Measures of central tendency are values that describe the middle or center of a data set. The three main measures are the mean, median, and mode. The mean is the average and is calculated by adding all values and dividing by the total number. The median is the middle number in a sorted list and divides the data set in half. The mode is the most frequent or common value in the data set. These measures can help summarize numerical data by identifying a single representative value.

1. Measures of Central
Tendencies
What is a Measure of Central Tendency?

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.

6. Mean of grouped data

7. Mean of a grouped data by three method

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

9. Formulas for median of a raw data.

10. Median formula for Grouped Data

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.

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