ANIMAL GENETICS BREEDING UNIT II Principles of Animal
ANIMAL GENETICS & BREEDING UNIT – II Principles of Animal & Population Genetics Lecture – 12 Variance and Standard Deviation Dr K G Mandal Department of Animal Genetics & Breeding Bihar Veterinary College, Patna Bihar Animal Sciences University, Patna
Measures of Dispersion • Measures of Dispersion ? Importance of measures of dispersion. Sl. No. 1. 2. 3. 4. 5. Total Mean Set – 1 01 02 03 04 90 100 20 Set – 2 20 18 22 23 17 100 20 Set - 3 20 20 20 100 20
• Properties of a good Measure of Dispersion – Simple to understand – Easy to compute – Based on each and every item of the dispersion – Use for further algebraic treatment – Should have sampling stability
Different Measures of Dispersion • Range : Xmax - Xmin • Mean Deviation : 1/N [ ∑ (Xi – X) Sl. No. 1. 2. 3. Xi 2 3 4 (Xi – X) 2 – 4 3 – 4 4 – 4 (Xi – X) -2 -1 0 4. 5. Total Mean (X) 5 6 20 4 5 – 4 6 - 4 1 2 0
Variance : 1/N [ ∑ (Xi – X)2 = ∑(xi 2 + x 2 - 2 xix) = ∑x 2 + ∑x 2 - 2 x∑xi = ∑x 2 + Nx 2 - 2 x Nx = ∑x 2 + Nx 2 - 2 N x 2 = ∑x 2 – N(∑x)2/N 2 =[ ∑x 2 – (∑x)2/N] / N-1.
Calculate the variance from the following set of data: Sl. No. 1. 2. 3. Xi 2 3 4 (Xi – X) 2 – 4 3 – 4 4 – 4 (Xi – X) -2 -1 0 (Xi – X)2 4 1 0 4. 5. Total Mean (X) 5 6 20 4 5 – 4 6 - 4 1 2 0 1 4 10 Variance = 10/4 = 2. 5
Variance =[ ∑x 2 – (∑x)2/N] / (N-1). Sl. No. 1. 2. 3. Xi 2 3 4 Xi 2 4 9 16 4. 5 5. Total Mean (X) 6 20 4 25 36 90 Variance =[ 90 - 202 /5 ] /4 = [90– 400/5]/4 = (90 – 80)/4 = 10/4 = 2. 5
Standard Deviation • Standard Deviation : + √ Variance SD = + √ 2
THANK YOU
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