2. introduction
• The role of statistics in research is to function
as a tool in designing research, analysing its
data and drawing conclusions there from.
Most research studies result in a large volume
of raw data which must be suitably reduced so
that the same can be read easily and can be
used for further analysis.
3. content
• (i) Coefficient of variation;
• (ii) Arithmetic average;
• (iii) Coefficient of skewness;
• (iv) Regression equation of X on Y;
4. Coefficient of variation
• Coefficient of Variation is a measure of spread
that describes the amount of variability
relative to the mean.
• The coefficient of variation (CV) is a measure
of relative variability.
• It is the ratio of the standard deviation to the
mean (average).
8. • Coefficient of Variance Example:
1. Find CV of {13,35,56,35,77}
Solution:
Number of terms (N) = 5
Mean:
Xbar = (13+35+56+35+77)/5
= 216/5 = 43.2
• step 2 -Standard Deviation (SD):
Formula to find SD is
σ=(1/(N - 1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2)) ½
=(1/(5-1)((13-43.2)2+(35-43.2)2+(56-43.2)2+(35-43.2)2+(77-43.2)2))½
σ = 1.92
• Step 3: calculate coefficient of variance
CV = (Standard Deviation (σ) / Mean (μ))
= 1.92 / 62.51
= 0.03071
9. Merits & Demerits of Coefficient of
Variation
• Merits
• 1. Best one
• 2. Most appropriate one
• 3. Based on Mean and Standard Deviation
• 4. COV is dimensionless or nonunitized
10. • Demerits
• It is impossible to calculate
if Mean is 0
•It is difficult to calculate if
the values are both positive
and negative numbers & if
the mean is close to 0.
11. Practical Uses of Coefficient of
Variance
• INVESTMENT ANALYSIS
• STOCK MARKET
• RISK EVALUATION
• COMBINED STANDARD DEVIATION OF
SEVERAL GROUPS
• PERFORMANCES OF TWO PLAYERS
• INDUSTRIES & FACTORIES
12. Arithmetic average
• In mathematics and statistics, the arithmetic
mean or simply the mean or average when
the context is clear, is the sum of a collection
of numbers divided by the number of
numbers in the collection.
14. Coefficient of skewness
• Skewness is asymmetry in a statistical
distribution, in which the curve appears
distorted or skewed either to the left or to the
right. Skewness can be quantified to define
the extent to which a distribution differs from
a normal distribution. ... This situation is also
called negative skewness.
15. • Skewed distributions
• There are three types:
• Symmetrical distribution
A.M = Median = Mode
• Positively skewed distribution
A.M > Median > Mode
• Negatively skewed distribution.
A.M < Median < Mode
21. Kelly’s co-efficient of skewness
• Kelly's Measure of Skewness is one of several ways to
measure skewness in a data distribution.
22. Bowley’s coefficient of skewness
• Bowley Skewness = Q3+Q1 – 2Q2 / (Q3 – Q1)
• Skewness = 0 means that the curve is
symmetrical.
• Skewness > 0 means the curve is positively
skewed.
• Skewness < 0 means the curve is negatively
skewed.
23. Bowley Skewness Worked Example
• Q. Find the Bowley Skewness for the following
set of data:
24. • Step 1: Find the Quartiles for the data set.
You’ll want to look for the “nth” observation
using the following formulas:
Q1 = (total cum freq + 1 / 4)th observation =
(230 + 1 / 4 ) = 57.75
Q2 = (total cum freq + 1 / 2)th observation =
(230 + 1 / 2 ) = 115.5
Q3 = 3 (total cum freq + 1 / 4)th observation =
3(230 + 1 / 4) = 173.25
25. • Step 2: Look in your table to find the nth
observations you calculated in Step 1:
Q1 = 57.75th observation = 0
Q2 = 115.5th observation = 1
Q3 = 173.25th observation = 3
• Step 3: Plug the above values into the
formula:
Skq = Q3 + Q1 – 2Q2 / Q3 – Q1
Skq = 3 + 0 – 2 / 3 – 0 = 1/3
• Skq = + 1/3, so the distribution is positively
skewed.
26. • Limitations of Bowley Skewness.
• Bowley Skewness is an absolute measure of
skewness. In other words, it’s going to give
you a result in the units that your distribution
is in. That’s compared to the Pearson Mode
Skewness, which gives you results in a
dimensionless unit — the standard deviation.
This means that you cannot compare the
skewness of different distributions with
different units using Bowley Skewness.
27. • Variation tells us about the amount
of the variation where as Skewness
tells about the direction of variation.
• In business and economic series,
measures of variation have greater
practical application than measures
of skewness.
28. Regression equation of X on Y
• Regression is the determination of a statistical
relationship between two or more variables
• In simple regression, we have only two variables,
one variable (defined as independent) is the
cause of the behaviour of another one (defined
as dependent variable). Regression can only
interpret what exists physically i.e., there must be
a physical way in which independent variable X
can affect dependent variable Y
29. • The basic relationship between X and Y is given
by
• Ŷ = a + bX
• where the symbol Ŷ denotes the estimated value
of Y for a given value of X.
• This equation is known as the regression
equation of Y on X (also represents the regression
line of Y on X when drawn on a graph)
• which means that each unit change in X produces
a change of b in Y, which is positive for direct and
negative for inverse relationships.
35. reference
Research methodology by C.R.KOTHARI
https://image.slidesharecdn.com/skewness
https://en.wikipedia.org/wiki/Coefficient_of_var
iation
https://en.wikipedia.org
