kopia lustrzana https://github.com/animator/learn-python
Update Descriptive_Statistics.md
Ankit Mahato
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@ -10,13 +10,11 @@ Data scientists utilize descriptive statistics to uncover patterns, identify out
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```python
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import pandas as pd
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import numpy as np
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```
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```python
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df = pd.read_csv("Age-Income-Dataset.csv")
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df
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```
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| | Age | Income |
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| --- | ----------- | ------ |
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| 0 | Young | 25000 |
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@ -70,14 +68,10 @@ df
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| 48 | Young | 68400 |
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| 49 | Middle Age | 51700 |
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```python
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df.describe()
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```
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| | Income |
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|-------|-------------|
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| count | 50.000000 |
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@ -101,18 +95,17 @@ $$ \overline{x} = \frac{\sum\limits_{i=1}^{n} x_i}{n} $$
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* $\sum$ (sigma) represents the summation symbol, indicating we add up all the values from i=1 to n.
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* $n$ represents the total number of values in the dataset.
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```python
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df['Income'].mean()
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```
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#### Result
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```
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50966.0
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```
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#### Without pandas
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```python
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@ -131,12 +124,10 @@ def mean_f(df):
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mean_f(df)
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```
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Without pandas Library ->
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Average of Income is 50966.0
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Average of Income:
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With pandas Library ->
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50966.0
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- Without pandas Library -> 50966.0
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- With pandas Library -> 50966.0
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### Median
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@ -163,21 +154,17 @@ $$ M = \frac{x_{n/2} + x_{(n/2)+1}}{2} $$
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* n represents the total number of observations in the dataset.
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* $x$ represents the individual value.
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```python
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df['Income'].median()
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```
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#### Result
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```
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46850.0
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```
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#### Without pandas
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```python
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def median_f(df):
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@ -198,18 +185,15 @@ def median_f(df):
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median_f(df)
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```
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Median without library ->
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Median of Income is 49850.0 \
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Median with library ->
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46850.0
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Median of Income:
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- Median without library -> 49850.0
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- Median with library -> 46850.0
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### Mode
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The mode is a measure of central tendency that represents the value or values that occur most frequently in a dataset. Unlike the mean and median, which focus on the average or middle value, the mode identifies the most common value(s) in the dataset.
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```python
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def mode_f(df):
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for col in df.columns:
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@ -240,17 +224,17 @@ def mode_f(df):
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mode_f(df)
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```
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#### Result
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```
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Column: Age
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Without pandas Library -> \
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Without pandas Library ->
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Mode of Age is Old
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With pandas Library -> \
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0 Old \
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With pandas Library ->
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0 Old
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Name: Age, dtype: object
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```
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### Standard Deviation
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@ -264,18 +248,17 @@ $$s = \sqrt{\frac{\sum(x_i-\overline{x})^{2}}{n-1}}$$
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* $\overline{x}$ (x bar) represents the mean value of the dataset.
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* $n$ represents the total number of values in the dataset.
