  # ML | Raw materials and focal points

Python Methods and Functions

For ungrouped data, i.e. discrete data, observations on the X variable are obtained as , For grouped data, that is, continuous data, observations on the variable X is obtained and tabulated with an interval of K classes in the frequency table. The middle of inertia is indicated by which occur with frequencies respectively and ,

Class Intervals Mid Points ( ) Absolute Frequency ( ) moment of variable X about arbitrary point A on observations is defined as:

For ungrouped data

For grouped data

where

A moment about any arbitrary point in Python —

Consider these points. Below is the time (in hours) that 20 different people spend on Python.Engineering every week.

` 15, 25, 18, 36, 40, 28, 30, 32, 23, 22, 21, 27, 31, 20, 14, 10, 33, 11, 7, 13 `

 ` # data points ` ` time ` ` = ` ` [` ` 15 ` `, ` ` 25 ` `, ` ` 18 ` `, ` ` 36 ` `, ` ` 40 ` `, ` ` 28 ` `, ` ` 30 ` `, ` ` 32 ` `, ` ` 23 ` `, ` ` 22 ` ,  ` 21 ` `, ` ` 27 ` `, ` ` 31 ` `, ` ` 20 ` `, ` ` 14 ` `, ` ` 10 ` `, ` ` 33 ` `, ` ` 11 ` `, ` ` 7 ` `, ` ` 13 ` `] `   ` # Arbitrary dot ` ` A ` ` = ` ` 22 `   ` # Moment for r = 1 ` ` moment ` ` = ` ` (` ` sum ` ` ([(item ` ` - ` ` A) ` ` for ` ` item ` ` in ` ` time])) ` ` / ` ` len ` ` (time) `

## Raw Moments — moment around source A = 0 known as a raw moment and defined as:

For ungrouped data,
For grouped data,

where,

Notes :

- & gt;  We can find first raw moment ( ) just by replacing r with 1 and second raw moment ( ) just by replacing r with 2 and so on.
- & gt;  When r = 0 the moment for both grouped and ungrouped data.

Raw moment in Python —

 ` # data points ` ` time ` ` = ` ` [` ` 15 ` `, ` ` 25 ` `, ` ` 18 ` `, ` ` 36 ` `, ` ` 40 ` `, ` ` 28 ` `, 30 , 32 , 23 , `` 22 , 21 , 27 , 31 , 20 , 14 , 10 , 33 , 11 , 7 , 13 ]      # A moment for g = 1 moment = sum (time) / len (time) `

## Central moments —

The moments of the X variable relative to the arithmetic mean ( ) are known as pivot moments and are defined as:

For ungrouped data,

For grouped data,

where and

Notes :

- & gt;  We can find first raw moment ( ) just by replacing r with 1 and second raw moment ( ) just by replacing r with 2 and so on.
- & gt;  When r = 0 the moment , and when r = 1 the moment for both grouped and ungrouped data.

Relationship between Raw and Central Moments — ## Books for developers

 ` # data points ` ` time ` ` = ` ` [` ` 15 ` `, ` ` 25 ` `, 18 , 36 , 40 , 28 , 30 , 32 , 23 , 22 , `` 21 , 27 , 31 , 20 , 14 , 10 , 33 , 11 , 7 , 13 ]   # Greedy A = sum (time) / len (time)    # Moment for r = 1 moment = ( sum ([(item - A) for item in time])) / len (time) `