The document discusses different measures of central tendency including the mean, median, and mode. The mean is the average value and considers all scores, but can be impacted by outliers. The median is the middle value when scores are arranged in order and is less impacted by outliers. The mode is the most frequently occurring value and can be used for both numerical and categorical data, but may not always indicate the true central tendency. Each measure has advantages and limitations, and different measures are better suited for certain types of data distributions.

1. MEASURES OF CENTRAL TENDENCY

2. Central Tendency
• In statistics, a central tendency (or measure of
central tendency) is a central or typical value
for a probability distribution. It may also be
called a center or location of the distribution.
• (आंकड़ों में, एक कें द्रीय प्रवृत्ति (या कें द्रीय
प्रवृत्ति का माप) एक संभावना त्तवतरण के लिए
एक कें द्रीय या त्तवलिष्ट मूल्य है।इसे त्तवतरण
का कें द्र या स्थान भी कहा जा सकता है)

3. • Normal distribution,
also known as
the Gaussian
distribution, is a
probability distribution t
hat is symmetric about
the mean, showing that
data near the mean are
more frequent in
occurrence than data far
from the mean. In graph
form, normal
distribution will appear
as a bell curve

4. Measures Of Central Tendency
• A measure of central tendency (also referred to
as measures of centre or central location) is a
summary measure that attempts to describe a
whole set of data with a single value that
represents the middle or centre of its
distribution.
There are three main measures of central
tendency: the mode, the median and the mean.
Each of these measures describes a different
indication of the typical or central value in the
distribution.

5. 3
2
Measure Of Central
Tendency
1. Mean
2. Median
3. Mode
1

6. Mean
• The mean (or average) is the most popular
and well known measure of central tendency.
• It can be used with both discrete and
continuous data, although its use is most
often with continuous data .

7. Advantages Of Mean
• Easy to calculate.
• It Consider all the scores of distribution.
• Useful in normally distributed data.
• It is best representation of all three measures.
• It gives correct and real info most stable value.
• It gives more accurate and reliable result.
• Useful in comparison of groups.
• Base of other measurements.

8. Limitation Of Mean
• Cant be used in incomplete data. (when CI
have zero frequency)
• When extreme scores are given ( data is
skewed)

9. When To Use Mean
• When data is normally distributed around a
central point.
• When each entry in data is to be valued.
• When measure of central tendency having the
greatest stability is wanted.
• When most reliable measure is required.
• When data is complete.

10. Median
The median is the middle value in distribution
when the values are arranged in ascending or
descending order.
The median divides the distribution in half (there are
50% of observations on either side of the median value)
Advantage
•The median is less affected by outliers and skewed
data than the mean.
• Its the preferred measure of central tendency when
the distribution is not symmetrical.
•Time saving ,gives actual middle value.
•Obtained on graph.

11. Limitations To Use Median
• The median cannot be identified
for categorical nominal data, as it cannot be
logically ordered.
• Do not depends on each entry or score.
• Not very helpful when data size is small.
• Affected by sampling fluctuations.

12. When To Use Median
• When data is skewed (extreme scores are
there).
• 11,14,18,19,23,90
• When true measure of central tendency is
required. (actual middle value is required)
• When we need to calculate typical value quickly
( only middle scores are considered)

13. • When incomplete distributions are given.
(some CI have no frequency).
• Useful for large data.

14. Mode
• The mode is the most commonly occurring
value in a distribution.
In 1,2,6,3,9,11,2,7,8,2,8
mode of data is most occuring digit i.e 2.
Advantage
•it can be found for
both numerical and
categorical (non-numerical) data.
• it is not affected by extreme scores.
•Obtained on graph.

15. Limitations To Use Mode
• It doesn’t always gives true central tendency.
• Sometimes Its not unique .
• In some cases, particularly where the data
are continuous, the distribution may have no
mode at all (i.e. if all values are different).
When the distribution of retirement age is ordered from lowest to highest value,
it is easy to see that the centre of the distribution is 57 years, but the mode is lower, at 54
years.
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

16. When To Use Mode
• When true / exact central value is not required.
• when we need to calculate central tendency
quickly.
• When data is categorical / nominal.
• When data is incomplete.
• When data is not normally distributed.
• When a rough estimate of central value is
enough.

17. median mode