Data Handling and Presentation · Lesson 7 of 7
Chapter Summary and Practice
“Bring collection, tables, pictographs, bar graphs, and honest interpretation together.”
• Trace a question from data collection through an organised display. • Choose and interpret keys and scales for different values. • Compare tables, pictographs, and bar graphs for the same information. • Check numerical claims and repair misleading displays. • Explain what a data pattern shows and what further evidence would test a cause.
A connected route through the chapter
Begin with a question: what do we want to learn, and whose observations are relevant? Collect each response using a consistent rule. A raw list retains detail; arranging numerical values or tallying categories helps us count them. A frequency table records how often each value occurs. Then we may choose a pictograph or bar graph to make comparisons visible. Finally we read the display, check its accuracy, and distinguish its measurements from our explanations of them.
| Stage | Question to ask | Example |
|---|---|---|
| Collect | What observation is needed and how will it be recorded? | Ask each student for one preferred activity. |
| Organise | Which categories and frequencies result? | Tally each activity; check counts against responses. |
| Represent | Which key or scale can show every value? | Draw pictures or equal-width bars with a labelled scale. |
| Interpret | What comparison or total answers the question? | Identify the largest count and compare other categories. |
| Check | Does the visual agree with the table? | Recount symbols and read every bar back into a number. |
What each representation keeps visible
A table is especially useful for exact counts and calculations. A pictograph draws attention through symbols, provided its key makes whole and partial symbols clear. A bar graph makes comparisons across categories quick, especially when counts are too large for many pictures. We can use more than one display for the same data, but each must preserve the original values.
| Representation | Strength | Essential check |
|---|---|---|
| Frequency table | Shows exact category counts compactly | Frequencies add to the number of observations. |
| Pictograph | Makes comparison visual with a chosen symbol | Every whole or partial picture matches its key. |
| Bar graph | Shows category comparisons through heights or lengths | Scale begins at zero; bars have equal width and correct heights. |
A key tells how many people or objects a pictograph symbol represents. A bar-graph scale tells how much a fixed length represents. If one picture equals five people, three pictures equal fifteen. If one graph unit equals five people, a bar that is three units long also means fifteen. The two drawings look different, but the same multiplication underlies both readings.
Problem
A class tallies reading 12, playing 18, and painting 6. Give a pictograph key and a bar-graph scale that work without partial units.
- 1.Choose one picture = 3 students: reading needs 4 symbols, playing 6, and painting 2.
- 2.Choose one bar unit = 3 students: draw bar heights 4, 6, and 2 equal units from zero.
- 3.Check both displays against the table: 4×3 = 12, 6×3 = 18, and 2×3 = 6. There are 36 responses in total.
Compare the right quantities
Always name what a number counts. In a sweets table, frequency gives how many children chose a sweet but not their names. In a wickets table, frequencies count matches, whereas total wickets requires multiplying wickets per match by matches before adding. In a time graph, add counts from non-overlapping intervals to find a total; subtract endpoint values to find a change. These operations answer different questions.
Problem
A player took 0 wickets in 2 matches, 1 wicket in 3 matches, and 2 wickets in 4 matches. How many matches and how many wickets?
- 1.Count matches by adding frequencies: 2 + 3 + 4 = 9 matches.
- 2.Count wickets by weighting each outcome: 0×2 + 1×3 + 2×4 = 0 + 3 + 8 = 11 wickets.
- 3.Eleven does not replace nine; both totals are correct for different questions.
Check the picture as well as the numbers
Before trusting a graph, read its title, category names, units, baseline, and key or scale. Check that equal numerical steps are evenly spaced and that the table’s values produce the drawn symbols or bar lengths. The ticket and tiger exercises show why a polished graph can still be wrong. A mountain-shaped infographic shows another risk: changes in width or perspective can imply facts that were never measured.
Problem
A picture makes an 8,848 m peak appear twice as high as a 5,642 m peak. How do we decide?
- 1.Twice 5,642 m is 11,284 m.
- 2.Because 8,848 m is smaller than 11,284 m, the first peak is not twice as tall.
- 3.The picture may be attractive, but its apparent two-to-one ratio is not supported by the values.
A graph may show more traffic in one hour, more books borrowed on Saturday, or more saplings planted on another day. It records counts, not people’s motives, weather, or attendance. Offer explanations as hypotheses and say what extra evidence would check them.
Quiz
Which order follows a data investigation?
One picture means 5 students. Three whole pictures represent…
A player’s wickets table has values and match frequencies. How do you total the wickets?
At a scale of 4 tickets per unit, a bar of 7 units represents…
Which is a supported conclusion from a weekly saplings graph?
What should be checked when an infographic looks dramatic?
A bar graph’s equal gaps matter because…
Practice Problems
- Survey at least 20 people on one clearly worded preference. Keep a raw list, make a tally table, and check that the frequencies add to the number surveyed.
- Use one picture = 2 responses to make a pictograph for categories with frequencies 6, 10, and 8. Then make a bar graph using two responses per unit. Compare what each shows clearly.
- A pictograph with one symbol = 10 shows 2½ symbols. Find the frequency. Explain whether the same key would easily show a count of 27.
- The railway-ticket table records Vidisha 24, Jabalpur 20, Seoni 16, Indore 28, Sagar 16. Recover the scale from a six-unit Vidisha bar and specify all five correct bar heights.
- For the wickets table in Lesson 1, separately calculate the number of matches and total wickets. Explain why adding just 0 + 1 + … + 7 answers neither question.
- Compare mountain heights of 8,848 m and 5,642 m. Check a picture that suggests the first is twice the second; describe a more trustworthy visual.
- A graph shows one day with the fewest library loans. Write a fact it establishes, a possible reason it does not establish, and a way to investigate that reason.
- A student draws different-width bars and labels successive equally spaced ticks 0, 5, 10, 20. Identify both errors and explain how to fix them.
Key Takeaways
• Collect data for a question, organise it into frequencies, and choose a display suited to its values. • The key or scale connects symbols and bar lengths to actual counts. • Calculate totals and differences from the right quantities, and check displays against their tables. • Keep visual design readable and honest; investigate causes rather than assuming them from a pattern.
Previous · Lesson 6
Designing Clear and Honest Visuals
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