Data Handling and Presentation · Lesson 3 of 7
Reading Bar Graphs
“Use bars and their scale to compare values, calculate totals, and make careful inferences.”
• Identify categories, quantity, scale, and bars in a bar graph. • Read exact or approximate values from a labelled axis. • Compare categories and combine values correctly. • Explain how bar graphs relate to frequency tables and pictographs. • Separate what a graph shows from possible explanations for its pattern.
A different way to show the same data
Picture symbols are inviting, but a large count can demand many symbols or awkward fractions. A bar graph uses equal-width bars instead. One axis lists categories; the other has a numbered scale. The height or length of each bar shows its category’s quantity, so we can compare the bars before reading their exact values.
A visual display with equal-width, separated bars whose heights or lengths represent the values of different categories.
Lakhanpal’s class-absence numbers—I to VIII: 3, 5, 4, 2, 0, 1, 5, 7—can be shown by either a pictograph or a bar graph. In the bar graph, the numbered axis begins at zero, rises in equal steps, and states that one unit length represents one student. Class V has no bar above zero because nobody was absent. Equal gaps between bars mark separate categories, not missing numerical values.
| Class | I | II | III | IV | V | VI | VII | VIII |
|---|---|---|---|---|---|---|---|---|
| Absent students | 3 | 5 | 4 | 2 | 0 | 1 | 5 | 7 |
Problem
Which class had the most absences, and which had full attendance?
- 1.Find the tallest bar. Class VIII reaches 7, higher than all other classes.
- 2.Find the category whose bar has zero height. Class V has 0 absent students.
- 3.Therefore Class VIII had the most absences and Class V had full attendance that day.
Read the axis before measuring a bar
A traffic graph may show time intervals along one axis and vehicles along the other, with one unit length standing for 100 vehicles. If a bar ends halfway between 100 and 200, read about 150, not 1½ vehicles. Some values are approximate because the bar ends between marked levels. A horizontal bar graph follows the same rule: read length along the numbered axis.
Problem
The traffic graph shows about 1,000 vehicles from 8–9 a.m. and 800 from 9–10 a.m. What was the total for these two hours?
- 1.Read both bars using the graph’s scale: approximately 1,000 and 800 vehicles.
- 2.The time intervals do not overlap, so add the two counts: 1,000 + 800 = about 1,800 vehicles.
- 3.Keep the word “about” because at least some graph readings are approximate.
The 7–8 a.m. bar is the largest, at about 1,200 vehicles, while 6–7 a.m. is the smallest, at about 150. We can propose that many people travel to work or school around 7–8 a.m.; the graph alone does not tell us why. To test an explanation, we would need further information about the crossing and travellers. Across all six time intervals, the displayed values total about 4,450 vehicles.
Notice changes over time
A bar graph of India’s population has the years 1951, 1961, 1971, 1981, 1991, and 2001, and quantities of 36, 44, 54, 68, 84, and 102 crore. Its scale uses one unit length for ten crore people, so a bar a little above eight units can represent 84 crore. The bars let us see growth across decades, while differences between values tell us how much the population changed.
| Year | 1951 | 1961 | 1971 | 1981 | 1991 | 2001 |
|---|---|---|---|---|---|---|
| Population in crore | 36 | 44 | 54 | 68 | 84 | 102 |
Problem
How much did the population increase from 1981 to 1991 and across the complete 1951–2001 interval?
- 1.In 1981 the value is 68 crore and in 1991 it is 84 crore, so the decade increase is 84 − 68 = 16 crore.
- 2.The beginning and ending values are 36 crore and 102 crore.
- 3.Over the whole interval the increase is 102 − 36 = 66 crore. An increase is a difference, not the final population itself.
A high traffic bar establishes that more vehicles were counted in that interval. It does not establish who travelled or why. State the numerical observation first, then label any explanation as a possibility that could be checked.
Quiz
What does the height of a bar represent?
For absences 3, 5, 4, 2, 0, 1, 5, 7, which class has no absent students?
If one marked unit means 100 vehicles, a bar of 8 units represents…
Traffic counts of about 1,000 and 800 in consecutive hours combine to…
Population changes from 68 crore to 84 crore. The increase is…
What can the tallest 7–8 a.m. traffic bar alone establish?
Practice Problems
- Use the attendance table to sketch a bar graph with categories I–VIII and a one-student scale. Explain why Class V has zero bar height.
- From the attendance values, identify the two classes tied at five absences and find their combined absences.
- A traffic bar reaches halfway between 100 and 200. Give an approximate reading and explain why 1.5 is wrong as a vehicle count.
- The population values for 1971, 1981, and 1991 are 54, 68, and 84 crore. Find the two consecutive increases and compare them.
- Propose one possible explanation for a busy morning traffic interval and describe one additional observation that could help check it.
- Write a question about the population table that asks for a difference rather than a single bar value, then answer it.
Key Takeaways
• Bar height or length corresponds to a quantity through a labelled, evenly spaced scale. • Separated bars of equal width represent distinct categories. • Use arithmetic on the values read from the bars for totals and differences. • Distinguish an observation in a graph from an untested explanation for it.