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Research Methodology
Notes
Figure 8.5
Frequency
O X
Figure 8.6
Symmetrical Distribution
Frequency
O X
d
X = M = M 0
Imagine a situation in which the symmetrical distribution is made asymmetrical or positively
(or negatively) skewed by adding some observations of very high (or very low) magnitudes, so
that the right hand (or the left hand) tail of the frequency curve gets elongated. Consequently,
the three measures will depart from each other. Since mean takes into account the magnitudes of
observations, it would be highly affected. Further, since the total number of observations will
also increase, the median would also be affected but to a lesser extent than mean. Finally, there
would be no change in the position of mode. More specifically, we shall have M < M < X, when
o d
skewness is positive and X < M < M , when skewness is negative, as shown in Figure 8.7.
d o
Figure 8.7
Positively Skewed Distribution
Frequency
O M M X X
0
d
Negatively Skewed Distribution
O XM M 0 X
d
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