Download (a) Why do we have so many different measures of central tendency

(a) Explain when to use the mean, median and mode as measures of central tendency. List and describe some
common measures of dispersion. Why are measures of central tendency not appropriate in interpreting a
distribution without being accompanied by measures of dispersion?
(a) We have many different measures of central tendency because each measure of central tendency requires
a minimum level of measurement. Each is applicable under specific conditions. The following table shows
when each is applicable:
Level of
Mean
Median
Mode
Variance / Standard Deviation
Nominal
x
x

x
Ordinal
x


x
Interval / Ratio




Measurement
Here are some actual examples for each application:
(i) We use Mean as the appropriate measure of central tendency for interval measures such as the
temperature in Celsius scale or Fahrenheit scale, and for ratio measures as in physical quantities, such as
mass, length, energy, and temperature measured in K.
(ii) We use Median as the appropriate measure of central tendency for ordinal data such as the results of a
horse race, which say only which horses arrived first, second, third, etc. but no time intervals are mentioned,
and for interval measures such as the temperature in Celsius scale or Fahrenheit scale.
(iii) We use Mode as the appropriate measure of central tendency for nominal/categorical data such as
gender, race, religious affiliation and birthplace.
It is clear from the above discussion that not all measures of tendency are required to describe the data (nor
all can be used). Depending upon the data type, we use one or the other to best describe the data.
(b) A dataset cannot be described completely using either the measures of central tendency or the measures
of dispersion (Range, Variance, Standard Deviation or Quartile Deviation) alone. They are always used
together so that the distribution can be described in sufficient detail. Range provides information about the
extreme values in a data set because Range = Maximum value - Minimum value. Standard deviation provides
information about how much the data vary from the mean value, on an average. Two data sets may have the
same measures of central tendency, say mean = median = mode = 6. This may make one to believe that they
are both identical. But when standard deviation is computed for both the sets (assume it is 2.3 for one set and
3.0 for the other), it becomes clear that the second set has more spread than the first. Therefore, for a
complete description of the data (this is very important for further statistical analysis), measures of central
tendency and measures of spread are used together.