Mathematics
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.
Statistics
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Answer
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.
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