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
Dr. S. S. KHOT
2.3 Measures of Dispersion
Range, Mean deviation, Standard Deviation, Coefficient of Variation
‘Dispersion: deviation of the individual values around the central value of data

2. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
skhot1976@gmail.com
Paper XIV
Unit. 2. Biostatistics
2.7 Measures of Dispersion
Dr. Sudhakar Sambhaji Khot
M.Sc., Ph.D., SET
Assistant Professor in Botany
Y. C. Warana Mahavidyalaya, Warananagar
Range,
Mean Deviation,
Standard Deviation,
Coefficient of Variation (CV)
(for Ungrouped data)

3. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT
2.3 Measures of Dispersion
‘Dispersion: deviation of the individual values around the central value of data
Dispersion
Range,
Mean
deviation,
Standard
Deviation,
Coefficient
of Variation

4. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT
2.3 Measures of Dispersion

5. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT
2.3 Measures of Dispersion
Range, Mean deviation, Standard Deviation, Coefficient of Variation
‘Dispersion: deviation of the individual values around the central value of data
Range: difference between the lowest and highest value of item in the set of data
Range for species A= 22-02 = 20
Range for species B= 12-08 = 04
Range for species C= 10-10 = 00

6. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT
2.3 Measures of Dispersion
Range, Mean deviation, Standard Deviation, Coefficient of Variation
‘Mean Deviation: Average of deviation of the individual values from mean.
Mean Deviation (MD)
MD= ∑IDI /n (for ungrouped data)
MD= ∑f IDI /n (for grouped data)
Where
I D I = Deviation from mean (without sign)
f= Frequency
n = total number of items

7. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT
2.3 Measures of Dispersion
Range, Mean deviation, Standard Deviation, Coefficient of Variation
‘Standard Deviation: Square Root of mean of squares of deviation from the mean.
• Standard deviation (sigma ‘σ’ or
SD) is the most widely used
measure of dispersion.
• σ is the positive SQRT of the
arithmetic mean of the squares of
deviations.
• Summarizes the deviation in one
figure used as a unit of variation.
• S.D. is based on all the
observations.
Coconut yield per season
Species
A
Species
B
Species
C
Jan-Mar 13 11 10
Apr-Jun 2 8 10
Jul-Sep 3 9 10
Oct-Dec 22 12 10
Total 40 40 40
Mean 10 10 10

8. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT
2.3 Measures of Dispersion
Range, Mean deviation, Standard Deviation, Coefficient of Variation
‘Standard Deviation: Square Root of mean of squares of deviation from the mean.
Coconut yield per season
Species A
(x)
Deviation
dx= x-x̄
Sq Dev.
dx2
Jan-Mar 13 3 9
Apr-Jun 2 -8 64
Jul-Sep 3 -7 49
Oct-Dec 22 12 144
Total (∑) 40 ∑ lDl =30 ∑dx2 = 266
Mean (x̄) 10 MD=7.5 𝝈 = 9.41
𝝈 =
∑𝒅𝒙
𝑵 − 𝟏
𝟐
𝝈 =
266
3
𝝈 = 9.41 coconuts

9. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT 9
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

10. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT
2.3 Measures of Dispersion
Range, Mean deviation, Standard Deviation, Coefficient of Variation
‘Coefficient of variation (CV): It is Std. Dev. (SD) expressed as a percentage of mean
CV = SD/x
̄ X 100
CV = 9.41/10 X 100
CV = 94.1 %
• Method developed by Pearson
• It is expressed in percentage
• It is relative measure of dispersion
• Useful to compare dispersion of different
data
• Higher CV represents more variability and
less uniformity within the set of data

11. skhot1976@gmail.com B.Sc.-III Paper- XIV (DSE –F26) Bioinformatics, Biostatistics and Economic Botany
Dr. S. S. KHOT
Questions, if any ?
Thank You