Learn the basics of data science and how to work with important libraries such as NumPy, pandas, Beautiful Soup, etc.

Become a Data Scientist

This module will get us familiar with the state of data science and its fundamental concepts. We'll be going through the applications of data science and a few libraries which are essential to solve any problem in this field, such as Beautiful Soup, Scrapy, NumPy, pandas, spaCy, etc.
We'll also learn about data manipulation with NumPy as well as probability and statistics.
By the end of this module, we'll have basic and essential knowledge of data science and its libraries.

Getting Started with Data Science


# Measures of variability or spread

Measures of variability, also known as measures of spread, show us the dispersion in the dataset and how the data is distributed around the center (measure of location) of the dataset. The most commonly used measures of variability are discussed below:

## Variance

The variance is the expected value (mean) of the squared differences of the data values from the mean. It shows us how close or far the values in a dataset are from the mean of the dataset in squared units. 

### Formula

$s^2={\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2}$

* $s^2$ is the variance.
* $n$ is the total number of values in the dataset
* $\sum_{i=1}^n$ is the sum of the values from 1 to n.
* $(x_i-\bar{x})^2$ is the square of the difference of each value in the dataset from the mean. 

* $\sum_{i=1}^n(x_i-\bar{x})^2$ is the sum of all the squared differences of values from the mean.

### Example

* Let's say we have a list of numbers as 
34, 56, 190, 10000, and 45.

* Here $n$ = 5 (number of values)

* The mean of the above list of numbers is calculated as: 

$\bar{x}=\frac{34 + 56 + 190 + 10000 + 45}{5}=\frac{10325}{5}=2065$

* The calculations are done below:


| x       |     x-x̄  |     (x-x̄)$^2$  | 
|---------|-----------|--------------| 
| 34      |     -2031 |     4124961  | 
| 56      |     -2009 |     4036081  | 
| 190     |     -1875 |     3515625  | 
| 10000   |     7935  |     62964225 | 
| 45      |     -2020 |     4080400  | 
|| |Σ(x-x̄)$^2$=78721292       | 

 
$s^2={\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2}=\frac{78721292}{5-1}=19680323$

The above value is a squared value. If some unit existed, that unit would also be squared.
 

## Standard deviation

Standard deviation is calculated by 
taking the square root of the variance. It gives us the same measure but in simplified form, and the units are not squared anymore. This makes the inference clearer.

### Formula

$s=\sqrt{\frac{1}{N-1}\sum_{i=1}^N(x_i-\bar{x})^2}$

* $s$ is the standard deviation.
* $n$ is the total number of values in the dataset
* $\sum_{i=1}^n$ is the sum of the values from 1 to n.
* $(x_i-\bar{x})^2$ is the square of the difference of each value in the dataset from the mean. 

* $\sum_{i=1}^n(x_i-\bar{x})^2$ is the sum of all the squared differences of values from the mean.

### Example

* Let's say we have a list of numbers as 
34, 56, 190, 10000, and 45.

* Here $n$ = 5 (number of values)

* The mean of the above list of numbers is calculated as: 

$\bar{x}=\frac{34 + 56 + 190 + 10000 + 45}{5}=\frac{10325}{5}=2065$

* We have calculated the variance from the above calculation, i.e., $s^2=19680323$.

* So, $s=\sqrt(19680323)=4436.25$

## Range

Range is defined as the difference between the largest and the smallest values in the dataset. It gives us an idea about the range of dataset values.

### Formula

Range =$x_L$ - $x_S$

Where:
* $x_L$ is the largest value in the list of numbers.

* $x_S$ is the smallest value in the list of numbers.

### Example 

* Let's say we have a list of numbers as 
34, 56, 190, 10000, 45, so $n$=5.

* Here $x_L$ = 10000 and $x_S$ = 34. 

* Range = $x_L$ - $x_S$ = 10000 - 34 = 9966

## Quartiles

Quartiles are numbers that divide the data values into quarters. They break the dataset into four segments. Like the median, they also have a precondition that the data should be sorted. 

Learn about measures of variability, which describe the dispersion in a dataset.

Measures of Variability

Measures of variability or spread

Variance

Formula

Example