100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
| Number of letters | Number of surnames |
|---|---|
| 1 - 4 | 6 |
| 4 - 6 | 30 |
| 6 - 8 | 44 |
| 8 - 12 | 16 |
| 12 - 20 | 4 |
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.
It can be observed from the given data that it has class intervals of varying widths.
The proportion of the number of surnames per 2 letters (class interval of minimum class size for reference) can be made.
(i) The length of rectangles are calculated as below:
| Number of letters | Number of surnames | Width of the class | Length of rectangle |
|---|---|---|---|
| 1 - 4 | 6 | 3 | (6 x 2)/3 = 4 |
| 4 - 6 | 30 | 2 | (30 x 2)/2 = 30 |
| 6 - 8 | 44 | 2 | (44 x 2)/2 = 44 |
| 8 - 12 | 16 | 4 | (16 x 2)/4 = 8 |
| 12 - 20 | 4 | 8 | (4 x 2)/8 = 1 |
Steps of construction :
Take the number of letters on the x-axis using scale 1 block = 1 letter.
Take the proportion of the number of surnames per every 2 letter interval on the y-axis.
To represent our first Head, i.e., (1 - 4) we draw a rectangular bar with width 3 units and length 4 units.
Similarly, other Heads are represented without leaving a gap between two consecutive bars, according to the table.
(ii) From histogram,
We observe that,
In class interval 6 - 8, 44 surnames lie.
Hence, 6 - 8 is the class interval in which the maximum number of surnames lie.
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
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)