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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 | 9 |
| 36 - 38 | 21 |
| 39 - 41 | 30 |
| 42 - 44 | 22 |
| 45 - 47 | 18 |
Calculate the mean diameter of the head of a screw by the ' Assumed Mean Method'.
Solution
Let A = 40
| Diameter (in mm) | Class Mark (X) |
d = X - A | no. of screws | f d |
| 33 - 35 | 34 | -6 | 9 | -54 |
| 36 - 38 | 37 | -3 | 21 | -63 |
| 39 - 41 | 40 | 0 | 30 | 0 |
| 42 - 44 | 43 | 3 | 22 | 66 |
| 45 - 47 | 46 | 6 | 18 | 108 |
| ∑ f =100 | ∑fd = 57 |
`bar"d" = (∑"f""d")/(∑ "f") = 57/100=0.57`
Mean by Assumed Mean Method
`bar"x" = "A" + bar"d"`
=40 + 0.57
= 40.57 mm
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