# COEFFICIENT OF VARIATION FOR UNGROUPED DATA

Coefficient of Variation for Ungrouped Data :

Here we are going to see, some example problems of finding coefficient of variation for ungrouped data.

## Coefficient of Variation for Ungrouped Data - Examples

Question 1 :

Find the coefficient of variation of 24, 26, 33, 37, 29, 31.

Solution :

First let us find the standard deviation for the given data. For that, let us arrange the given data in ascending order.

24, 26, 29, 31, 33, 37

 x242629313337 d = x - Ad=x-31-7-5-2026 d2482540436

Σd2/n  =  117/6

(Σd/n)2  =  (-6/6)2  =  1

σ  =  √(19.5 - 1)

=  √18.5

σ  =  4.30

x̄  =  Σx/n

=  (24 + 26 + 29 + 31 + 33 + 37)/6

x̄  =  180/6

x̄  =  30

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

C.V  =  (4.30/30⋅ 100%

C.V  =  0.143 ⋅ 100%

C.V  =  14.33%

Hence the coefficient of variation of the given data is 14.4%

Question 2 :

The time taken (in minutes) to complete a homework by 8 students in a day are given by 38, 40, 47, 44, 46, 43, 49, 53. Find the coefficient of variation.

Solution :

38, 40, 43, 44, 46, 47, 49, 53

 x3840434446474953 d = x - Ad=x-44-6-4-102359 d2361610492581

Σd2/n  =  172/8

(Σd/n)2  =  (8/8)2  =  1

σ  =  √(21.5 - 1)

=  √20.5

σ  =  4.53

x̄  =  Σx/n

=  (38+40+43+44+46+47+49+53)/8

x̄  =  360/8

x̄  =  45

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

C.V  =  (4.52/45⋅ 100%

C.V  =  0.1006 ⋅ 100%

C.V  =  10.07%

Hence the coefficient of variation of the given data is 10.07%

Question 2 :

The total marks scored by two students Sathya and Vidhya in 5 subjects are 460 and 480 with standard deviation 4.6 and 2.4 respectively. Who is more consistent in performance?

Solution :

Sathya

Sum of marks in 5 subjects  =  460

mean mark of Sathya (x̄)  =  Σx/n   =  460/5  =  92

Standard deviation (σ)  =  4.6

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

C.V  =  (4.6/92⋅ 100%

C.V  =  0.05 ⋅ 100%

C.V  =  5%

Vidhya :

Sum of marks in 5 subjects  =  480

mean mark of Sathya (x̄)  =  Σx/n   =  480/5  =  96

Standard deviation (σ)  =  2.4

Coefficient of variation (C.V) =  (σ/x̄) ⋅ 100%

C.V  =  (2.4/96⋅ 100%

C.V  =  0.25 ⋅ 100%

C.V  =  25%

Hence we decide that Vidhya is more consistent.

After having gone through the stuff given above, we hope that the students would have understood, "Coefficient of Variation for Ungrouped Data".

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