about skewness in quantitative techniques

1. WELCOME
PRESENTED BY,
S1-MBA
G.K.M.C.M.T

2. MEASURE OF SKEWNESS

3. SKEWNESS
• Skewness means lack of symmetry.
• In skewed distribution, the mean and the
median are pulled away from the mode.
• Mean, median and mode are not equal.
• A skewed distribution is an asymmetrical
distribution.
• It has a long tail on one side and short tail on
the other side.
• Eg:- Income, Savings, etc

4. TEST OF SKEWNESS
To test whether a distribution is skewed or
not, the following are to be noticed. A
distribution is skewed if
1. mean, median and mode are not equal.
2. sum of positive deviations from median or
not equal to the sum of negative deviation
from median

5. 3. (a) Q1 and Q3 are not equidistant from
median.
(b) D1 and D9 are not equidistant from
median.
(c) P10 and P90 are not equidistant from
median.
4. Frequencies on either side of modes are not
equal.
5. The frequency curve has longer tail on the
left side or on the right side.

6. POSITIVE AND NEGATIVE
SKEWNESS

7. • Skewness maybe either positive and
negative.
• Skewness is said to be positive when the
mean is greater than the median and median
is greater than mode.
• Skewness is sais to be negative when the
mean is less than the median and the median
is less than mode.
• For a positively skewed curve, there is longer
tail to the right and for a negatively skewed
curve, there is longer tail to left.

8. MEASURE OF SKEWNESS
• Idea about the direction and extent of
asymmetry in a series.
• Compare two or more series and say which
series has more skewness.
• Absolute or relative .
• Relative measures of skewness are also
known as coefficients of skewness.

9. 1.) First measure of skewness:
 For skewed distribution the values of mean,
median and mode are not equal.
 The distance between the mean and the mode
can be used to measure the skewness.
 Coefficient of skewness,
𝐽 =
𝑀𝑒𝑎𝑛 − 𝑀𝑜𝑑𝑒
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
 J will be between -3 and 3.
 Mode is indeterminate, then Mean-Mode can be
taken as 3(Mean-Median)
 Also known as Karl Pearson’s coefficient of
skewness

10. 2.) Second measure of skewness:-
 Q1 and Q3 are not equidistant from median.
 Difference between M-Q1 and Q3-M gives
the measure of skewness.
 Coefficient of skewness,
𝑄3−𝑀 −(𝑀−𝑄1)
𝑄3−𝑄1
=
(𝑄3+𝑄1−2𝑀)
𝑄3−𝑄1
 This formula is known as Bowley’s coefficient
of skewness.

11. 3.) Third measure of skewness:-
 The difference between D9-Median and
Median-D1 give the measure of skewness.
 Absolute measure.
 Also known as Kelley’s coefficient of
skewness
(𝐷9 − 𝐷1 − 2𝑀𝑒𝑑𝑖𝑎𝑛)
𝐷9 − 𝐷1
4.) Fourth measure of skewness:-
 Based on third moment.
 The value of µ3 gives the absolute measure
and the coefficient of the skewness =
µ3
√µ2³

12. USES
 Concentrations is in higher and lower values.
 to study the distribution is normal or not.