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Question
Calculate AM, GM and HM from the following data and also find its relationship:
| Marks: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |
| No. of students: | 5 | 10 | 25 | 30 | 20 | 10 |
Solution
| X | f | fX | log X | f log X | `"f"/"X"` |
| 5 | 5 | 25 | 0.6990 | 3.4950 | 1.0000 |
| 15 | 10 | 150 | 1.1761 | 11.761 | 0.6667 |
| 25 | 25 | 625 | 1.3979 | 34.9475 | 1 |
| 35 | 30 | 1050 | 1.5441 | 46.323 | 0.8571 |
| 45 | 20 | 900 | 1.6532 | 33.0664 | 0.4444 |
| 55 | 10 | 550 | 1.7404 | 17.404 | 0.1818 |
| N = 100 | ∑fX = 3300 | `∑"f log X"` = 146.9969 | `sum("f"/"X")` = 4.15 |
AM = `(sum"fX")/"N" = 3300/100` = 33
GM = Antilog `((sum "f log X")/"N")`
= Antilog `((146.9969)/100)`
= Antilog (1.469969)
= Antilog (1.4700)
= 29.51
HM = `"N"/(sum("f"/"X")) = 100/4.15` = 24.096 = 24.10 (approx.)
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