Bar graphs

A bar graph is a chart where each category is shown as a rectangle (bar), and the length or height of the bar tells the count. Bar graphs are clean, easy to compare, and the most common chart in newspapers, books, and websites.

Concept

To draw a bar graph you need:

1. A list of categories.
2. A frequency for each.
3. Two axes , usually horizontal (the categories) and vertical (the counts).
4. A scale on the count axis , for example, "$1$ unit on the axis = $5$ people".

Each bar is drawn over its category, with a height equal to its frequency (after applying the scale). Bars have equal width and equal spacing , this is important, because uneven widths can mislead the eye.

Bar graphs can be vertical (bars going up from the bottom) or horizontal (bars going right from the left side). Both work the same way; the choice is mostly aesthetic. Long category names look neater on a horizontal graph.

A few rules of clean bar graphs:

• The count axis must start at $0$. If it does not, comparisons are wrong.
• The scale must be evenly spaced , equal jumps for equal increases.
• Bars must have equal widths.
• Always include a title and label both axes.

Bar graphs are excellent when:

• You want to compare counts across categories.
• The categories are clearly separated (not a continuous variable like temperature).

For continuous data , like heights, weights, or temperatures , you would use a slightly different chart (a histogram), which you will meet in later years.

Worked examples

Example 1. Draw a bar graph for: favourite sports in a class , Cricket $18$, Football $12$, Hockey $8$, Tennis $4$, Other $3$. Suggest a scale.

• The largest count is $18$. A scale of $1$ unit = $2$ children fits well: max bar height $= 9$ units.
• Heights: Cricket $9$, Football $6$, Hockey $4$, Tennis $2$, Other $1.5$.

Example 2. A bar graph (scale $1$ unit = $5$ kg) shows:

• Bag A: $4$ units → $4 \times 5 = 20$ kg.
• Bag B: $7$ units → $35$ kg.
• Bag C: $5.5$ units → $27.5$ kg.

What is the total weight?

• $20 + 35 + 27.5 = 82.5$ kg.

Example 3. From a bar graph showing monthly book sales of a shop:

(a) In which month were the most books sold? (b) In which two months were sales equal-ish?

• (a) March, with $55$ books.
• (b) None are exactly equal. April ($30$) is closest to February ($25$).

Example 4. A bar graph of "students per class" uses scale $1$ unit = $4$ students. A bar has height $7.5$ units. How many students?

• $7.5 \times 4 = 30$ students.

Try it yourself

1. Draw a bar graph for these test scores by class: A $35$, B $42$, C $28$, D $50$. Choose a sensible scale.
2. In a bar graph with scale $1$ unit = $10$ rupees, a bar has height $6$ units. How much money?
3. From your graph in question $1$, which class scored lowest?
4. A bar graph compares school enrolments: $230, 145, 310, 280$. Suggest a scale that keeps bar heights between $1$ and $12$ units.
5. Why must the vertical axis start at $0$? What can go wrong if it does not?
6. Why do all bars have the same width?
7. Sketch a horizontal bar graph for: state capitals' approximate populations (in lakhs): Mumbai $200$, Bengaluru $135$, Chennai $110$, Kolkata $148$.
8. Design: go through any newspaper. Find one bar graph and check it has a title, axis labels, and a clear scale.

Activity

Class rainfall. With your classmates or family, measure (or look up) the rainfall in your city for each of the last $6$ months. Draw a vertical bar graph on graph paper. Label the months on the horizontal axis and rainfall in mm on the vertical axis. Pick a scale that keeps your tallest bar under $10$ squares high. Write two true statements about what your graph shows.