8. Biostatistics standard deviation and coefficient of variation for grouped data
- 1. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany skhot1976@gmail.com Paper XIV Unit. 2. Biostatistics 2.8 Measures of Dispersion Standard Deviation and Coefficient of Variation (CV) (for grouped data) Dr. Sudhakar Sambhaji Khot M.Sc., Ph.D., SET Assistant Professor in Botany Y. C. Warana Mahavidyalaya, Warananagar
- 2. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany Dr. S. S. KHOT 2 B.Sc. Part- III Botany Paper- XIV DSE –F26 Bioinformatics, Biostatistics and Economic Botany Unit 2: Biostatistics (11) 2.1 Introduction, definition, terminology. 2.2 Collection and presentation of data: Types of data, techniques of data collection- Census method, sampling method- simple random, stratified and systematic sampling. Classification, tabulation, graphical representation- Histogram and polygon. 2.3 Measures of central tendency and Dispersion: Arithmetic mean, Mode, Median, Range, Deviation, Mean deviation, Standard Deviation, Coefficient of Variation. 2.4 Statistical methods for testing the hypothesis’ i) Students’ T-test ii) Chi-square test
- 3. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany Dr. S. S. KHOT 3 Story of SIX SIGMA (6σ) SIX SIGMA (6σ): defined and disciplined business methodology to increase customer satisfaction and profitability by streamlining operations, improving quality and eliminating defects in any organization-wide process. Originated at Motorola in 1980s 6σ = 99.99966 % Chance of defect = 0.00034 % = 3.4 defects /10,00,000
- 4. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany Number of seeds per pod (x) No. of pods (f) fx Deviation (dx= x-x̄ ) Deviation square (dx2 ) fdx2 2 2 4 -3.5 12.25 24.5 3 2 6 -2.5 6.25 12.5 4 3 12 -1.5 2.25 6.75 5 8 40 -0.5 0.25 2 6 7 42 0.5 0.25 1.75 7 4 28 1.5 2.25 9 8 3 24 2.5 6.25 18.75 9 1 9 3.5 12.25 12.25 ∑f=30 ∑fx=165 ∑dx= 0 ∑dx2 = 42 ∑fdx2 =87.5 Dr. S. S. KHOT 4 Example 2: The data on number of seeds per pod in Albizia lebbeck is as below. Calculate mean and standard deviation and CV. Solution: This is a grouped data. Number of seeds (x) 2 3 4 5 6 7 8 9 Number of pods (f) 2 2 3 8 7 4 3 1 Mean (x̄ ) = ∑fx/ ∑f = 165/30 = 5.5
- 5. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany ∑f = 30 ∑fx = 165 ∑dx= 0 ∑dx2 = 42 ∑fdx2 = 87.5 Dr. S. S. KHOT 5 Example 2: The data on number of seeds per pod in Albizia lebbeck is as below. Calculate mean and standard deviation. Solution: This is a grouped data. Number of seeds (x) 2 3 4 5 6 7 8 9 Number of pods (f) 2 2 3 8 7 4 3 1 Mean (x bar) = ∑fx/ ∑f = 165/30 = 5.5 Computation of S.D. for grouped data 𝝈 = ∑𝒇𝑿 ∑𝒇 𝟐 = ∑𝒇𝒅𝒙 ∑𝒇 𝟐 𝝈 = 𝟖𝟕. 𝟓/𝟑𝟎 𝝈 = 𝟐. 𝟗𝟐 = 1.71 seeds per pod Answer: Mean= 5.5 seeds per pod and SD (σ) = 1.71 seeds per pod CV = 31.09 % Computation of CV 𝑪𝑽 = 𝑺𝑫 𝒙 𝒙 𝟏𝟎𝟎 CV= 1.71/5.5 x 100 CV= 31.09 %
- 6. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany Dr. S. S. KHOT Questions, if any ? Thank You