COEFFICIENT OF VARIATION FOR UNGROUPED DATA

Example 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

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%

Example 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

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%

Example 3 :

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 :

Hence we decide that Vidhya is more consistent.

Apart from the stuff given given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.