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The Measurements (In Mm) of the Diameters of the Head of the Screws Are Given Below - Algebra

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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’.

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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.

Concept: Mean of Grouped Data
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