Statistics are mathematical branches associated with collecting, analysis, interpretations and data presenting. In practice, statistics divide into two major categories, which is descriptive statistics and inferential statistics. They both have important roles in different fields, from business, scientific research, to decision-making in everyday life.

Decryptive Statistics

Decryptive statistics It focuses on techniques to describe and summarize data. The data collected from the population or samples can be represented in the form of tables, graphs, or numeric sizes to give a general picture of the dataset.

Expiration Size

The process size describes the middle value of the dataset and gives a sense of the general location of the data. The three types of mush used is:

1. Mean (Flat): The arithmetic average of all values in dataset.
2. Median: Middle value in sorted dataset.
3. Mode: Most common values appear in dataset.

For example, if we had income data from a group of individuals, mean would give you an idea of average income, the medians would show income in the middle of distribution, and the mode would show the income most frequently accepted by individuals in that group.

Depth Size

In addition to the solution, it's important to understand how data spreads or varies. Some of the size of the spread is often used to include:

1. Range (Range): The difference between maximum and minimum value in dataset.
2. Variance (Variants): The size of how far each value is in the dataset spreads from the average.
3. Standard Deviation: Square root of variants, giving information about average distance between values in dataset and dataset average.

The dispersal size helps understand whether data is widely distributed or centralized around certain values. For example, in daily measurement, low deviation standards suggest that daily temperatures tend to be stable, while high standard deviations show enormous variations.

Graphics representation

The graph is a visual way of showing data and connections between variables. Some types of graphs are commonly used in descriptive statistics include:

1. Histogram: Show frequency distribution of numerical data.
2. Bar Diagram: Used for category data, showing frequency or number in each category.
3. Box Plot: Show median, quartile, and outlier potential in dataset.

The graph helps provide a quick and intuitive understanding of patterns in data, such as distribution, trends, and aberrations.

Inferential Statistics

Unlike descriptive statistics, inferential statistics It involves making conclusions or predictions about the population based on data samples. Its primary goal is to generalization The findings from samples to larger populations. Infinential statistics are used when it's impossible to collect data from the entire population, so we use smaller samples and try to draw conclusions from there.

Probability and Estimation Theory

Inferential statistics rely heavily on probability theories to make an estimate. There are two types of estimate that are commonly used:

1. Point Estimation (Point Estimation): Using one value from the sample to estimate population parameters. For example, use mean samples to estimate mean population.
2. Interval Estimation (Interval Estimation): Gives a range of values where population parameters are expected to be, like trust interval (confidence interval). Trust interval 95%, for example, suggests that we're 95% sure that the population parameters are within that range.

Hypothesis Test

A hypothesis test is another method in inferential statistics used to test statements or assumptions about population parameters. This process involves two hypotheses:

1. Hypothetically Zero (H0): The assumed initial statement is true until proven otherwise.
2. Alternative hypothesis (H1)A statement we want to prove.

A hypothesis test helps make decisions based on sample data. The practical example of a hypothesis test is a test of effectiveness of a drug in a clinical study, where researchers are testing whether it has significant effects or not compared to placebo.

Regression and Correlation

Regression and correlation is a technique used to analyze relationships between two or more variables. Correlation measures the strength and direction of the relationship between the two variables, while regression tries to model that relationship and make predictions.

For example, in business, linear regression can be used to predict sales based on the marketing budget. Correlation helps determine whether there's a significant relationship between budget and sale.

Description and Inferential Statistics Applications

Decryptive and inferential statistics have extensive applications in many fields, including:

1. Economic: Analysis of economic trends, such as inflation or unemployment, often uses descriptive statistics to give us an idea of the current situation. On the other hand, inferential statistics are used to predict future economic trends.
2. Health: In medical studies, inferential statistics are used to draw conclusions from sample data about larger populations, such as vaccine effectiveness or the effects of diet on health.
3. Data Science: Statistics are the basis in large data analysis, where descriptive statistics are used to analyze large dataset, while inferential statistics are used to predict results or identify hidden patterns.

Conclusion

Good descriptive statistics or inferential statistics has an important role in data analysis. The descriptive statistics provide a way to summarize and visualize data in an easy way, while inferential statistics allow us to make generalization and conclusions based on data samples. Both are required in research and decision-making in different areas.

source: McClave, J. T., & Sincich, T. Statistics. Pearson.