Tests Of Skewness
1. The values of mean, median and mode do not coincide. The more the difference between them, the more is the skewness.
2. Quartiles are not equidistant from the median.
i.e. ( Q_{3} Me ) ¹ ( Me  Q_{1}
).
3 The sum of positive deviations from the median is not equal to the sum of the negative deviations.
4. Frequencies are not equally distributed at points of equal deviation from the mode.
5. When the data is plotted on a graph they do not give the normal bellshaped form.
Measure Of Skewness
1. First measure of skewness It is given by Karl Pearson
Measure of skewness Coefficient of skewness
Skp = Mean  Mode J =
i.e. Skp =
 Mo
Pearson has suggested the use of this formula if it is not possible to determine the mode (Mo) of any distribution,
( Mean  Mode ) = 3 ( mean  median )
Skp = 3 ( 
Mo ) Thus J =
Note : i) Although the coefficient of skewness
is always within ± 1, but Karl Pearson’s
coefficient lies within ± 3.
ii) If J = 0, then there is no skewness
iii) If J is positive, the skewness is also positive.
iv) If J is negative, the skewness is also negative.
Unless and until no indication is given, you must use only Karl Pearson’s formula.
Example Find Karl Pearson’s coefficient of skewness from the following data:
Marks above : 
No.of students: 
0 
150 
10 
140 
20 
100 
30 
80 
40 
80 
50 
70 
60 
30 
70 
14 
80 
0 
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