue: "Read scale, count icons, multiply."
Spot the difference
| Day | Icons | Two-wheelers |
|---|---|---|
| Monday | 4 | 12 |
| Wednesday | 3 | 9 |
| Friday | 5 | 15 |
Practice questions
- 11 icon = 3. Monday 4 icons. How many two-wheelers?
- 2Which day had the most? (Mon 12, Wed 9, Fri 15)
- 3Total two-wheelers in three days?
- 4How many fewer on Wednesday than on Monday?
- 5How many more on Friday than on Wednesday?
- 6Redraw the data with 1 icon = 6. How many icons for Monday?
- 7A pictograph has books 6 icons and pens 4 icons with 1 icon = 8. How many more books than pens?
- 8On Saturday Deepti counts 21 two-wheelers. How many icons (1 icon = 3) should she draw?
Show answers (try them yourself first)
- 112
- 2Friday
- 336
- 43
- 56
- 62
- 7(6 − 4) × 8 = 16
- 87
Reading a bar graph
Sheela drew bars to show how many hours she spent sleeping, in school, studying, eating and playing, and on other things. Tall bars mean more time.
A bar graph uses bars of equal width. The horizontal line (base) shows the categories; the vertical line shows the numbers on a scale. The height of each bar shows the value, so the tallest bar is the biggest and the shortest is the smallest.
Formula: Value = height of the bar (× scale). Total = sum of all bars. Difference = taller − shorter.
In the figure: Sleep 8, School 6, Study 2, Eat and play 4, Other 4: the bars add to 24 hours.
Rule 1: Reading values — Go from the top of the bar straight across to the vertical scale and read the number.
Reading a bar graph
In the app you can move this figure with your finger.
Open in the app- Easy: Sleep bar reaches 8: 8 hours.
- Medium: Study 2 and Other 4: other is 2 hours more.
- Exam-type: Eat and play 4 and Other 4: the same time.
Rule 2: Totals and comparisons — Add the bar values for the total. For more or fewer subtract the shorter bar from the taller bar.
- Easy: 8 + 6 + 2 + 4 + 4 = 24 hours: a whole day.
- Medium: School 6 and Sleep 8: sleep is 2 hours more.
- Exam-type: If the scale is 1 square = 2 units and a bar is 5 squares tall: 10.
Bars start from zero. Check what the scale of the vertical line is before reading.
Reading the number from the wrong side of the bar or ignoring the scale (1 square = 2 units).
Use a ruler along the top of the bar to reach the scale. Memory clue: "Tall bar, big number."
Spot the difference
| Activity | Hours |
|---|---|
| Sleep | 8 |
| School | 6 |
| Study | 2 |
| Eat and play | 4 |
| Other | 4 |
Practice questions
- 1Sleep 8, School 6, Study 2, Eat and play 4, Other 4. Which bar is tallest?
- 2Which bar is shortest?
- 3How many hours in all?
- 4How many more hours in school than studying?
- 5Which two activities take equal time?
- 6Raman sleeps 9 hours and Sheela 8. Whose bar is taller, and by how much?
- 7Scale 1 square = 2 hours; a bar is 4 squares tall. How many hours?
- 8Whose day looks more balanced: sleep 8, school 6, study 2 or sleep 10, school 6, study 0? Give a reason.
Show answers (try them yourself first)
- 1Sleep
- 2Study
- 324
- 44
- 5Eat and play, and Other
- 6Raman, by 1 hour
- 78
- 8The first; it has time for studying too
Making a graph and choosing a scale
Rani's school canteen records food wasted each day. To draw the graph she must choose the scale so that the tallest bar fits on the page and every number can be shown.
To make a graph: (1) collect data in a table; (2) choose a scale (1 square or 1 icon = ? units) so the biggest number fits and all numbers are shown neatly; (3) draw bars or icons; (4) add a title and label both lines.
Formula: Bar height in squares = value ÷ scale. Best scale divides all the values.
In the figure: Food wasted: 5, 3, 8, 4, 6 kg; the tallest bar (8) needs 8 squares with 1 square = 1 kg. For 35 toys a scale of 5 needs 7 icons, a scale of 1 needs 35.
Rule 1: Choose the scale — Pick a scale that divides all the values and keeps the tallest bar short enough.
Making a graph and choosing a scale
In the app you can move this figure with your finger.
Open in the app- Easy: Values 20, 40, 60: scale 10 gives 2, 4, 6 squares.
