Coefficient of variation

Coefficient of variation

1. C oefficient of variation NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS

2. Coefficient of Variation Coefficient of Variation is a relative measure of dispersion . Coefficient of Variation is useful in comparing the variability of two or more sets of data. The one which has less Coefficient of Variation is considered more consistent in the performance . Coefficient of Variation is expressed as a percentage . 4. Coefficient of Variation indicates that the standard deviation is as a percent of the mean.      

3. Example-1: For the data 2, 4, 6, 8 and 10 Find (a) Mean and Standard deviation. (b) Coefficient of Variation Solution : X x 2 2 4 4 16 6 36 8 64 10 100

4. C.B f X fx fx 2 22 – 26 3 24 72 1728 26 – 30 6 28 168 4704 30 – 34 7 32 224 7168 34 – 38 10 36 360 12960 38 – 42 10 40 400 16000 42 – 46 8 44 352 15488 46 – 50 6 48 288 13824     Example-2: Find Mean, standard deviation and coefficient of variation. Solution :

5. Example-3 : Which city had more stable prices? Price in city A 20 22 19 23 16 Price in city B 10 20 18 12 15 Solution: For city A City (A) x x 2 20 400 22 484 19 361 23 529 16 256

6. For city B City (B) x x 2 10 100 20 400 18 324 12 144 15 225 Since C.V (A) < C.V (B). Therefore City A had more stable prices.

7. Example-4: A manufacturing company owns two plants which manufacture the same product. The weekly output of the two plants for the past 5 years was as follows : Weekly Output (in 1000 units) Number of Weeks Plant I Plant II 11 – 15 10 15 16 – 20 15 20 21 – 25 135 60 26 – 30 65 150 31 – 35 35 15 a. Calculate coefficient of variation for the two plants . b. Which plant gives more stable production ?

8. Solution: For Plant I C.I F x fx fx 2 11 – 15 10 13 130 1690 16 – 20 15 18 270 4860 21 – 25 135 23 3105 71415 26 – 30 65 28 1820 50960 31 – 35 35 33 1155 38115   ∑f=260   ∑ fx = 6480 ∑fx 2 = 167040 (a)

9. C.V (I) (b)

10. For Plant II C.I F x fx fx 2 11 – 15 15 13 195 2535 16 – 20 20 18 360 6480 21 – 25 60 23 1380 31740 26 – 30 150 28 4200 117600 31 – 35 15 33 495 16335   ∑f=260   ∑ fx =6630 ∑fx 2 = 174690 (a)

11. C.V (II) Since C.V (II) < C.V (I) Therefore Plant II gives more stable production. (b)