RESEARCH METHODOLOGY

STATISTICAL TECHNIQUES AND TOOLS

MEASURES OF CENTER AND SPREAD

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
If a distribution is skewed to the right with no outliers,
A
mean<median
B
mean>median
C
mean=median
D
can not determine
Explanation: 

Detailed explanation-1: -A right-skewed distribution has a few large observations (that are not outliers). The median is unaffected by these large observations, while the mean is affected by these large observations. Thus the mean will be larger than the median.

Detailed explanation-2: -When the distribution is skewed to the right, the mean is often greater than the median. In symmetric distributions, we expect the mean and median to be approximately equal in value. This is an important connection between the shape of the distribution and the relationship of the mean and median.

Detailed explanation-3: -Right skewed: The mean is greater than the median. The mean overestimates the most common values in a positively skewed distribution. Left skewed: The mean is less than the median. The mean underestimates the most common values in a negatively skewed distribution.

Detailed explanation-4: -The median is less affected by outliers and skewed data than the mean and is usually the preferred measure of central tendency when the distribution is not symmetrical.

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