- Medium: Values 12, 18, 6, 15: scale 3 gives 4, 6, 2, 5 squares.
- Exam-type: Values 5, 10, 15: scale 5 gives 1, 2, 3 squares.
Rule 2: Draw and label — Equal width, equal gaps, bars from the base line; title and labels on both lines.
- Easy: Title: "Food wasted in a week".
- Medium: Vertical label: kg; horizontal label: day.
- Exam-type: Pictograph: show 45 as 4 icons and a half icon when 1 icon = 10.
The same data can be drawn with different scales; the numbers do not change, only the picture.
Starting the bars at different heights, or leaving out the title and labels.
Divide the biggest value by the number of squares you have. Memory clue: "Scale, bars, title, labels."
Spot the difference
| Values | Good scale |
|---|---|
| 20, 40, 60 | 10 |
| 12, 18, 6, 15 | 3 |
| 5, 10, 15 | 5 |
| 8, 12, 4, 10 | 2 |
Practice questions
- 1Values 8, 12, 4, 10. With 1 square = 2 units, how many squares tall is the tallest bar?
- 2Choose a scale for 15, 30 and 45.
- 31 square = 5 units. How many squares for 35?
- 4Show 45 books in a pictograph with 1 icon = 10.
- 5Make a bar graph for Mon 5, Tue 3, Wed 8, Thu 4, Fri 6. What scale will you use?
- 6Why would 1 square = 1 be a poor scale for 200, 400 and 600?
- 7Paper strips for index fingers are 6, 7, 9 and 8 cm. Draw bars with 1 square = 1 cm. How tall is the longest?
- 8Draw a pictograph for apples 20, bananas 35, mangoes 15 with 1 icon = 5. How many icons for each?
Show answers (try them yourself first)
- 16
- 215 (1, 2, 3 squares) or 5
- 37
- 44 icons and a half icon
- 51 square = 1 kg (tallest bar 8 squares)
- 6The bars would need hundreds of squares
- 79 squares
- 84, 7 and 3 icons
Data word problems
Rani was shocked when she saw how much food her canteen wasted in a week. With a graph she can find the total, the worst day and even how many children could have eaten that food.
Use the graph: read the values, then add for totals, subtract for differences, multiply for "each" and divide for "share". Then think about what the data tells us and what we can do.
Formula: Total = sum of values. Difference = bigger − smaller. People fed = kg × (people per kg).
In the figure: 5 + 3 + 8 + 4 + 6 = 26 kg wasted. At 3 children per kg, 26 × 3 = 78 children could have been fed.
Rule 1: Choose the operation — "In all" → add; "how many more" → subtract; "each / for every" → multiply; "shared" → divide.
Data word problems
In the app you can move this figure with your finger.
Open in the app- Easy: Total waste: 26 kg.
- Medium: Wednesday 8 kg, Tuesday 3 kg: 5 kg more.
- Exam-type: 1 kg feeds 3 children: 26 kg feeds 78.
Rule 2: Think and predict — Use the data to say what will probably happen and what we can do.
- Easy: If the same food comes again next week, Wednesday's dish is likely to be wasted most.
- Medium: We can take smaller helpings and share leftovers.
- Exam-type: Fewer waste kg means more children fed.
Data tells a story: use it to make good decisions, like saving food.
Using the number of bars instead of the values on the vertical line.
Write each value next to its bar before adding. Memory clue: "Read, choose the operation, check."
Spot the difference
| Day | kg wasted |
|---|---|
| Monday | 5 |
| Tuesday | 3 |
| Wednesday | 8 |
| Thursday | 4 |
| Friday | 6 |
Practice questions
- 1Total food wasted in the week?
- 2On which day was the wastage highest?
- 3How many kg less was wasted on Tuesday than on Friday?
- 4If 1 kg feeds 3 children, how many children could the 26 kg feed?
- 5Which day had less waste: Monday or Thursday?
- 6Name two ways to reduce food wastage in a canteen.
- 7In a pictograph (1 icon = 5) toys show 4 icons, games 7 icons and sports 3 icons. How many items are there in total, and how many more games than sports items?
- 8If next week the waste drops by 2 kg every day, what is the new weekly total?
Show answers (try them yourself first)
- 126 kg
- 2Wednesday
- 33 kg
- 478
- 5Thursday (4 kg)
- 6Take small helpings; share or donate leftovers
- 770 items; 20 more games
- 826 − 5 × 2 = 16 kg