From the given data, we can observe that the class intervals have varying widths. The areas of the rectangles should be proportional to the frequencies in a histogram.
For example, when the class size is 5, the length of the rectangle is 10. So when the class size is 1, the length of the rectangle will be 10/5 × 1 = 2
| Age (in years) | Number of children | Width of class | Length of rectangle |
|---|---|---|---|
| 1 - 2 | 5 | 1 | (5 x 1)/1 = 5 |
| 2 - 3 | 3 | 1 | (3 x 1)/1 = 3 |
| 3 - 5 | 6 | 2 | (6 x 1)/2 = 3 |
| 5 - 7 | 12 | 2 | (12 x 1)/2 = 6 |
| 7 - 10 | 9 | 3 | (9 x 1)/3 = 3 |
| 10 - 15 | 10 | 5 | (10 x 1)/5 = 2 |
| 15 - 17 | 4 | 2 | (4 x 1)/2 = 2 |
Steps of construction :
Take the age of children on x-axis, using scale 1 unit = 1 year.
Take proportion of children per 1 year interval on y-axis, using scale 1 unit = 1 child.
To represent our first Head, i.e., (1 - 2) we draw a rectangular bar with width 1 unit and length 5 units.
Similarly, other Heads are represented without leaving a gap between two consecutive bars, according to the table.
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Mathematics | StatisticsWeb Content • Interactive Notes
Statistics — Interactive Study Guide
Histogram vs Bar Graph
| Feature | Bar Graph | Histogram |
|---|---|---|
| Data type | Discrete/categorical | Continuous/grouped |
| Gaps | Yes (between bars) | No (bars touch) |
| Unequal widths | Not applicable | Use frequency density |
Mean, Median, Mode
Mean: Sum of all values / count. Affected by extreme values.
Median: Middle value (after sorting). Not affected by extreme values.
Mode: Most frequent value. Can have multiple modes or no mode.
Quick Self-Check
- Mean of 2, 4, 6, 8, 10? (30/5 = 6)
- Median of 3, 1, 7, 5, 9? (Sorted: 1,3,5,7,9. Median = 5)
- Mode of 2, 3, 3, 5, 5, 5, 7? (5)