STANDARD DEVIATION (SD) AND COEFFICIENT OF VARIATION (CV)
Introduction
Standard Deviation (S.D.) and Coefficient of
Variation (C.V.) are statistical measures used to assess data variability. S.D.
measured the dispersion of data points around the mean, while C.V. expresses S.D.
as a percentage of the mean, allowing comparison across different datasets.
Standard Deviation (S.D.)
- Standard
Deviation measures how much individual values in a dataset vary from the
mean (average).
- A low
S.D. means data points are close to the mean, while a high S.D. indicates
they are spread out.
- It
helps understand the consistency or volatility of a dataset.
Formula:
where:
X = Individaul
data points
X̄ = Mean
of dataset
N =
Number of observations
Coefficient of Variation (C.V.):
C.V. is the ratio of
the Standard Deviation to the Mean, expressed as a percentage.
- It is useful for comparing
the variability of datasets with different units or scales.
- A higher C.V. means
more relative variation, while a lower C.V. indicates
more consistency.
Formula:
Where:
σ = Standard deviation (S.D.)
µ = Mean
Practical Example
Q1. What is the primary source of income for your
household.
a.
Agriculture. b. Business. C. Employment
Q2. What farming techniques do you use.
a. Traditional farming methods. b. Mechanized farming. c. Organic
farming. d. Precision farming.
Here, we have X and Y.
X is use for Question 1 and Y is use for Question 2
X: 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 3, 1, 1, 3, 2, 3, 2, 3, 1, 3
Y: 1, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 4, 1, 1
For X datasets
X: 1,1,2,2,2,1,1,1,1,2,3,1,1,3,2,3,2,3,1,3
n = 20
Mean(x)
1+1+1+1+1+1+1+1+1+2+2+2+2+2+2+3+3+3+3+3 = 36/20 =1.8
S.D. = (X)
Value (X)
Deviation (X-X̄), X̄=1.8
Square of deviation (X-X̄)2
1
-0.8
0.64
1
-0.8
0.64
2
0.2
0.04
2
0.2
0.04
2
0.2
0.04
1
-0.8
0.64
1
-0.8
0.64
1
-0.8
0.64
1
-0.8
0.64
2
0.2
0.04
3
1.2
1.44
1
-0.8
0.64
1
-0.8
0.64
3
1.2
1.44
2
0.2
0.04
3
1.2
1.44
2
0.2
0.04
3
1.2
1.44
1
-0.8
0.64
3
1.2
1.44
Total
=13.2
Therefore,
0.64+0.64+0.64+0.64+0.64+0.64+0.64+0.64+0.64+0.04+0.04+0.04+0.04+0.04+0.04+1.44+1.44+1.44+1.44+1.44
=13.2
S.D. = √13.2/20
= √0.66
S.D. = √0.66 = 0.81
Coefficient of variation
C.V. = (σ /X)100
C.V. = (0.81/1.8)100
C.V. = 45%
For Y datasets
Y: 1, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 4, 1, 1
n = 20
Mean(x)
1+1+1+1+1+1+1+1+1+1+1+1+2+2+2+2+2+2+3+4 = 31/20
= 1.55
S.D. = (X)
Value (X)
Deviation (X-X̄), X̄=1.55
Square of deviation (X-X̄)2
1
-0.55
0.3025
2
0.45
0.2025
1
-0.55
0.3025
1
-0.55
0.3025
2
0.45
0.2025
2
0.45
0.2025
3
1.45
2.1025
1
-0.55
0.3025
1
-0.55
0.3025
1
-0.55
0.3025
1
-0.55
0.3025
2
0.45
0.2025
2
0.45
0.2025
1
-0.55
0.3025
1
-0.55
0.3025
1
-0.55
0.3025
2
0.45
0.2025
4
2.45
6.0025
1
-0.55
0.3025
1
-0.55
0.3025
Total
12.95
Therefore,
03025+03025+03025+03025+03025+03025+03025+03025+03025+03025+03025+03025+0.2025+0.2025+0.2025+0.2025+0.2025+0.2025+2.1025+6.0025
= 12.95
S.D. = √12.95/20
= 0.6475
S.D. = √0.6475 = 0.8047
Coefficient of variation
C.V. = (σ /X)100
C.V. = (0.8047/1.55)100
= 51.92%
Data set
Mean
Variance
Sd deviation
C V
X
1.8
0.66
0.81
45
Y
1,55
0.6475
0.8047
51.92
Introduction
Standard Deviation (S.D.) and Coefficient of
Variation (C.V.) are statistical measures used to assess data variability. S.D.
measured the dispersion of data points around the mean, while C.V. expresses S.D.
as a percentage of the mean, allowing comparison across different datasets.
Standard Deviation (S.D.)
