Graphs and Plotting

Exploratory Data Analysis

• Exploratory data analysis is a power technique to explore and analyse data. It is a technique that data professionals can use understand a dataset before they start to model it.

• Definition:  Exploratory data analysis is a process of exploring, summarizing, visualizing, and discovering patterns or relationships in data to get more insight for data.

Techniques of EDA

• Exploratory data analysis can be done in two main ways ‒

1.Graphical or Visual techniques : Using charts and plots the data exploration is done.

2. Non‒graphical techniques: Using statistical methods and summaries the data exploration and analysis is done.

1. Introduction to Graphical or Visual Techniques

• Visual aids are essential tools in Exploratory Data Analysis (EDA) to help understand, summarize and present data in a clear and meaningful way. Here are some common visual aids used in EDA:

1. Line chart: A line chart shows data points connected by lines. It's great for visualizing trends over time. It shows increase or decrease in the data. For example ‒ Tracking monthly sales of a product throughout the year.

2.Scatter plot : A scatter plot uses dots to represent the relationship between two variables. It helps to identify correlations.

3. Area plot and stacked plot : An area plot is like a line chart but with the area below the line filled in. A stacked plot shows multiple datasets on top of each other. Example (Area Plot): Showing website traffic over a week.

• Example (Stacked plot) : Showing contributions from different sources to total sales.

4. Polar chart: A polar chart (or radar chart) displays multivariate data in a circular format. It's good for comparing multiple categories. For example Comparing skills of employees.

2. Non‒Graphical Techniques

•  Non‒graphical methods use numbers and statistics to describe data instead of plots and graphs. It can be done using central tendency, spread and shape of data distribution.

1. Central tendency

•  It is used to locate where the data is centered, that means it try to find the middle values. Central tendencies give us an idea of the average or most common values in our data.

•  There are three commonly used measures for central tendency

1) Mean 2) Median and 3) Mode

•  Let us discuss them one by one with the help of examples

1) Mean : The mean can be defined as sum of all the values divided by total number of values. The formula for mean is

Mean = ∑X / N

For example ‒

Consider the data as 10,20,30,40,50,60,70,80,90,100.

Mean = (10+20+30+40+50+60+70+80+90+100)/10=55

2) Median : It is basically the middle value when the data is arranged.

For example ‒

Consider odd number of elements

5, 10, 15, 20, 25, 30, 35

the median is 20

Consider even number of elements

5, 10, 15, 20

the median is

 (10+ 15) / 2 = 12.5

3) Mode: The mode is the value that occurs frequently in the dataset. If each element appears only once in the dataset then there is no mode.

For example ‒ 1, 2, 3, 5, 5, 5, 6 here the mode is 5

2. Measures of spread or dispersion :

•  Dispersion is a technique to describe how spread out the data is. In other words, the dispersion measures show how much the data varies.

•  Following are types of summaries of spread

1) Range: It is the difference between largest and smallest values or difference between max and min value. For example ‒

Consider 10,20,30,40,50 are the data points then range = max ‒ min = 50–10 = 40

2) Variance: It represents how far each value is from the mean. The formula is –

For example ‒ If data is 5, 10, 15 mean 10

Variance = [ (5 − 10)2 + (10 − 10)2 + (15 – 10)2  ] / 3

= [25+0+25] / 3

= 16.67

3) Standard deviation: It is square root of variance. The formula used is ‒

σ = √ Variance

If variance is 16.67 then standard deviation is = √16.67 = 4.08

3. Frequency tables

•  Frequency table shows how often values often. For example ‒ following is a frequency table for data analysis, that represents the relationship between two variables –