Biological data shows variations in the qualitative and quantitative attributes. Each individual value of observation scatters around the central tendency. measurement of the dispersion helps to understand the distribution of individual values around the central tendency. this ppt explains measures of dispersion namely range, mean deviation, standard deviation, and coefficient of deviation.

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