for finance statistics use only.

1. Measures of Central Tendency/
StatisticalAverage

2. Definition and Meaning
The statistical measure which tell us the location
of central value to describe the central tendency
of the entire mass of data is known as statistical
average.
According to Croxton and Cowden, “ An average
is a single value within the range of the data that
is used to represent all of the values in the
series.”

3. Objects of StatisticalAverage
❖ To get single value that describe the
characteristics of the entire group
❖To facilitate comparison

4. Functions/Use of Measures of Central
Tendency
• Gives information about the whole group
•Become the basis of future planning and
actions
•Provide a basis for analysis
•Helps in decision making

5. Limitations of Averages
• An average is a single value representing a
group of values, but it is not always safe to
depend on it because there is every
possibility of getting wrong conclusions.
•An average may give us a value that does
not exist in the data.
•A wrong choice of an average for a
particular problem might give fallacious
conclusions

6. Types of Measures of Central Tendency
(A) Mathematical Average:
(i) Arithmetic Mean
(ii) Geometric Mean
(iii) Harmonic Mean
(iv) Quadratic Mean
(B) Average of Position:
(i) Median
(ii) Partition Values
(iii) Mode

7. (C) Commercial Averages:
(i) Moving Average
(ii) Progressive Average
(iii) Composite Average

8. Simple and Weighted Averages
Simple Average: When each value in a statistical
series is given equal importance, then the
average is called simple average.
Weighted Average: When each value in a
statistical series is not given equal importance,
then some weight are assign to them. Here
weight is numerical multiplier which is assigned
to each value of the variable in order to indicate
its relative importance. The average with weight
is called weighted average.

9. Merits and Demerits Of Arithmetic Mean:-
Merits:-
(1)Rigid and definite
(2)Simple to calculate and to understand
(3) It is based on all observations.
(4)The computation of arithmetic mean does not
require arranging like median.
(5)It is least affected by fluctuations of sampling.

10. Demerits:-
(1)Effect of extreme items
(2)Difficulty in case of unknown values
(3)Fallacious conclusions
(4)Not suitable in qualitative facts
(5)May not exist in data
(6)Absurd results:- ex. There are seven persons in
one family and two persons in other family.
Their arithmetic mean will be 4.5, which is
absurd because persons cannot divided in
fractions.

11. Merits and Demerits Of Median:-
Merits:-
(1)Unaffected by the extreme items
(2)Location by observation
(3)Location in incomplete data
(4)Appropriate in qualitative variables
(5)Exact middle item in the distribution.

12. Limitations:
(1)Difficulty in case of even numbers in individual
series
(2)Problem of array
(3)Not suitable for further algebraic treatment
(4)Lack of representation
(5)Lack of proper affect of all items

13. Merits and Demerits Of Mode:-
Merits:-
(1)Not affected by extreme values
(2)In individual and discrete series, it can be
located even by inspection.
(3)It can be very easily found from the graph.
(4)Most representative value
(5)The value of mode remains almost stable in
sampling.

14. Demerits:-
(1)Indeterminate and ill-defined
(2)Not based on all values
(3)Not capable of further mathematical treatment
(4)It vanishes even if a single value of the variate
is zero.
(5)Not rigidly defined measure