AVERAGE :- Average is a single value of any series which can represent the whole set of data.
It is very difficult to obtained any conclusion of different subjects, from large comparision of data. But if a single number is taken from each, then it is easy to comparision between them all. Such a number is called measure of central tendency.
TYPES OF AVERAGE :-
- ARITHMETIC MEAN or AVERAGE [ AM] .
- GEOMETRIC MEAN [GM].
- HARMONIC MEAN [HM].
- MEDIAN
- MODE
Here, we will discuss only about arithmetic mean (Average).
AVERAGE IS CALCULATED BY :-
average = $\left ( \frac{Sum\: of\, observations}{Number\, of\, observations}\right )$
Average of n observations $x_{1},x_{2},x_{3},...x_{n}$ is given by,
average = $\frac{(\, x_{1}\, +\, x_{2}\, +\, x_{3}\, +...+\, x_{n}\, )\, }{n}$
For eg. :-
The marks obtained by student of class 9 in mathematics are 7, 8, 5, 6, 7, 8, 9, 4, 5 and 6 respectively then find the average marks of students.
sol. average = $\frac{Sum\, of\, marks}{no.\, of\, students}$
= $\frac{7 + 8 + 5 + 6 + 7 + 8 + 9 + 4 + 5 + 6}{10}$
= $\frac{65}{10}$
= 6.5 marks
MERITS AND DEMERITS OF ARITHMETIC MEAN :-
MERITS :-
- It is easy to calculate.
- It is based upon all the terms.
- This mean is fixed and always same.
- It is also used in other statistical analysis.
DEMERITS :-
- Sometimes in its calculation, such value may occur which is not possible according to nature, e.g. number of members in a family is 3.5 or 7.2
- It is not possible to calculate if any one value is missing.
- It is affected very much by extreme values.
AVERAGE RELATED TO SPEED :-
Suppose a person travels a distance at a speed of x km/h and the same distance at a speed of y km/h , then the average speed during the whole journy is given by $\frac{2xy}{x+y}$ km/h.
For eg. A train travels from A to B at the rate of 30 km/h and from B to A at the rate of 20 km/h. Find the average rate for whole journey?
sol. average = $\frac{2xy}{x+y}$
= $\frac{2\times 30\times 20}{30\, +\, 20}$
= 24 km/h.
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