PPT - Measures of Skewness | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year PDF Download

 Page 1


Concept of Skewness
A distribution is said to be skewed-when the mean, median and mode fall at
different position in the distribution and the balance (or center of gravity) is
shifted to one side or the other i.e. to the left or to the right.
Therefore, the concept of skewness helps us to understand the 
relationship between three measures-
• Mean.
• Median.
• Mode.
Page 2


Concept of Skewness
A distribution is said to be skewed-when the mean, median and mode fall at
different position in the distribution and the balance (or center of gravity) is
shifted to one side or the other i.e. to the left or to the right.
Therefore, the concept of skewness helps us to understand the 
relationship between three measures-
• Mean.
• Median.
• Mode.
Symmetrical Distribution
• A frequency distribution is said to be symmetrical if the frequencies 
are  equally distributed on both the sides of central value.
• A symmetrical  distribution may be either bell – shaped or U shaped.
• In symmetrical distribution, the values of mean, median and mode are
equal i.e. Mean=Median=Mode
Page 3


Concept of Skewness
A distribution is said to be skewed-when the mean, median and mode fall at
different position in the distribution and the balance (or center of gravity) is
shifted to one side or the other i.e. to the left or to the right.
Therefore, the concept of skewness helps us to understand the 
relationship between three measures-
• Mean.
• Median.
• Mode.
Symmetrical Distribution
• A frequency distribution is said to be symmetrical if the frequencies 
are  equally distributed on both the sides of central value.
• A symmetrical  distribution may be either bell – shaped or U shaped.
• In symmetrical distribution, the values of mean, median and mode are
equal i.e. Mean=Median=Mode
Skewed Distribution
• A frequency distribution is said to be skewed if the  frequencies are not 
equally distributed on both the sides  of the central value.
• A skewed distribution maybe-
• Positively Skewed
• Negatively Skewed
Page 4


Concept of Skewness
A distribution is said to be skewed-when the mean, median and mode fall at
different position in the distribution and the balance (or center of gravity) is
shifted to one side or the other i.e. to the left or to the right.
Therefore, the concept of skewness helps us to understand the 
relationship between three measures-
• Mean.
• Median.
• Mode.
Symmetrical Distribution
• A frequency distribution is said to be symmetrical if the frequencies 
are  equally distributed on both the sides of central value.
• A symmetrical  distribution may be either bell – shaped or U shaped.
• In symmetrical distribution, the values of mean, median and mode are
equal i.e. Mean=Median=Mode
Skewed Distribution
• A frequency distribution is said to be skewed if the  frequencies are not 
equally distributed on both the sides  of the central value.
• A skewed distribution maybe-
• Positively Skewed
• Negatively Skewed
Skewed Distribution
• Negatively Skewed
• In this, the distribution is skewed 
to the left (negative)
• Here, Mode exceeds Mean and 
Median. 
• Positively Skewed
• In this, the distribution is skewed 
to the right (positive)
• Here, Mean exceeds Mode and 
Median. 
Mean<Median<Mode
Mode<Median<Mean
Page 5


Concept of Skewness
A distribution is said to be skewed-when the mean, median and mode fall at
different position in the distribution and the balance (or center of gravity) is
shifted to one side or the other i.e. to the left or to the right.
Therefore, the concept of skewness helps us to understand the 
relationship between three measures-
• Mean.
• Median.
• Mode.
Symmetrical Distribution
• A frequency distribution is said to be symmetrical if the frequencies 
are  equally distributed on both the sides of central value.
• A symmetrical  distribution may be either bell – shaped or U shaped.
• In symmetrical distribution, the values of mean, median and mode are
equal i.e. Mean=Median=Mode
Skewed Distribution
• A frequency distribution is said to be skewed if the  frequencies are not 
equally distributed on both the sides  of the central value.
• A skewed distribution maybe-
• Positively Skewed
• Negatively Skewed
Skewed Distribution
• Negatively Skewed
• In this, the distribution is skewed 
to the left (negative)
• Here, Mode exceeds Mean and 
Median. 
• Positively Skewed
• In this, the distribution is skewed 
to the right (positive)
• Here, Mean exceeds Mode and 
Median. 
Mean<Median<Mode
Mode<Median<Mean
Tests of Skewness
In order to ascertain whether a distribution is skewed or not the  following 
tests may be applied. Skewness is present if:
•The values of mean, median and mode do not coincide.
•When the data are plotted on a graph they do not give the normal bell  shaped 
form i.e. when cut along a vertical line through the center the  two halves are not 
equal.
•The sum of the positive deviations from the median is not equal to the  sum of 
the negative deviations.
•Quartiles are not equidistant from the median.
•Frequencies are not equally distributed at points of equal deviation from the 
mode.