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Summary Measures of Central Tendency
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Numerical Descriptive Statistics▪ Measures of central tendency are statistical measures
which describe the position of a distribution.
▪ They are also called statistics of location, and are the
complement of statistics of dispersion, which provide
information concerning the variance or distribution of
observations.
▪ In the univariate context, the mean, median and mode
are the most commonly used measures of central
tendency.
▪ computable values on a distribution that discuss the
behavior of the center of a distribution.
, Measures of Central Tendency
• The value or the figure which represents the whole
series is neither the lowest value in the series nor the
highest it lies somewhere between these two extremes.
• The average represents all the measurements made
on a group, and gives a concise description of the
group as a whole.
• When two are more groups are measured, the central
tendency provides the basis of comparison between
them.
, Definition
• Simpson and Kafka defined it as “ A measure of
central tendency is a typical value around which other
figures congregate” Waugh has expressed “An average
stand for the whole group of which it forms a part yet
represents the whole”.
• Common Measures of Central Tendency are the :
– Mean
– Median
– Mode
– Geometric mean
– Harmonic mean
– Percentiles
– Quartiles
, Arithmetic Mean
Arithmetic mean is a mathematical
average and it is the most popular
measures of central tendency. It is
frequently referred to as ‘mean’ it is
obtained by dividing sum of the values of all
observations in a series (ƩX) by the number
of items (N) constituting the series.
Thus, mean of a set of numbers X1, X2,
X3,………..Xn denoted by x̅ and is defined as
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