A histogram shows the frequency distribution of continuous (numerical) data using adjacent bars; a pie chart shows how a whole is divided into parts using sectors of a circle.
Histogram
- Class intervals on the x-axis, frequencies on the y-axis.
- Bars touch each other because the classes are continuous.
- Area of each bar is proportional to frequency (if class widths differ, use frequency density = frequency/width).
- Shows the shape of the data (symmetric, skewed, bimodal) and helps find the mode.
Example: marks of 27 students.
| Marks | 0–10 | 10–20 | 20–30 | 30–40 |
|---|---|---|---|---|
| Students | 3 | 7 | 12 | 5 |
Draw four touching bars of heights 3, 7, 12 and 5 over the intervals; the tallest bar (20–30) is the modal class.
Pie chart
- A circle (360°) divided into sectors, one per category.
- Angle of a sector \(= \dfrac{\text{value}}{\text{total}}\times 360^\circ\).
- Best for showing proportions of a whole with a few categories.
Example: monthly budget: Food 40%, Rent 30%, Savings 20%, Travel 10%.
- Food: \(0.40\times360 = 144^\circ\)
- Rent: \(0.30\times360 = 108^\circ\)
- Savings: \(0.20\times360 = 72^\circ\)
- Travel: \(0.10\times360 = 36^\circ\)
Total = 360°. Draw the sectors with a protractor and label each.
Difference: a histogram shows distribution of numerical data over intervals; a pie chart shows parts of a total for categories and is unsuitable when there are many categories or when values do not add up to a meaningful whole.