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Question
Calculate AM, GM and HM and also verify their relations among them for the following data.
| X | 5 | 15 | 10 | 30 | 25 | 20 | 35 | 40 |
| f | 18 | 16 | 20 | 21 | 22 | 13 | 12 | 16 |
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Solution
| X | f | fX | log X | f log X | `"f"/"X"` |
| 5 | 18 | 90 | 0.6990 | 12.5820 | 3.6 |
| 15 | 16 | 240 | 1.1761 | 18.8176 | 1.0667 |
| 10 | 20 | 200 | 1.0000 | 20.0000 | 2.000 |
| 30 | 21 | 630 | 1.4771 | 31.0191 | 0.7000 |
| 25 | 22 | 550 | 1.3979 | 30.7538 | 0.880 |
| 20 | 13 | 260 | 1.3010 | 16.9130 | 0.6500 |
| 35 | 12 | 420 | 1.5441 | 18.5292 | 0.3429 |
| 40 | 16 | 640 | 1.6021 | 25.6336 | 0.4000 |
| N = 138 | ∑fX = 3030 | `∑"f log X"` = 174.2483 | `sum("f"/"X")` = 9.6396 |
AM = `(sum"fX")/"N" = 3030/138` = 21.9565
GM = Antilog `((sum "f log X")/"N")`
= Antilog `((174.2483)/138)`
= Antilog (1.26267)
= 18.3092
= 18.31
HM = `"N"/(sum("f"/"X")) = 138/9.6396` = 14.3159 = 14.32
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