Measures of central tredencies ppt M.lib.notes. M.lib.seceond semester notes Median mean tredencies

1. Seminar
Session(2020-2021)
MEASURES OF CENTRAL TENDENCIES: MEAN,MEDIAN, MODE
JIWAJI UNIVERSITY
SOS in library and information science,
Guided By:-
All teacher’s
Presented By:-
Ankit
M.Lib. I.Sc. 2nd sem

2. Contents
• MEASURES OF CENTRAL TENDENCY
• Objectives and functions of Central Tendencies
• Essentials of a good average / measure of central tendency
• Scales of Measurement and Measures of Central Tendency
• THE MEAN
• Median
• Mode
• conclusion
• Reference

3. MEASURES OF CENTRAL TENDENCY
Central tendency is the central value or score of a group
The most commonly used measures of central tendency are:
Mean
Median
Mode

4. Objectives and functions of Central Tendencies
1. To present huge data in a summarised form: It is difficult to grasp a large amount of data or
numerical figures. Averages summarise such data into a single figure which makes it easier to
understand and remember.
2. To facilitate comparison: Averages are very helpful for making comparative studies as they
reduce the mass of statistical data to a single figure or estimate.
3. To facilitate further statistical analysis: Various tools of statistical analysis like standard
deviation, correlation etc. are based on averages.
4. To trace precise relationship: Averages are helpful and even essential when it comes to
establishing relationships between different groups of data or variables.
5. To help in decision-making: Averages provide values which act as a guideline for decision
makers. Most of the decisions to be taken in research or planning are based on the average value
of certain variables.

5. Essentials of a good average / measure of
central tendency
1. It should be rigidly defined: ➢ An average should be clear and there should be only one form of
interpretation. ➢ It should have a definite and fixed value irrespective of method of calculations or formulae
used.
2. It should be based on all observations: ➢ Average should be calculated by taking into consideration each
and every item of the series. ➢ If it is not based on all observations, it will not be representative of the whole
group.
3. It should not be affected much by extreme values: ➢ The value of an average should not be affected much
by extreme values. ➢ One or two very small or very large values should not unduly affect the value of the
average significantly.
4. It should be least affected by fluctuations of sampling: ➢ An average should possess sampling stability i.e.
If we take two or more samples from a given population and compute averages for each, then the values thus
obtained from different samples should not differ much from each other.
5. It should be easy to understand and compute: ➢ The value of an average should be computed by using a
simple method without reducing its accuracy and other advantages.
6. It should be capable of further algebraic treatment: ➢ It should be capable of further mathematical and
statistical analysis to expand its utility such as to be further used in calculation of measures of dispersion,
correlation etc.

6. Scales of Measurement and Measures of
Central Tendency
• Data on Nominal Scale: If data is on nominal scale which is mostly qualitative in nature, we can
simply count the number of cases in each category and obtained frequencies. In such cases, if the
data is in nominal scale, we can use the statistics ‘The Mode’ as the measure of central tendency. It
supports the definition of the mode, i.e., ‘mode is the most frequent item/score of the group’.
• Data on Ordinal Scale: Ordinal scale implies that the scores are in an order, either ascending or
descending. When data is arranged in rank order the measure of central tendency found by locating
a point that divides the whole distribution into two equal halves. In such cases, we use the statistics
‘median’ as the measure of central tendency. It supports the definition of median, i.e., ‘median is a
point on the scale of measurement below and above which lie exactly 50 percent of the cases. It
may be noted that median is defined as a point and not as a score or any particular measurement.
• Data on Equal Interval Scale: When data is presented in class intervals and there is scope to
convert the data into class intervals, we can best use statistics ‘Mean’ as the measure of central
tendency. Mean is the most popular measures which is highly used in schools. Mean of a
distribution of scores may be defined as the point on the scale of measurement obtained by
dividing the sum of all the scores by the number of scores. Mean is also called as the most
appropriate measures of central tendency

7. Conti…
• Ratio scale is used in measurement of physical sciences where there is a concept
of absolute zero point in measurement. But in educational measurement, we
consider zero point measurement as the relative zero point. The use of different
methods of calculating measures of central tendency depends upon the nature of
the data and its scales of measurement.

8. THE MEAN
Mean is calculated when the data is presented or have the scope to
present it in interval scale. It is also popularly known as ‘Arithmetic
Mean’. Mean can be calculated by adding sum of the
observations/scores by dividing by total number of cases. The formula
of calculating Mean is as follows:

9. Arithmetic Mean

10. Median
• Median is defined as the middle value in the data set when its elements are
arranged in a sequential order, that is, in either ascending or descending order.
• It is a positional value. Positional average determines the position of variables in
the series

11. Calculation of Median- Methods

12. MODE
• Mode is defined as the value occurring most frequently in a given series and
around which other items of the set cluster most densely.
• The word mode has been derived from the French word ‘la Mode’ which signifies
the most fashionable values of a distribution, because it is repeated the highest
number of times in the series.

13. Conti…
INDIVIDUAL SERIES The value which occurs maximum number of times is the
mode.
• DISCRETE SERIES There are two methods of calculating mode using grouped
data:
a) Inspection or Observation method
b) Grouping method
a) Inspection or observation method :The value of the variable against the highest
frequency will give the mode.
b) Grouping method:-

14. Conti…
• b) Grouping method:-

15. Mode in special cases
1) Cumulative Series (Less-than or More-than series) Cumulative frequency series
is first converted into simple frequency series and then mode is calculated in the
usual manner.
2) Mid-Value series: Mid- values are first converted into class intervals and then
mode is calculated in the usual manner
3) Inclusive series: The inclusive series is first converted into exclusive series and
then mode is calculated in the usual manner.
4) Open-ended series: There is no need to complete the class intervals to calculate
the mode.
5) Unequal class series: The unequal classes need to be first converted into equal
width classes and frequencies are adjusted before calculating the mode in the usual
manner.

16. Merits of Mode
➢ It is not affected by values of extreme items.
➢ It can be obtained graphically using histogram.
➢ It can be used to describe quantitative as well as qualitative data.
➢ It can be calculated even in case of open-ended distributions without finding
class limits.

17. Demerits of Mode
• ➢ It is not rigidly defined.
• ➢ It is not based on all observations.
• ➢ It is not capable of further algebraic treatment.
• ➢ It is affected by fluctuations of sampling.

19. Reference
• www.epgpathshala.com
• ignou