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```python
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df['Income'].std()
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```
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#### Result
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```
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21096.683267707253
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```
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#### Without pandas
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```python
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import math
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@ -304,17 +287,17 @@ With pandas library: ->
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Std : 20884.6509187968
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### Count
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```python
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df['Income'].count()
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```
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#### Result
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```
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50
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```
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### Minimum
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@ -323,13 +306,13 @@ df['Income'].count()
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df['Income'].min()
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```
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#### Result
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```
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15000
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```
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#### Without pandas
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```python
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def min_f(df):
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@ -354,13 +337,13 @@ With pandas Library-> 15000
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df['Income'].max()
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```
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#### Result
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```
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93000
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```
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#### Without pandas
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```python
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def max_f(df):
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@ -374,8 +357,8 @@ def max_f(df):
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max_f(df)
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```
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Without pandas Library-> 93000
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With pandas Library-> 93000
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Without pandas Library-> 93000
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With pandas Library-> 93000
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### Percentile
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@ -385,25 +368,23 @@ max_f(df)
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df['Income'].quantile(0.25)
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```
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#### Result
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```
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33475.0
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```
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```python
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df['Income'].quantile(0.75)
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```
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#### Result
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```
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65400.0
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```
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#### Without pandas
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```python
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def percentile_f(df,percentile):
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@ -432,9 +413,6 @@ df = pd.read_csv('Iris.csv')
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df.head(5)
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```
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| | Id | SepalLengthCm | SepalWidthCm | PetalLengthCm | PetalWidthCm | Species |
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|---|----|---------------|--------------|---------------|--------------|-------------|
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| 0 | 1 | 5.1 | 3.5 | 1.4 | 0.2 | Iris-setosa |
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@ -443,9 +421,6 @@ df.head(5)
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| 3 | 4 | 4.6 | 3.1 | 1.5 | 0.2 | Iris-setosa |
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| 4 | 5 | 5.0 | 3.6 | 1.4 | 0.2 | Iris-setosa |
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```python
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df.drop(['Id','Species'],axis=1,inplace= True)
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```
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@ -463,13 +438,10 @@ $$ COV(X,Y) = \frac{\sum\limits_{i=1}^{n} (X_i - \overline{X}) (Y_i - \overline{
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* $\overline{X}$ and $\overline{Y}$ represent the mean values for variables X and Y, respectively.
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* $n$ represents the total number of observations in the dataset.
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```python
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df.cov()
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```
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| | SepalLengthCm | SepalWidthCm | PetalLengthCm | PetalWidthCm |
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|-------------------|-------------- |---------------|-----------------|--------------|
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| **SepalLengthCm** | 0.685694 | -0.039268 | 1.273682 | 0.516904 |
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@ -477,7 +449,7 @@ df.cov()
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| **PetalLengthCm** | 1.273682 | -0.321713 | 3.113179 | 1.296387 |
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| **PetalWidthCm** | 0.516904 | -0.117981 | 1.296387 | 0.582414 |
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#### Without pandas
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```python
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def cov_f(df):
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@ -496,27 +468,29 @@ def cov_f(df):
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cov_f(df)
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```
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Covariance of SepalLengthCm and SepalLengthCm is : 0.6856935123042504 \
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Covariance of SepalLengthCm and SepalWidthCm is : -0.03926845637583892 \
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Covariance of SepalLengthCm and PetalLengthCm is : 1.2736823266219246 \
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#### Result
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```
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Covariance of SepalLengthCm and SepalLengthCm is : 0.6856935123042504
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Covariance of SepalLengthCm and SepalWidthCm is : -0.03926845637583892
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Covariance of SepalLengthCm and PetalLengthCm is : 1.2736823266219246
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Covariance of SepalLengthCm and PetalWidthCm is : 0.5169038031319911
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Covariance of SepalWidthCm and SepalLengthCm is : -0.03926845637583892 \
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Covariance of SepalWidthCm and SepalWidthCm is : 0.1880040268456377 \
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Covariance of SepalWidthCm and PetalLengthCm is : -0.32171275167785235 \
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Covariance of SepalWidthCm and SepalLengthCm is : -0.03926845637583892
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Covariance of SepalWidthCm and SepalWidthCm is : 0.1880040268456377
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Covariance of SepalWidthCm and PetalLengthCm is : -0.32171275167785235
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Covariance of SepalWidthCm and PetalWidthCm is : -0.11798120805369115
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Covariance of PetalLengthCm and SepalLengthCm is : 1.2736823266219246 \
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Covariance of PetalLengthCm and SepalWidthCm is : -0.32171275167785235 \
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Covariance of PetalLengthCm and PetalLengthCm is : 3.113179418344519 \
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Covariance of PetalLengthCm and SepalLengthCm is : 1.2736823266219246
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Covariance of PetalLengthCm and SepalWidthCm is : -0.32171275167785235
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Covariance of PetalLengthCm and PetalLengthCm is : 3.113179418344519
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Covariance of PetalLengthCm and PetalWidthCm is : 1.2963874720357946
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Covariance of PetalWidthCm and SepalLengthCm is : 0.5169038031319911 \
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Covariance of PetalWidthCm and SepalWidthCm is : -0.11798120805369115 \
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Covariance of PetalWidthCm and PetalLengthCm is : 1.2963874720357946 \
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Covariance of PetalWidthCm and SepalLengthCm is : 0.5169038031319911
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Covariance of PetalWidthCm and SepalWidthCm is : -0.11798120805369115
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Covariance of PetalWidthCm and PetalLengthCm is : 1.2963874720357946
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Covariance of PetalWidthCm and PetalWidthCm is : 0.5824143176733781
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````
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### Correlation
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@ -527,9 +501,6 @@ $$r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{n(\sum x^2) - (\sum x)^2} \cdot
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* r represents the correlation coefficient.
