Descriptive Statistics

Descriptive statistics uses data that provides a description of the population either through numerical calculated graphs or tables. It provides a graphical summary of data.

It is simply used for summarizing objects, etc. There are two categories in this as follows.

Measure of Central Tendency
Measure of Variability

Let’s discuss both categories in detail.

Measure of Central Tendency

Measure of central tendency is also known as summary statistics that are used to represent the center point or a particular value of a data set or sample set. In statistics, there are three common measures of central tendency that are:

Mean
Median
Mode

Statistics formula

Statistic	Formula	Definition	Example
Mean	x̄=∑ x/n	The arithmetic average of a set of values. It’s calculated by adding up all the values in the data set and dividing by the number of values.	Example: Consider the data set {2, 4, 6, 8, 10}. (2+4+6+8+10/ 5) Mean = 5
Median	Middle value in an ordered data set	The middle value of a data set when it is arranged in ascending or descending order. If there’s an odd number of observations, it’s the value at the center position. If there’s an even number, it’s the average of the two middle values.	Example: Data set {3, 6, 9, 12, 15}. Median = 9
Mode	Value that appears most frequently in a data set	The value that occurs most frequently in a data set. There can be one mode (unimodal), multiple modes (multimodal), or no mode if all values occur with the same frequency.	Example: Data set {2, 3, 4, 4, 5, 6, 6, 6, 7}. Mode = 6

Mean

It is the measure of the average of all values in a sample set. The mean of the data set is calculated using the formula:

Mean = ∑x/n

For example:

Cars	Mileage	Cylinder
Swift	21.3	3
Verna	20.8	2
Santra	19	5

Mean = (Sum of all Terms)/(Total Number of Terms)

⇒ Mean = (21.3 + 20.8 + 19) /3 = 61.1/3

⇒ Mean = 20.366

Median

It is the measure of the central value of a sample set. In these, the data set is ordered from lowest to highest value and then finds the exact middle. The formula used to calculate the median of the data set is, suppose we are given ‘n’ terms in s data set:

If n is Even

Median = [(n/2)^th term + (n/2 + 1)^th term]/2

If n is Odd

Median = (n + 1)/2

For example:

Cars	Mileage	Cylinder
Swift	21.3	3
Verna	20.8	2
Santra	19	5
i 20	15	4

Data in Ascending order: 15, 19, 20.8, 21.3

⇒ Median = (20.8 + 19) /2 = 39.8/2

⇒ Median = 19.9

Mode

It is the value most frequently arrived in the sample set. The value repeated most of the time in the central set is actually mode. The mode of the data set is calculated using the formula:

Mode = Term with Highest Frequency

For example: {2, 3, 4, 2, 4, 6, 4, 7, 7, 4, 2, 4}
4 is the most frequent term in this data set.
Thus, mode is 4.

Measure of Variability

The measure of Variability is also known as the measure of dispersion and is used to describe variability in a sample or population. In statistics, there are three common measures of variability as shown below:

1. Range of Data

It is a given measure of how to spread apart values in a sample set or data set.

Range = Maximum value – Minimum value

2. Variance

In probability theory and statistics, variance measures a data set’s spread or dispersion. It is calculated by averaging the squared deviations from the mean. Variance is usually represented by the symbol σ2.

S²= ∑ⁿ_i=1 [(xi – ͞x)² / n]

n represents total data points

͞x represents the mean of data points

x_i represents individual data points

Variance measures variability. The more spread out the data, the greater the variance compared to the average.

There are two types of variance:

Population variance: Often represented as σ²

Sample variance: Often represented as s².

Note: The standard deviation is the square root of the variance.

Dispersion

It is the measure of the dispersion of a set of data from its mean.

σ= √ (1/n) ∑ⁿ_i=1 (x_i – μ)²

Introduction of Statistics and its Types

Statistics and its Types: Statistics is a branch of math focused on collecting, organizing, and understanding numerical data. It involves analyzing and interpreting data to solve real-life problems, using various quantitative models. Some view statistics as a separate scientific discipline rather than just a branch of math. It simplifies complex tasks and offers clear insights into regular activities. Statistics finds applications in diverse fields like weather forecasting, stock market analysis, insurance, betting, and data science.

In this article, we will learn about, What is Statistics, Types of Statistics, Models of Statistics, Statistics Examples, and others in detail.

Table of Content

What are Statistics?
Types of Statistics
Descriptive Statistics
Inferential Statistics
Hypothesis Testing
Data in Statistics
Representation of Data
Models of Statistics
Data Analysis
Types of Data Analysis
Coefficient of Variation
Applications of Statistics
Business Statistics
Scope of Statistics
Limitations of Statistics
Solved Problems – Statistics