Arithmetic Mean Concept

Arithmetic Mean Concept

Arithmetic mean can be calculated by a simple equation i.e. sum of all observation is divided by the number of observation.

Arithmetic Mean Formula

Arithmetic mean = Sum of all observation/Number of observation

Arithmetic Mean Example

There are five students in a class who obtained 56, 68, 72, 83, 49 in statistic paper, what is average mark of the class?

Arithmetic mean = Sum of all observation/Number of observation

= 56+68+72+83+49/5

=328/5

=65.6 (arithmetic mean or average marks)

Arithmetic Mean Types

Arithmetic mean can be broadly classified into two type i.e. simple arithmetic mean and weighted arithmetic mean. In case of weighted arithmetic mean weights (importance) is assigned to observation and then average is calculated.

Arithmetic mean (weighted) = ∑xw/∑w

Subject	Marks (x)	Weight (w)	xw
maths	40	10	400
English	34	8	272
		18	672

= 672/18

=37.33

Arithmetic mean of Grouped Data

Arithmetic mean of Group data may be calculated with the help of midpoint i.e. midpoint is multiplied with frequency and total is divided by the sum of frequency.

Class	Frequency (f)	Mid Point (x)	(f)*(x)
25-44	40	34.5	1380
45-64	33	54.5	1798
	73		3178

=3178/73

=43.53

Arithmetic Mean Short Cut Method

Arithmetic mean can be calculated by a short cut method by following formula

Arirthmetic mean = a+hu

Where

a-midpoint of largest frequenc

h- class width

u – ∑f*u/∑f