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* n is the number of data points.
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```python
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df.corr()
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```
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@ -541,6 +512,7 @@ df.corr()
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| **PetalLengthCm** | 0.871754 | -0.420516 | 1.000000 | 0.962757 |
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| **PetalWidthCm** | 0.817954 | -0.356544 | 0.962757 | 1.000000 |
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#### Without using pandas
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```python
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import math
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@ -576,24 +548,26 @@ def corr_f(df):
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corr_f(df)
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```
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Correlation of SepalLengthCm and SepalLengthCm :1.0 \
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Correlation of SepalLengthCm and SepalWidthCm :-0.10936924995067286 \
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Correlation of SepalLengthCm and PetalLengthCm :0.8717541573048861 \
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#### Result
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```
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Correlation of SepalLengthCm and SepalLengthCm :1.0
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Correlation of SepalLengthCm and SepalWidthCm :-0.10936924995067286
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Correlation of SepalLengthCm and PetalLengthCm :0.8717541573048861
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Correlation of SepalLengthCm and PetalWidthCm :0.8179536333691775
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Correlation of SepalWidthCm and SepalLengthCm :-0.10936924995067286 \
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Correlation of SepalWidthCm and SepalWidthCm :1.0 \
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Correlation of SepalWidthCm and PetalLengthCm :-0.42051609640118826 \
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Correlation of SepalWidthCm and SepalLengthCm :-0.10936924995067286
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Correlation of SepalWidthCm and SepalWidthCm :1.0
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Correlation of SepalWidthCm and PetalLengthCm :-0.42051609640118826
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Correlation of SepalWidthCm and PetalWidthCm :-0.3565440896138223
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Correlation of PetalLengthCm and SepalLengthCm :0.8717541573048861 \
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Correlation of PetalLengthCm and SepalWidthCm :-0.42051609640118826 \
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Correlation of PetalLengthCm and PetalLengthCm :1.0 \
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Correlation of PetalLengthCm and SepalLengthCm :0.8717541573048861
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Correlation of PetalLengthCm and SepalWidthCm :-0.42051609640118826
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Correlation of PetalLengthCm and PetalLengthCm :1.0
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Correlation of PetalLengthCm and PetalWidthCm :0.9627570970509656
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Correlation of PetalWidthCm and SepalLengthCm :0.8179536333691775 \
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Correlation of PetalWidthCm and SepalWidthCm :-0.3565440896138223 \
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Correlation of PetalWidthCm and PetalLengthCm :0.9627570970509656 \
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Correlation of PetalWidthCm and SepalLengthCm :0.8179536333691775
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Correlation of PetalWidthCm and SepalWidthCm :-0.3565440896138223
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Correlation of PetalWidthCm and PetalLengthCm :0.9627570970509656
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Correlation of PetalWidthCm and PetalWidthCm :1.0
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```
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