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

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.

Concept: Mean of Grouped Data
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