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Statistics is a field of mathematics concerned with the study of data collection, analysis, interpretation, presentation, and organization. Statistics is described as the process of gathering data, classifying it, displaying it in a way that is easy to understand, and analyzing it further. Statistics is often defined as the process of drawing conclusions from a sample of data obtained through surveys or trials. Statistics can be used in the variety of fields, including psychology, sociology, geology, probability, and so on.
Mathematical Statistics:
Statistics is mostly utilized to obtain a better understanding of data and to focus on specific applications. The process of assessing, gathering, and summarizing data into the mathematical form is known as the statistics. Initially, statistics were associated with state science, in which they were used to gather and analyses facts and data about a country’s economy, population, and so on. Mathematical statistics uses tools such as linear algebra, differential equations, mathematical analysis, and probability theories.
In mathematical statistics, there are two approaches for analyzing data that are widely used:
Descriptive Statistics
Inference Statistics
There are two types of statistics and they are descriptive and inferential statistics.
Inferential statistics are used to make predictions while descriptive statistics are used to describe data. Different tools can be used to derive inferences about the data in descriptive and inferential statistics.
In descriptive statistics, methods like central tendency and dispersion are used, whereas inferential statistics includes hypothesis testing, regression analysis, and confidence intervals.
The goal of descriptive and inferential statistics is to use various techniques to evaluate different types of data. Inferential statistics tries to make conclusions and generalisations regarding population data, whereas descriptive statistics helps to explain and arrange existing data using charts, bar graphs, and other visual aids.
Descriptive Statistics:
Descriptive statistics are a type of statistical analysis that may be used to describe information. It’s used to summarise a sample’s characteristics so that a pattern may be derived from the group. It allows researchers to display data in a more relevant fashion, allowing for easier interpretation. To organise and characterise data, descriptive statistics employs two methods. The following are the list of them:
1. Measures of Center Tendency – These use measures like mean, median, and mode to describe the data’s central location.
2. Measures of Dispersion – Dispersion measures show how spread out the data in a distribution is in relation to a central point. The metrics of dispersion are range, standard deviation, variance, quartiles, and absolute deviation.
Inferential Statistics:
By examining a sample, inferential statistics is a branch of statistics that is used to make conclusions about the population. It becomes difficult to use enormous amounts of population data. In such circumstances, samples that are typical of the entire population are taken. Inferential statistics uses these samples to derive inferences about the population. To choose appropriate samples from the population, sampling procedures such as simple random sampling, cluster sampling, stratified sampling, and systematic sampling must be utilised. The following are some examples of inferential statistics methodologies:
Hypothesis Testing – This approach includes making conclusions about the population data using hypothesis tests such as the z test, f test, and t test, among others. It includes establishing the null hypothesis, alternative hypothesis, and decision criteria, as well as testing them.
Regression Analysis: Regression Analysis is a method for determining the connection between dependent and independent variables. Linear regression is the most common kind of regression.
Difference Between Descriptive and Inferential Statistics:
In order to evaluate data, descriptive and inferential statistics are equally crucial. The mean, standard deviation, charts, and other descriptive statistics are used to arrange data and characterise the sample. This sample data is used in inferential statistics to forecast the trend of the population data. The following table summarises the distinctions between descriptive and inferential statistics:
Basis | Descriptive Statistics | Inferential Statistics |
Definition | Descriptive statistics is a type of statistics that is used to characterise the characteristics of a population based on a sample. | Inferential statistics use a variety of analytical techniques to derive conclusions about a population based on samples. |
Tools | Measures of central tendency and measures of dispersion are two types of measures. | Regression analysis and hypothesis testing |
Uses | With the use of charts and graphs, organises, explains, and shows data in a relevant way. | Data from diverse samples is tested, predicted, and compared. |
Relevance | It’s utilised to compile known data into a format that may be used for additional research and predictions. | It seeks to derive inferences about the population using the summarised samples. |
Conclusion
Statistics can be considered as the science of data collecting and organization. The analysis employing measures of central tendencies and measures of dispersion is used to interpret the results.Bar graphs, histograms, pie charts, stem and leaf plots, line graphs, and ogives are all used to show the frequency distribution of data.
Quantitative (numerical: discrete and continuous) or qualitative data might be obtained (categorical).To evaluate data, acquire samples, and make inferences about the population, descriptive and inferential statistics are utilized. Measures of central tendency and dispersion are employed in descriptive statistics. Hypothesis testing and regression analysis are two methods used in inferential statistics.
