# Statistics for Data Science

A measure of spread, sometimes also called a measure of dispersion, is used to describe the variability in a sample or population.


![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1665568632160/Q66I8ypQH.png align="left")

Just like the measure of central tendency , we also have measures of the spread, which comprises of the following measures:



- 
**Range: **It is the given measure of how spread apart the values in a data set are. The range can be calculated as -
     
            Range = Max(x_i) - Min(x_i)

            Here,

            Max(x_𝑖): Maximum value of x

            Min(x_𝑖):  Minimum value of x




- 
**Quartile:** Quartiles tell us about the spread of a data set by breaking the data set into quarters.To better understand how quartile and the IQR are calculated, let’s look at an example. 

 Consider a list containing Marks of students in a class-
            Marks=[10,11,12,15,17,18,19,20,22,23,24,25]

The quartiles lie in the following ranges:

- 

The first quartile (Q1) lies between the 3rd and 4th observation.

- 
The second quartile (Q2) lies between the 6th and 7th observation.

- 
The third quartile (Q3) lies between the 9th and 10th observation.



- 
**Inter Quartile Range (IQR)**: It is the measure of variability, based on dividing a data set into quartiles. The interquartile range can be calculated as 
            IQR = Q3 – Q1

**Variance**: It describes how much a random variable differs from its expected value.Variance can be calculated by using the below formula:

               
![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1665570237556/ADHLRHYMf.png align="left")


Here,

x: Individual data points
n: Total number of data points
x̅: Mean of data points


Deviation is the difference between each element from the mean. It can be calculated by using the below formula:

Deviation = (𝑥_𝑖 – µ)


- 
**Population Variance** is the average of squared deviations. It can be calculated by using the below formula:

![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1665570435024/pIRUEM80-.png align="left")


- 
**Sample Variance **is the average of squared differences from the mean. It can be calculated by using the below formula:


![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1665570479097/fuWw4az09.png align="left")


- 
**Standard Deviation**: It is the measure of the dispersion of a set of data from its mean. It can be calculated by using the below formula:


![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1665570513291/cul25VbfS.png align="left")


To better understand how the Measures of spread are calculated, will look at a use case in the upcoming blogs.

Thanks for Reading!! Happy Learning!!