Types of Statistics: Descriptive and Inferential Statistics

Ever looked at a pile of numbers and wondered what they mean? Statistics are like tools that help us understand data! This article will explore two main types: descriptive statistics and inferential statistics. Imagine describing your sock collection (descriptive) versus guessing how many socks are in the whole world (inferential). We'll break down what each type does so you can unlock the secrets hidden in your data!

What is Statistics?

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numeric data. It is a tool that helps to make sense of the vast amount of data that we encounter in our day-to-day life. Whether you are trying to evaluate the market trends, the effectiveness of medical drugs, or want to predict who will win the cricket match, statistics plays an important role in extracting meaningful insights from complex data.

Here are some applications of Statistics in different domains.

Applications of Statistics

• Business and Finance uses statistics o make informed pricing, marketing strategies, and risk management decisions.
• Healthcare industries use statistics to design clinical trials, analyze patient data and evaluate treatment outcomes.
• The meteorological department uses statistics for weather forecasts by analyzing the weather data such as humidity, wind speed, thunder, etc.
• Statistics is widely used in sports to analyze player performance, evaluate team strategies, and make informed decisions about game plans.
• Statistics is used in social sciences to study human behaviour and social phenomena by analyzing data from surveys, experiments, and other sources.
  • Used in elections to predict election results and to understand voting behaviour.

Must Check: Free Statistics for Data Science Online Courses and Certification

Must Check: Free Mathematics for Data Science Online Courses and Certification

Types of Statistics

On a broader scale, statistics is classified into Descriptive Statistics and Inferential Statistics.

Descriptive Statistics

It involves the collection, organization, and presentation of data in such a way that it is easy to understand and interpret. Descriptive statistics are used to answer questions like, what is the:

• average income of people in a state.
• most common type of car on the road.
• ranges of ages of employees working in a particular company. 

It helps us better understand the data we are looking at by summarizing the important information, such as the highest and lowest value, the middle value (median), and how spread out the data is (range and variance). These pieces of information help to conclude the group we are studying.

Must Read:

Must Read: Difference Between Descriptive and Inferential Statistics

Descriptive Statistics is further classified into two different categories:

Measure of Central Tendency

It is a statistical measure that describes where the center of the data is located or concentrated. The three most common types of central tendency are Mean, Median, and Mode.

Must Read: Measure of Central Tendency

Mean

It is also referred to as the average value of the numerical dataset. It is often used for continuous data such as heights or weights.

Mean Formula for

• Ungrouped Data

Mean Formula = Sum of all Observations / Total Number of Data Points (Observations)

• Grouped Data

If x₁, x₂, x₃, …, x_n are the data points, and f₁, f₂, f₃, …., f_n, then the mean of the data is:

Mean Formula =  x₁*f₁ + x₂*f₂ + … + x_n*f_n / f₁ + f₂ + f₃ + … + f_n

Must Read: Mean Formula

Median Formula

The median is the middle value or the average of two middle values if the list has an even number of data values. In simple terms, the median divides the group into two halves.

Median Formula for

Ungrouped Data

• If the number of Observation is Even

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

• If the Number of Observations is Odd

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

Grouped Data

Median = L + ((n/2 – F) / f) x W

where,

L: Lower Limit of the median group

n: Total Frequency

F: Cumulative Frequency of the group before the median group

f: frequency of the median group

W: width of the median group

Must Read: Median Formula

Must Read: Difference Between Median and Average

Mode

Mode is the only measure of central tendency used for nominal data. It represents the maximum frequency of the number in the dataset.

Mode Formula for

• Ungrouped Data

Arrange all the data values in ascending order and find the most frequent value. The most frequent value is the mode.

