2. Measures of central tendency
A measure of central tendency is a single value that attempts to describe
a set of data by identifying the central position within that set of data.
Measures of central tendency are numbers that tend to cluster around the “middle” of
a set of values. Three such middle numbers are the mean, the median, and the mode.
3. There are three commonly used measures of
central tendencies.
4. In a nut shell they are described and calculated as
follows for raw data/ungrouped data.
5. Mean
• In mathematics and statistics,
the arithmetic mean, or simply
the mean or the average, is
the sum of a collection of
numbers divided by the count
of numbers in the collection.
The collection is often a set of
results of an experiment or an
observational study. Mean is
denoted by M.
8. Median
• The median is the middle number in a sorted, ascending or
descending, list of numbers and can be more descriptive of that
data set than the average.
• (or)
• Median is a value which divides the given set of observations
into two equal sets, one set of values are lower than the median
and the another set of values are higher than the median. It is
denoted by Md
11. Mode
Definition of Mode
• Mode is defined as the most
repetitive or common number in
the entire given set of
observations, and it is denoted
by Mo
• For a give raw data, we simply
find mode by picking up the
most repetitive value.
• Modes can be multiple.
Mode formula for grouped Data
12. Relationship between Mean,
Median & Mode.
Mode= 3 Median-2 Mean
Mo= 3 Md-2 M
Note : The above formula is supposed to be used to find the value of mode,
if the highest frequency, either occurs at the extreme beginning or ending.
