# Statistics formulas

**Statistics**:

Statistics is a branch of mathematics which deals with the study of collection , organization and interpretation of data.

**a>** **Arithmetic mean formulas**:

1> The mean for ungroup ( individual ) data or the arithmetic mean is denoted by: and it’s formula is:

2>The arithmetic mean for group (discrete) data is calculated using formula:

3> The arithmetic mean for continuous data is calculated using the formulas:

Direct method:

Deviation method:

Step deviation method:

Where , d = X – A , A = assumed mean and i = height of the class.

## b> **Median formulas**:

1> Median for ungroup data:

i> Median = ‘th observation if the “N” is odd.

ii> Median = average of and observation if “N” is even.

2> Median for group data:

Median = ( For continuous frequency distribution )

where , l= lower limit of median class , f= frequency of median class , c.f. = cumulative frequency of pre-median class , h= size of median class , N = total numbers of items.

## c> **Quartiles formulas** :

1> First quartile:

For individual data:

observation in the data arranged in ascending or decreasing order.

For group ( discrete) data:

observation in the data arranged in ascending or decreasing order.

For continuous data:

lies in place.

and exact first quartile =

where , , l= lower limit of first quartile class , f= frequency of first quartile class , c.f. = cumulative frequency of pre-first quartile class , h= size of first quartileclass , N = total numbers of items.

2> Third quartile:

For individual data:

observation in the data arranged in ascending or decreasing order.

For group ( discrete) data:

observation in the data arranged in ascending or decreasing order.

For continuous data:

lies in place.

and exact third quartile =

where , , l= lower limit of third quartile class , f= frequency of third quartile class , c.f. = cumulative frequency of pre-third quartile class , h= size of third quartileclass , N = total numbers of items.

## d> **Mode formulas**:

1> Mode = value with highest frequency for ungroup and discrete frequency distribution.

2> Mode () = ( for continuous frequency distribution)

3> If or then,

Mode =

4> If then ,

Mode =

5> If two or more than two highest frequency data are present then ,

Mode =

Where , l = lower limit of mode class , = frequency of modal class , = frequency of the class preceding modal class , = the frequency of class succeeding modal class , h = class width or height

## e>** Deviation formulas**:

1> Mean deviation:

Mean deviation from mean ( )

For ungroup data:

For group ( continuous and discrete ) data:

and

Mean deviation from mode ( )

For ungroup data:

and

For group ( continuous and discrete ) data:

where ,

2> Quartile deviation:

Inter quartile range =

Quartile deviation or semi – Inter quartile range =

Co-efficient of quartile deviation =

4> Standard deviation:

For ungroup data:

Standard deviation ( ) = where , ( is assumed mean).

For group data i :

Standard deviation ( ) = where , ( is actual mean).

For group data ii :

Standard deviation ( ) =

where , ( is assumed mean).

5> Range:

Range = Largest item – smallest item =

Co-efficient of range =

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