- Standard
Deviation measures how much individual values in a dataset vary from the
mean (average).
- A low
S.D. means data points are close to the mean, while a high S.D. indicates
they are spread out.
- It
helps understand the consistency or volatility of a dataset.
Formula:
Coefficient of Variation (C.V.):
C.V. is the ratio of the Standard Deviation to the Mean, expressed as a percentage.
- It is useful for comparing the variability of datasets with different units or scales.
- A higher C.V. means more relative variation, while a lower C.V. indicates more consistency.
Formula:
σ = Standard deviation (S.D.)
µ = Mean
Q1. What is the primary source of income for your
household.
a.
Agriculture. b. Business. C. Employment
Q2. What farming techniques do you use.
a. Traditional farming methods. b. Mechanized farming. c. Organic
farming. d. Precision farming.
Here, we have X and Y.
X is use for Question 1 and Y is use for Question 2
X: 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 3, 1, 1, 3, 2, 3, 2, 3, 1, 3
Y: 1, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 4, 1, 1
X: 1,1,2,2,2,1,1,1,1,2,3,1,1,3,2,3,2,3,1,3
n = 20
Mean(x)
1+1+1+1+1+1+1+1+1+2+2+2+2+2+2+3+3+3+3+3 = 36/20 =1.8
S.D. = (X)
|
Value (X) |
Deviation (X-X̄), X̄=1.8 |
Square of deviation (X-X̄)2 |
|
1 |
-0.8 |
0.64 |
|
1 |
-0.8 |
0.64 |
|
2 |
0.2 |
0.04 |
|
2 |
0.2 |
0.04 |
|
2 |
0.2 |
0.04 |
|
1 |
-0.8 |
0.64 |
|
1 |
-0.8 |
0.64 |
|
1 |
-0.8 |
0.64 |
|
1 |
-0.8 |
0.64 |
|
2 |
0.2 |
0.04 |
|
3 |
1.2 |
1.44 |
|
1 |
-0.8 |
0.64 |
|
1 |
-0.8 |
0.64 |
|
3 |
1.2 |
1.44 |
|
2 |
0.2 |
0.04 |
|
3 |
1.2 |
1.44 |
|
2 |
0.2 |
0.04 |
|
3 |
1.2 |
1.44 |
|
1 |
-0.8 |
0.64 |
|
3 |
1.2 |
1.44 |
|
|
Total |
=13.2 |
Therefore,
0.64+0.64+0.64+0.64+0.64+0.64+0.64+0.64+0.64+0.04+0.04+0.04+0.04+0.04+0.04+1.44+1.44+1.44+1.44+1.44
=13.2
S.D. = √13.2/20
= √0.66
S.D. = √0.66 = 0.81
Coefficient of variation
C.V. = (σ /X)100
C.V. = (0.81/1.8)100
C.V. = 45%
For Y datasets
n = 20
Mean(x)
1+1+1+1+1+1+1+1+1+1+1+1+2+2+2+2+2+2+3+4 = 31/20
= 1.55
S.D. = (X)
|
Value (X) |
Deviation (X-X̄), X̄=1.55 |
Square of deviation (X-X̄)2 |
|
1 |
-0.55 |
0.3025 |
|
2 |
0.45 |
0.2025 |
|
1 |
-0.55 |
0.3025 |
|
1 |
-0.55 |
0.3025 |
|
2 |
0.45 |
0.2025 |
|
2 |
0.45 |
0.2025 |
|
3 |
1.45 |
2.1025 |
|
1 |
-0.55 |
0.3025 |
|
1 |
-0.55 |
0.3025 |
|
1 |
-0.55 |
0.3025 |
|
1 |
-0.55 |
0.3025 |
|
2 |
0.45 |
0.2025 |
|
2 |
0.45 |
0.2025 |
|
1 |
-0.55 |
0.3025 |
|
1 |
-0.55 |
0.3025 |
|
1 |
-0.55 |
0.3025 |
|
2 |
0.45 |
0.2025 |
|
4 |
2.45 |
6.0025 |
|
1 |
-0.55 |
0.3025 |
|
1 |
-0.55 |
0.3025 |
|
|
Total |
12.95 |
Therefore,
03025+03025+03025+03025+03025+03025+03025+03025+03025+03025+03025+03025+0.2025+0.2025+0.2025+0.2025+0.2025+0.2025+2.1025+6.0025
= 12.95
S.D. = √12.95/20
= 0.6475
S.D. = √0.6475 = 0.8047
Coefficient of variation
C.V. = (σ /X)100
C.V. = (0.8047/1.55)100
= 51.92%
|
Data set |
Mean |
Variance |
Sd deviation |
C V |
|
X |
1.8 |
0.66 |
0.81 |
45 |
|
Y |
1,55 |
0.6475 |
0.8047 |
51.92 |
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