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Question
The distribution of heights (in cm) of 100 people is given below. Construct a histogram and the frequency polygon imposed on it.
| Height (in cm) |
125 − 135 | 136 − 146 | 147 − 157 | 158 − 168 | 169 − 179 | 180 − 190 | 191 − 201 |
| Frequency | 12 | 22 | 18 | 24 | 15 | 7 | 2 |
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Solution
The given distribution is discontinuous.
Converting into continuous distribution we have
Lower boundary = lower limit – `1/2` ...(gap between adjacent class interval)
= `125 - 1/2`
= 124.5
Upper boundary = Upper limit + `1/2` ...(gap between the adjacent class interval)
= `135 + 1/2`
= 135.5
∴ The new frequency table is
| Height (in cm) |
124.5 − 135.5 | 135.5 − 146.5 | 146.5 − 157.5 | 157.5 − 168.5 | 168.5 − 179.5 | 179.5 − 190.5 | 190.5 − 201.5 |
| Frequency | 12 | 22 | 18 | 24 | 15 | 7 | 2 |
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