Question

What standard deviation signifies from the distribution table ? find standard deviation and coefficient of veriation from the following data :
size of item : 0-10 10-20 20-30 30-40 40-50 50-60
frequency : 10 20 30 40 10 20

Answer 1

Given:

size of item : 0-10  10-20  20-30  30-40  40-50  50-60

frequency :     10       20        30        40       10       20

To find:

(i) What standard deviation signifies from the distribution table?

(ii) Find the standard deviation and coefficient of variation from the given data

Solution:

(i) Standard Deviation:- The standard deviation signifies if the measurements of the given data are close to the mean [known as Low standard deviation] or more spread out from the mean [known as high standard deviation].

(ii) Finding the standard deviation and the coefficient of variation of the following data :

To find the S.D. and C.V. we have to find a few other calculations which are done in the figure attached below

Now, referring to the figure, we will find the standard deviation and the coefficient of variation

Mean = [∑fixi] / [∑fi] = $\frac{4050}{130}$ = 31.15

Variance = [∑fixi²/N] – [Mean]² = [$\frac{153250}{130}$] – [31.15]² = 1178.84 – 970.32 = 208.52

Standard Deviation, S.D. = √Variance = √208.52 = 14.44

Coefficient of Variation, C.V. = $\frac{S.D.}{Mean} * 100$ = $\frac{14.44}{31.15} * 100$ = 46.35%

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