**Coefficient of Variation for Ungrouped Data :**

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

**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

x 24 26 29 31 33 37 |
d = x - A d=x-31 -7 -5 -2 0 2 6 |
d 48 25 4 0 4 36 |

Σd^{2}/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

x 38 40 43 44 46 47 49 53 |
d = x - A d=x-44 -6 -4 -1 0 2 3 5 9 |
d 36 16 1 0 4 9 25 81 |

Σd^{2}/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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