Data Handling and Presentation · Lesson 4 of 7
Drawing Bar Graphs and Choosing Scales
“Build accurate bar graphs from tables and choose scales that fit the values.”
• Plan category and value axes with labels and units. • Select and mark a scale that starts at zero and fits the data. • Convert table entries into accurate bar heights. • Keep bar widths and gaps consistent, including for zero values. • Check a completed graph against its source table.
Plan the graph before drawing
A table gives the exact numbers, while a bar graph makes comparison easier. Start by deciding where the categories and quantities will go. Draw perpendicular axes; put categories at equal intervals on one axis, and mark a numerical scale with equal intervals from zero on the other. Give the graph and both axes clear labels so a reader knows what was counted and in what units.
For sweet preferences, the categories are jalebi, gulab jamun, gujiya, barfi, and rasgulla. Their frequencies are 6, 9, 13, 3, and 7 students. Since the largest is 13, a value axis from 0 to 14 in steps of one fits comfortably. Draw equal-width bars of heights 6, 9, 13, 3, and 7, leaving equal gaps between them.
| Sweet | Jalebi | Gulab jamun | Gujiya | Barfi | Rasgulla |
|---|---|---|---|---|---|
| Students | 6 | 9 | 13 | 3 | 7 |
Problem
How would you place the bars for gujiya and barfi using one unit length per student?
- 1.Label the horizontal categories and vertical axis “Number of students”, marking zero and each successive unit equally.
- 2.Place a bar of height 13 over gujiya and a bar of height 3 over barfi; make both bars the same width.
- 3.Leave the same category gap on each side. Read the bars back to check that they give 13 and 3.
Choose a scale for larger values
If Smriti scores 80 runs in one match, drawing eighty one-unit steps is unnecessary. Her eight scores are 80, 50, 10, 100, 90, 0, 90, and 50. A scale of ten runs per unit lets the largest score fit in ten equal steps. Zero runs still has a category position but a zero-height bar.
| Match | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Runs | 80 | 50 | 10 | 100 | 90 | 0 | 90 | 50 |
Problem
With one unit length representing ten runs, how tall are the bars for matches 1, 4, and 6?
- 1.Divide each score by 10 to find its number of graph units.
- 2.Match 1: 80 ÷ 10 = 8 units; match 4: 100 ÷ 10 = 10 units.
- 3.Match 6: 0 ÷ 10 = 0 units. Keep the label for match 6 even though no raised bar appears.
The marked numbers must agree with the scale. If successive lines are labelled 0, 10, 20, and so on, they must be equally far apart. A score of 50 reaches the 50 line, and both matches with 90 runs should reach the same height. We cannot make each bar a different width just to improve its appearance; only its height is meant to encode the score.
Represent money without losing precision
Imran’s family expenditure ranges from ₹400 for electricity to ₹3,400 for food. A scale of ₹200 per unit allows every amount in the table to be drawn exactly and fits the largest value into 17 units. Divide an amount by 200 to obtain the bar height, then label the value axis in rupees rather than merely writing unit numbers.
| Item | House rent | Food | Education | Electricity | Transport | Miscellaneous |
|---|---|---|---|---|---|---|
| Expenditure (₹) | 3,000 | 3,400 | 800 | 400 | 600 | 1,200 |
| Height with ₹200 per unit | 15 | 17 | 4 | 2 | 3 | 6 |
Problem
Find the graph heights for food, education, and electricity when one unit represents ₹200.
- 1.Food: ₹3,400 ÷ ₹200 = 17 units.
- 2.Education: ₹800 ÷ ₹200 = 4 units; electricity: ₹400 ÷ ₹200 = 2 units.
- 3.The electricity bar is half the education bar because ₹400 is half of ₹800. Both are below the food bar; ₹800 is less than one-fourth of ₹3,400, which is ₹850.
If one unit stands for ₹200, every consecutive tick must increase by ₹200. A bar of height 4 units then means ₹800 everywhere on the graph. An inconsistent scale makes visual comparisons unreliable.
For a tea-garden observation with 6 mites, 10 caterpillars, 5 beetles, 3 butterflies, and 2 grasshoppers, one critter per unit is convenient. Choose a scale from the largest value, label every category, make the bars uniform, and compare the final graph with the table. The objective is an accurate reading, not simply a neat drawing.
Quiz
Which vertical scale is convenient for scores up to 100 runs?
At 10 runs per unit, a score of 80 makes a bar of…
At ₹200 per unit, ₹1,200 makes a bar of…
How is a zero score shown?
Why must all bars have equal width?
Which graph labels correctly show a ₹200 step?
Practice Problems
- Draw a graph for the five sweet preferences, starting the numerical axis at zero. State your chosen scale and identify the tallest and shortest bars.
- Graph the eight match scores using ten runs per unit. Why must match 6 remain labelled even though its score is zero?
- Use the expenditure table to calculate bar heights for every item at ₹200 per unit, then verify that your food bar reaches ₹3,400.
- Draw a bar graph for 6 mites, 10 caterpillars, 5 beetles, 3 butterflies, and 2 grasshoppers. Label both axes.
- Two bars represent 50 and 90 on a scale of ten per unit. Give their heights and explain why their widths should be the same.
- A student marks 0, 10, 20, 50 at equally spaced successive ticks. Explain the fault and repair the axis.
Key Takeaways
• Plan labels and an even scale before constructing the bars. • Choose a scale that fits the largest number without making small values unreadable. • Divide each data value by the amount per unit to find its bar height. • Equal bar widths, equal gaps, and a zero starting point make comparisons reliable.