• Grouped Data

Mode = L + ((f₁ – f₀) / (2f₁ – f₀ – f₂)) * h,

where

L: Lower limit of the modal class

f₀, f₁, f₂ : frequency of the class before the modal class (preceding the modal class), frequency of the modal class, and the frequency of the class after the modal class (succeeding the modal class)

h: the size of the class interval

Must Read: Mode Formula

Must Read: Difference Between Mean, Median, and Mode

Measure of Dispersion

A statistical concept that describes how spread out the data is. It quantifies the difference between values in the dataset and indicates the degree to which the values deviate from the central tendency or average. In simple terms, it shows how much the values in a data set differ from the central tendency or average.

The common measures of dispersion include ranges, variance, and standard deviation, which are used to compare the variability of the different datasets.

Must Read: Measure of Dispersion: Range, IQR, Variance and Standard Deviation

Range

It is defined as the difference between the largest and smallest values in a data set. It is a simple measure of variability but very sensitive to outliers.

Range = Maximum Value – Minimum Value

Variance

It is defined as the average of the squared difference between each value and mean, i.e., it measures the average distance of each value from the mean. It is a more precise measure of dispersion than the range.

Variance = (1/n) * Σ(x – μ)²

where,

n: sample size

x: individual data point

μ: mean of the dataset

Standard Deviation

It is the square root of the variance. It provides a measure of how much the value deviates from the mean in the same unit as the original data.

Standard Deviation = √(Variance)

Must Read: Difference Between Variance and Standard Deviation

Inferential Statistics

Inferential statistics is the branch of statistics that makes inferences (or predictions) about the population dataset based on the sample dataset. It involves hypothesis testing, a process of using statistical methods to determine whether the hypothesis about the population is likely true.

Inferential statistics are widely used in Scientific & Market Research and social sciences to make predictions, test hypotheses, and make decisions based on a solid understanding of the data. It also helps to minimize errors and biases in the result.

Must Read: Inferential Statistics

Inferential statistics are used to answer questions like:

• How likely is it that new medicine will be effective based on results from clinical trials?
• What is the probability of winning party A based on the result of the survey?
• How likely is that a certain event will happen in the future based on the historical data?

Types of Inferential Statistics

There are different types of inferential statistics, including:

Confidence Interval

It is a range of values that is likely to contain the true value of the population parameter with a certain level of confidence. Mathematically it is defined as the mean of your estimate plus and minus the variation in that estimate. It is useful as it provides a range of plausible values for a population parameter based on the sample data.

Regression Analysis

It is a technique for analyzing the relationship between two or more variables. In simple terms, it predicts the value of one variable based on the other variables.

The regression analysis aims to find the best-fit line that can explain the relationship between variables. There are two types of regression analysis: Simple Regression and Multiple Regression.

Hypothesis Testing

A statistical technique used to evaluate (or verify) the hypothesis (or assumptions) of the sample dataset about the population dataset. Hypothesis Testing involves:

• formulation of Null Hypothesis
• formulation of Alternate Hypothesis
• select the sample from the population
• perform the statistical test
• check the p-value
• if the p-value is less than a significant level, then reject the null hypothesis
• if the p-value exceeds the significance level, we fail to reject the null hypothesis.

Analysis of Variance

Analysis of Variance (ANOVA) is a statistical method to analyze the difference between two or more groups. It is a type of hypothesis testing that compares the variance of different groups to determine if the mean difference between them is statistically significant.

There are two types of ANOVA: One-way ANOVA (includes only one variable) and Two-way ANOVA (used when there are two independent variables).

Bayesian Interface

The statistical method uses Baye’s theorem to update the probability of a hypothesis based on new data or evidence. It is useful for predictions, estimating probabilities, and making decisions under uncertainty.

Conclusion

Statistics is a branch of mathematics used to make sense of the vast amount of data we encounter in our day-to-day life. It is broadly classified into descriptive and inferential statistics. Descriptive statistics summarise the data through the measure of central tendency and measure of dispersion. Inferential statistics uses sample data and probability theory to infer the population dataset.

This article discusses the different types of statistics. Hope you will like the article.

Happy Learning!!

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