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Question
The measurements (in mm) of the diameters of the head of the screws are given below:
| Diameter (in mm) | No. of Screws |
| 33 — 35 | 10 |
| 36 — 38 | 19 |
| 39 — 41 | 23 |
| 42 — 44 | 21 |
| 45 — 47 | 27 |
Calculate mean diameter of head of a screw by ‘Assumed Mean Method’.
Solution
Let A be the assumed mean.
A is taken as the class mark of the middle class.
Hence, let us take 40 as the assumed mean.
Then A = 40 and deviation di = xi – A = xi – 40
| Diameter | Class | Deviations | Number of | fidi |
| (in mm) | marks | di=xi-A | Screws | - |
| - | xi | di=xi-40 | fi | - |
| 33-35 | 34 | -6 | 10 | -60 |
| 36-38 | 37 | -3 | 19 | -57 |
| 39-41 | 40=A | 0 | 23 | 0 |
| 42-44 | 43 | 3 | 21 | 63 |
| 45-47 | 46 | 6 | 27 | 162 |
| Total | - | - | ∑fi=100 | ∑fidi=108 |
Here,∑fidi=108, ∑fi=100
`bard=(Sigmaf_id_i)/(Sigmaf_i)=108/100=1.08`
`barx=A+bard`
=40+1.08
=41.08
Thus, the mean diameter of the screw heads is 41.08 mm.
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