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Question
The following is the distribution of height of students of a certain class in a certain city:
| Height (in cm): | 160 - 162 | 163 - 165 | 166 - 168 | 169 - 171 | 172 - 174 |
| No. of students: | 15 | 118 | 142 | 127 | 18 |
Find the average height of maximum number of students.
Solution
| Height(exclusive) | Height(inclusive) | No. of students |
| 160 - 162 | 159.5-162.5 | 15 |
| 163 - 165 | 162.5-165.5 | 118 |
| 166 - 168 | 165.5-168.5 | 142 |
| 169 - 171 | 168.5-171-.5 | 127 |
| 172 - 174 | 171.5-174.5 | 18 |
Here the maximum frequency is 142, then the corresponding class 165.5 – 168.5 is modal class
L = 165.5, h = 168.5 – 165.5 = 3, f = 142, f1 = 118, f2 = 127
Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`
`=165.5+(142-118)/(2xx142-118-127)xx3`
`=165.5+(24xx3)/39`
`= 165.5 + 72/39`
= 165.5 + 1.85
= 167.35 cm
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