Q. 104.5( 21 Votes )

# The diameters of circles (in mm) drawn in a design are given below:

Calculate the standard deviation and mean diameter of the circles.

[Hint: First make the data continuous by making the classes as 32.5-36.5, 36.5-40.5,

40.5-44.5, 44.5 - 48.5, 48.5 - 52.5 and then proceed.]

Answer :

Let the assumed mean, A = 42.5 and h = 4

We obtain the following table from the given data:

We know that Mean,

∴

We know that Variance σ^{2} =

∴ σ^{2} =

We know that Standard Deviation = σ

∴ σ = √30.84 = 5.553

Ans. Mean = 43.5, Variance = 30.84 and Standard Deviation = 5.553

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