Statistics

Statistics is a branch of mathematics, particularly applied mathematics. In differential and integral calculus, linear algebra, and probability theory are where statistics are mainly used in mathematics. In statistics for data collection and analysis, they use different techniques like simple random, systematic, stratified, or cluster sampling. 

Descriptive and inferential are the two types of statistics. The descriptive statistic summarizes and describes the characteristics of the data. It includes measures of central tendency and measures of dispersion. For instance, to analyze the performance of a class, we use descriptive statistics. In this case, it helps summarize the data using the average, variability, and test scores of students in the class. 

Inferential statistics is used to predict or generalize a large population with only a sample of data by using statistical techniques like hypothesis testing, analysis of variance, and regression analysis. For instance, inferential statistics helps us to estimate the preference of students in a school to find their favorite subjects.  

Statistics is a branch of mathematics. Naturally, there will be similarities between math and statistics. Now, let’s learn a few differences between math and statistics. 
 

Let us first understand what data representation is. It is a technical process of representing data visually. Now, before learning how we can represent data, we should be aware of the types of data: quantitative and qualitative. Qualitative data is the categorical data that describes the characteristics or categories such as gender, colors, names, etc. Quantitative data is the numerical data that involves measurable quantities and numbers such as weight, height, age, temperature, and so on. There are different types of data representation, such as:

• Bar Graph

• Pie Chart

• Line Graph

• Pictograph

• Histogram

• Frequency distribution

Bar Graph

The visual representation of data using rectangular bars. A bar graph can be a vertical or horizontal bar graph. 
 

Pie Chart

It is a circular graph that is divided into sectors based on the data, each sector represents different data or categories. 
 

Line Graph

A line graph is used to represent the data in series, which changes over time, and it is connected with a straight line. 
 

Pictograph

In pictograms data is represented using symbols, ideas, pictures, or objects. 
 

Histogram
 

A histogram may look like a bar graph, but it shows the frequency of continuous data. Unlike a bar graph, a histogram has bars that touch each other, indicating that the data has no gaps between intervals.
 

Frequency distribution.

The table organizes data in ascending order, while the frequencies form a frequency distribution, showing how often the values appear. 

Data plays a major role when coming to statistical analysis, so there are different methods to collect data in statistics. Let’s see some sampling techniques in statistics. 

Data plays a major role when coming to statistical analysis, so there are different methods to collect data in statistics. Let’s see some sampling techniques in statistics. 

Simple Random Sampling
In simple random sampling, the opportunity is given to the entire population to be selected for analysis. That is based on the chance that a few from the group are selected for the analysis. For example, from a class of 50, any and five students can be chosen. 

Systemic Sampling
In Systemic sampling, individuals are called at regular intervals from the starting point. For instance, in a line of 50 students, the individuals are decided randomly from a point.  

Stratified Sampling
In stratified sampling, a population is divided into subgroups based on shared characteristics. That is, 50 students are grouped based on gender, height, and weight. 

Cluster Sampling
In cluster sampling, the population is divided into groups known as clusters, and some clusters are selected randomly for analysis. 

The central tendency is the mid-value in the data. Measuring the central tendency in statistics is a part of descriptive statistics. It is finding the central value or the most repeating value in the given data set. The different measures of central tendency are:

• Arithmetic Mean

• Median

• Mode

• Geometric Mean

• Harmonic mean

The measure of dispersion is the way of spreading the data around the central value. It includes range, quartile deviation, mean deviation, and standard deviation. Now let’s see what these are in detail:

Range: The difference between the highest and lowest values in the dataset.

Quartile deviation: It measures how to spread out a set of numbers. Dividing the data point into 4 quarters and finding the median of the data points. The median of the data point to the left is the upper quartile, while the median of the data point to the right is the lower quartile. The interquartile range is the difference between the upper and the lower quartile. 

Mean deviation: It is to find how far each number is from the average and find the average of the difference

Standard deviation: It shows the deviation of numbers from the average.

As we discussed, statistics is used in different fields, so let’s now see how statistics are used in our real life.  

• In health care, statistics are used for analyzing the effectiveness of treatments, designing clinical trials for new drugs or treatments, and so on. 

• The government uses statistics to plan and analyze public policy, population, resource allocation, and so on.

• In business, statistics are used to analyze and compare sales, market research, and finance. 

• Statistics is used to visualize the data using bar graphs, pie charts, and histogram for comparing and analyzing.