# Absolute Deviation and Absolute Mean Deviation Using NumPy | python

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Rejection:
Rejection — it is a measure of the difference between the observed value of a variable and some other value, often the mean of that variable.

Absolute Deviation:
The absolute deviation of a dataset item — it is the absolute difference between this element and this point. The absolute deviation of observations X1, X2, X3,… .., Xn around the value A is defined as —

For discrete (ungrouped) data For continuous (ungrouped) data  Absolute mean deviation:
Absolute mean deviation measures spread and spread of data, preferably mean -median-mode-in-python-without-libraries/">median, in terms of absolute deviation. The absolute deviation of observations X1, X2, X3, ……, Xn is minimal when measured around the mean -median-mode-in-python-without-libraries/">median, i.e. A — mean -median-mode-in-python-without-libraries/">median of data. Then the resulting absolute deviation is called the absolute average deviation and is defined as:

For discrete (ungrouped) data — For continuous (ungrouped) data —  Decide:

1. A dataset with a higher absolute mean deviation (or absolute deviation) has more variability.
2. A dataset with a lower absolute mean deviation (or absolute deviation) is preferred.
-" If there are two datasets with absolute averages AMD1 and AMD2 and AMD1" AMD2, then AMD1 data is considered to have more volatility than AMD2 data.

Example:
Below is the number of candidates enrolled each day within the last 20 days for Python.Engineering -DS & amp; Algo —
75, 69, 56, 46, 47, 79, 92, 97, 89, 88, 36, 96, 105, 32, 116, 101, 79, 93, 91, 112

Code # 1: Absolute rejection using NumPy

 ` # Import mean , absolute value from numy ` ` from ` ` numpy ` ` import ` ` mean , absolute `   ` data ` ` = ` ` [` ` 75 ` `, ` ` 69 ` `, ` ` 56 ` `, ` ` 46 ` `, ` ` 47 ` `, ` ` 79 ` `, ` ` 92 ` `, ` ` 97 ` `, ` ` 89 ` `, ` ` 88 ` `, ` ` 36 ` `, ` ` 96 ` `, ` ` 105 ` `, ` ` 32 ` `, ` ` 116 ` `, ` ` 101 ` `, ` ` 79 ` `, ` ` 93 ` `, ` ` 91 ` `, ` ` 112 ` `] `   ` # Suppose any point A about which ` ` # absolute deviation is calculated ` ` A ` ` = ` ` 79 `   ` sum ` ` = ` ` 0 ` ` # Initialize sum to 0 `   ` # Absolute deviation calculation ` ` `  ` for ` ` i ` ` in ` ` range ` ` (` ` len ` ` (data)): ` ` av ` ` = ` ` absolute (data [i] ` ` - ` ` A) ` ` # Absolute difference value ` ` ` ` # of each data point and A `   ` # Sum all these absolute values ​​` ` sum ` ` = ` ` sum ` ` + ` ` av `   ` # Amount divided by the length of data outputs ` ` # absolute rejection ` ` print ` ` (` ` sum ` ` / ` ` len ` ` (data)) `

Exit:

``` 20.15    Code # 2:  Absolute  mean  deviation using NumPy           ` # Import  mean , absolute value from numy `   ` from ` ` numpy ` ` import ` `  mean , absolute `     ` data ` ` = ` ` [` ` 75 ` `, ` ` 69 ` `, ` ` 56 ` `, ` ` 46 ` `, ` ` 47 ` `, ` ` 79 ` `, ` ` 92 ` `, ` ` 97 ` `, ` ` 89 ` `, ` ` 88 ` `, `   ` 36 ` `, ` ` 96 ` `, ` ` 105 ` `, ` ` 32 ` `, ` ` 116 ` `, ` ` 101 ` `, ` ` 79 ` `, ` ` 93 ` `, ` ` 91 ` `, ` ` 112 ` `] `    ` # Absolute  mean  deviation `   `  mean  (absolute (data ` ` - ` `  mean  (data))) `   Exit:20.055   Code # 3:  Absolute  mean  deviation using pandas           ` # Import pandas library as pd `   ` import ` ` pandas as pd `     ` data ` ` = ` ` [` ` 75 ` `, ` ` 69 ` `, ` ` 56 ` `, ` ` 46 ` `, ` ` 47 ` `, ` ` 79 ` `, ` ` 92 ` `, ` ` 97 ` `, ` ` 89 ` `, ` ` 88 ` `, `  ` ` ` 36 ` `, ` ` 96 ` `, ` ` 105 ` `, ` ` 32 ` `, ` ` 116 ` `, ` ` 101 ` `, ` ` 79 ` `, ` ` 93 ` `, ` ` 91 ` `, ` ` 112 ` `] `    ` # Create a given data data frame `   ` df ` ` = ` ` pd.DataFrame (data) `  ` `  ` # Absolute  mean  deviation `   ` df.mad () ` ` # mad () - function of  mean  absolute deviation `           Exit:   20.055

```

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