E ExamMaster

CBSE Class 6 · Mathematics

Data Handling and Presentation

Official NCERT chapter from Ganita Prakash (book code fegp1). ExamMaster notes are original teaching at CBSE Class 6 depth.

This lesson follows the official chapter “Data Handling and Presentation” in Ganita Prakash. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 6
  • Easy level
  • 8 concepts

1Collecting and Organising Data

Data here are records of a question: one observation, one mark, then a table of labels. Organising is sorting into those labels.

A pile of opinions with no labels is not organised.

Figure. Each upright stroke is one observation. The fifth stroke crosses the first four and is still five, not a new kind of mark. Cats 5, dogs 3, birds 2 — the numbers under the groups must match the strokes.

How it works

  1. Name the questionOne label-set.
  2. Collect one mark per observationHonest.
  3. Put marks into labelled rowsA table.

2Pictographs

A pictograph uses pictures as marks. It needs a key when one picture stands for many. Without a key the picture is mute.

A taller drawing with a thicker crayon is not more data if the key is the same.

Figure. A pictograph needs a key before it is a count. Here one box stands for 2 votes, so three boxes are 6, two boxes are 4, one box is 2. Changing the key mid-chart would silently double a row.

How it works

  1. Read the key1 picture = ?
  2. Count the picturesFor one label.
  3. Multiply by the keyThe count.

3Bar Graphs

A bar’s height (or length) is the count. Bars need a scale and equal width. Compare heights, not how decorated a bar is.

A 3-D bar that looks “bigger” at the same height is a cheat.

Figure. Bar length tracks the count. Cats 8 is the longest bar; birds 3 is the shortest. One scale serves the whole chart. The bars are not decorations around the names.

How it works

  1. Read the scaleWhat one grid step means.
  2. Read each bar against the scaleA number.
  3. Compare those numbersMost, least, how many more.

4Drawing a Bar Graph

Choose a scale that fits the largest count. Draw equal-width bars from a common baseline. Label the axis.

A scale that cannot fit the largest count is a broken graph.

Figure. To draw a bar graph: pick one scale, mark it, then grow each bar to its count. The dashed rule at 4 is a scale tick, not a category. Cats reach 8, dogs 5, birds 3 on that same scale.

How it works

  1. Find the largest countFits the scale.
  2. Pick a friendly step1, 2, 5, or 10.
  3. Draw from the same baselineEqual widths, labels on.

5A tally is one mark for one observation

Five is a gate-tally: four sticks and a cross. Two tallies for one child doubles the pile.

A scribble of many lines is not a counted tally until you can read fives.

Figure. A tally is one mark for one observation. Four upright strokes are four. The fifth stroke crosses those four and is still one more — five, not a new unit. Do not count the gate as ten.

How it works

  1. One observationOne mark.
  2. Bundle five as a gateEasier count.
  3. Total = 5×gates + leftover sticksThe count.

6A key is needed when one picture stands for many

40 observations as 40 pictures is painful. 1 picture = 5 makes 8 pictures. Write the key on the graph.

Inventing a key after you drew is a lie unless you redraw.

Figure. A key is needed when one picture stands for many. The key box says 1 box = 5. Four pictures are 20, not 4. Drop the key and the row becomes an honest-looking lie.

How it works

  1. Choose a key that divides the counts honestlyOr show a half-picture only if the key allows.
  2. Write it on the graph1 picture = …
  3. Compute counts as pictures × keyTable must match.

Pictograph key

Key: 1 book = 4 students. “Maths” shows 5 books. How many students?

  • Key4
  • Pictures5
  • Count5×4=20

Pro tip. Pictures times the key. No key means mute.

7Bars compare counts, not decorations

Most is the tallest honest bar on a shared scale. Colour and clip-art do not add students.

Compare the scale-readings.

Figure. Bars compare counts, not decorations. Red 10 is longest because 10 is the biggest count, not because the name is louder. How many more red than green is 10 − 4 = 6 — read it from the lengths, then check the numbers.

How it works

  1. Read each bar on the scaleNumbers.
  2. Name the largestMost.
  3. Ignore decorationNot data.

8A table and a graph must agree

If the table says 20 and the bar reads 16, one record is wrong. Recount both.

A story about “rounding for beauty” is not a fix.

Figure. A table and a graph must agree. The left column says cats 8, dogs 5, birds 3. The bars use those same three numbers at true length: 8, 5 and 3 parts on a shared 8-part scale (0.48, 0.30, 0.18). If a bar and its table cell disagree, one of them was copied wrong — do not average them.

How it works

  1. Read the table cellA number.
  2. Read the graph with scale or keyA number.
  3. Demand they matchOr redo the collection.
A bar that is more decorated at the same height
  1. Does not mean a larger count
  2. Means more students
  3. Replaces the scale

Bars compare scale-heights, not clip-art.

Notes

  • The official chapter title is “Data Handling and Presentation”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • Count = pictures \times key.
  • How many more = larger count - smaller count.
  • Tally total = 5\times gates + leftover marks.

Recap

Hold these pegs from the official chapter “Data Handling and Presentation”. The wording is ExamMaster’s teaching, not a textbook recap.

Collecting and Organising Data
Data here are records of a question: one observation, one mark, then a table of labels.
Pictographs
A pictograph uses pictures as marks. It needs a key when one picture stands for many. Without a key the picture is mute.
Bar Graphs
A bar’s height (or length) is the count. Bars need a scale and equal width. Compare heights, not how decorated a bar is.
Drawing a Bar Graph
Choose a scale that fits the largest count.
A tally is one mark for one observation
Five is a gate-tally: four sticks and a cross.
A key is needed when one picture stands for many
40 observations as 40 pictures is painful.

Practise Data Handling and Presentation

Reading is free and needs no account. Practice, mocks and progress live in the app.

  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
Continue with Google — freeNo card, no trial. Works offline once installed.