Connecting the Dots... · Lesson 7 of 13
Visualising Data
“Build clear double-column graphs that preserve category comparisons and time patterns.”
• Construct and interpret double-column graphs. • Choose appropriate scales and label units and categories. • Use a legend to identify series. • Organise raw category responses into frequencies. • Compare actual measurements with estimates.
Visualising Data
A numerical table can answer precise questions, but a picture can reveal a comparison much faster. The onion-price table contains two values for each month. By making a pair of bars for every month, we can keep the time order and see how the towns compare throughout the year.
Clubbing the Columns
Start with one column graph for each town. Both must use the same price scale if we want a fair visual comparison. Putting the corresponding columns beside each other turns two separate displays into one double-column graph.
A graph with related vertical bars placed side by side within each category. A pair of bars per category makes a double-column graph.
A key identifying what each colour, pattern, or symbol represents.
The horizontal axis lists the months in chronological order. The vertical axis measures price in rupees per kilogram. Successive labelled horizontal gridlines are 10 rupees per kilogram apart. The legend identifies the town represented by each bar. Both towns use the same baseline and scale, so a taller bar represents a higher price.
Use equal bar widths, equal spacing inside each pair, and a slightly larger gap between pairs. Use a title and units. If people cannot distinguish the colours, outlines or patterns can preserve the distinction. When plotting, check each bar against the original table, not against a remembered impression of the data.
Problem
On a scale marked 0, 10, 20, 30, and so on, where should a ₹25/kg bar end?
- 1.The value lies between 20 and 30.
- 2.Its distance above 20 is 5 out of the 10-rupee interval, so place its top halfway between the two gridlines.
- 3.A ₹24/kg bar ends slightly below that point. Whole gridlines are not the only permitted bar heights.
Problem
What do the November and June pairs show?
- 1.November has Yahapur 59 and Wahapur 52. Their difference is 59 − 52 = ₹7/kg.
- 2.June has 35 in both towns, so the two bars reach the same height.
- 3.The pair compares the same category; do not compare November in one town with June in the other unless that is the stated question.
Problem
A sports survey has counts up to 1240. How can we draw a double-bar graph?
- 1.Choose a scale that reaches at least 1240, such as labels from 0 to 1400 in steps of 200.
- 2.Keep watching and participating counts beside each other for every sport.
- 3.Place values between gridlines accurately, provide a legend, and use a zero baseline for proportional bar lengths.
From raw responses to a graph
Sometimes the source data is a list of category responses rather than a count table. First count how often each response occurs in each group. Then plot those frequencies; the letters themselves are category labels, not heights.
| Response | Meaning | Grade 5 count | Grade 9 count |
|---|---|---|---|
| w | Aquatic | 6 | 6 |
| a | Aerial | 13 | 8 |
| s | Spaceborne | 2 | 9 |
| n | None | 4 | 2 |
Each grade has 25 responses. Adding the four category counts in a row checks that no student was lost or counted twice. Unlike months, these response categories do not have a necessary time order. You may reorder them as long as the matching pair stays together and the labels are clear.
A category axis can list labels in different sensible orders. A numerical axis must keep equal value differences at equal distances. Do not use different vertical scales for the groups in one comparative graph.
| Sport | Prefer watching | Participate |
|---|---|---|
| Cricket | 1240 | 620 |
| Basketball | 470 | 320 |
| Swimming | 510 | 320 |
| Hockey | 430 | 250 |
| Athletics | 250 | 105 |
| Time | Day 1 temperature (°C) | Day 2 temperature (°C) |
|---|---|---|
| 12 am | 20 | 37 |
| 3 am | 18 | 34 |
| 6 am | 16 | 30 |
| 9 am | 20 | 33 |
| 12 pm | 26 | 37 |
| 3 pm | 34 | 43 |
| 6 pm | 30 | 42 |
| 9 pm | 24 | 39 |
Quiz
In the onion graph, what does the legend identify?
On gridlines 20 and 30, a value 25 lies:
What makes paired bar heights directly comparable?
Before graphing category responses such as w, a, s, n, first:
Which category order should be preserved for a yearly month-by-month pattern?
Practice Problems
- Draw the double-column onion graph and check the May pair.
- Use the ability-response count table to compare the grades.
- Draw a graph for the two temperature days with gridlines 4°C apart. Describe the pattern.
- Draw the watching-versus-participating sports graph. Which has the largest difference?
- Estimate and measure the lengths of a pen, eraser, palm, geometry box, and mathematics notebook. Graph both sets and calculate the mean positive difference.
- Why should a bar graph for proportional quantity comparisons ordinarily start at zero?
Use months in order, a 0–60 price axis, and a legend. May bars end at 30 for Yahapur and 38 for Wahapur; the difference is ₹8/kg.
Key Takeaways
• A clustered graph places related bars together for each category. • A double-column graph has two bars per category. • Read the title, axes, units, scale, and legend. • Count raw category responses before plotting frequencies. • Use shared scales and accurate bar heights. • Choose colours or patterns that preserve distinctions for all readers.