Range Definition

Range Definition

Range is calculated as difference between two extreme value i.e. highest value and lowest value. Range can be expressed mathematically as below

Range= Xm-X0

Where

Xm= larges value

X0 = lowest value

Range limitations

Range limitation includes ignorance of middle values and misleading idea about the spread of data. The fundamental reason for these limitations is its extreme value consideration.

Median Definition

Median Concept

Median is a point which divides the ordered data in two equal points. It is fundamental for median calculation that data is in order i.e. data is arranged from lower value to high value. Median can also be defined as point below which 50% order data lies.

Median Formula

Median has two different formulas for two different cases i.e. n/2 integer and non integer.

1)    [{n/2}+1]th observation ( where n/2 is integer

2)    [n+1]/2 th observation  (where n/2 is not integer)

Median & Quin tiles

Median as well as quin-tile may be calculated for large data, typically there are three types of quintiles calculated Q1, Q2, and Q3 which divided the ordered data into 25%, 50% and 75% respectively.

Q1 = [n/4+1] th

Q3 = [3n/4] th observation

Mode Concept

Mode Concept

Mode means most frequent observation or observation occurring more frequently. There may be more than one mode; there may also be no mode for a data. In simple term observation with most number of frequencies is known as mode.

Mode for un grouped & Grouped Data

Mode for ungrouped data can be found by simpler observation. While mode for grouped data is found by a formula given below;

Mode for Grouped Data = l+       [fm-  f1]             x h

                                                   [fm-f1]+[fm-f2]

l=lower class boundary

h=class interval

fm = highest frequency

f1= previous class frequency

f2= nex class frequency

Mode Empirical Relationship Formula

Mode can be calculated by the following formula, it is important to remember that this formula will not work for the highly skewed or u shaped frequency distribution.

Mode = 3 median – 2 mean

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