Statistics is important to understand the data. It is a major field in the study of data with two basic types: descriptive statistics and inferential statistics. Descriptive statistics report facts and summaries about the data the researcher has collected, whereas inferential statistics report inferences or predictions about the larger population based on the sample of that data. The purpose of this article is to help you better understand descriptive and inferential statistics and differentiate between the two.
Table of Contents:
Pre-requisite Knowledge: Population and Sample
Let us begin by defining two terms that are important as we move into descriptive and inferential statistics: Population and Sample.
- Population: A population is the entire collection you intend to observe, study, and make inferences about. For example, you wanted to study the average height of adult women in a country, the population is all the adult women in that country. Also, make sure that you are considering every woman in this case.
- Sample: A sample is a subset of data points drawn from the population. Once the size of the population gets large enough, sampling becomes a necessity. For example, if the population is a large one, like India, you cannot possibly attempt to acquire data from every single person. It just takes too long. Therefore, you would take data from a sample of the population so that you can, at least, eliminate a portion of the data you will need to analyze and report on. In this way, we will be able to make inferences or predictions about the population based on the sample taken.
What Is Descriptive Statistics?
Descriptive statistics is the branch of statistics that presents an accurate summary of the data that is calculated using the collected data. It describes, organizes, and presents the results with the help of graphs, which even non-statisticians can understand. Descriptive statistics summarize and present the key features and properties of the data without extending the results and inferences towards the larger population.
What Is Inferential Statistics?
Inferential statistics make predictions about a population based on the analysis performed on the sample extracted from that population. It allows you to make conclusions and estimates of the parameters of populations, especially when it is impractical to study every individual, by utilizing probability theory and testing hypotheses.
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Descriptive vs Inferential Statistics
Descriptive Statistics and Inferential Statistics are two branches of statistics, and each serves a specific purpose in data analysis. They differ in terms of methods, goals, and insight. Below, we have discussed the key differences between Descriptive and Inferential Statistics.
1. Purpose and Objective
- Descriptive Statistics: The primary goal of descriptive statistics is to provide a basic summary of the dataset. This includes central tendency, variation, etc. It describes “what is” happening with the dataset.
- Inferential Statistics: The main purpose is to analyse sample data and use the results to draw conclusions or make predictions about a larger population. The objective is to answer questions about “what could be”. It is performed by estimating population parameters, testing scientific hypotheses, and making probabilistic inferences about populations based on data from a sample.
2. Scope
- Descriptive Statistics: The methods of descriptive statistics only apply to the data that has been collected or observed. So, it can only be applied to the sample data.
- Inferential Statistics: This branch of statistics estimate or generalise the entire population by using sample information. Therefore, the scope of inferential statistics extend beyond the observed data and includes unobserved data as well.
3. Data Requirements
- Descriptive Statistics: It applies to population and sample data. It requires actual values of all elements in the data set.
- Inferential Statistics: It generally applies to sample data. It makes assumptions about the population distribution.
4. Complexity
- Descriptive Statistics: The methods are simple to calculate and interpret, since they require simple calculations and simple graphical displays.
- Inferential Statistics: The methods are more complicated and mathematical, and require an understanding of probability theory, sampling distributions, and statistical models.
5. Results Interpretation
- Descriptive Statistics: It focuses on creating an understanding of the present state and characteristics of the data. Therefore, the results of descriptive statistics are straightforward, without any uncertainty or probabilistic predictions.
- Inferential Statistics: The outcomes of inferential statistics will involve estimates with margins of error and confidence intervals, which express uncertainty. It will use the data as a basis for decisions, predictions based on data, and approaches to developing policies.
6. Role of Probability
- Descriptive Statistics: It does not use probability theory.
- Inferential Statistics: It relies heavily on probability theory to make estimates and predictions about populations.
7. Outcome Nature
- Descriptive Statistics: It produces factual, exact summaries of data without assumptions or predictions.
- Inferential Statistics: It produces probabilistic outcomes reflecting uncertainty in sampling and prediction
Descriptive vs Inferential Statistics: Comparison Table
| Aspect |
Descriptive Statistics |
Inferential Statistics |
| Purpose |
Summarize and describe data |
Draw conclusions about a population from a sample |
| Scope |
Limited to observed data |
Extends beyond data to the whole population |
| Data Requirement |
Full dataset (sample or population) |
Sample data with assumptions about the population |
| Complexity |
Simple and straightforward |
Complex; involves probability and statistical modeling |
| Interpretation |
Exact and direct |
Probabilistic, includes uncertainty (e.g., confidence intervals) |
| Role of Probability |
Not involved |
Fundamental for estimation and prediction |
| Outcome |
Factual summaries |
Probabilistic inferences and predictions |
Types of Descriptive Statistics
Descriptive statistics provide an accurate summary of the dataset. There are three main types of descriptive statistics.
1. Measures of Central Tendency
Descriptive statistics focus on where the data are located, that is, the central range or average of the data set. The measure of central tendency includes the following:
- Mean: The mean is the average of the data set.
- Median: The median is the middle value when data are arranged in ascending or descending order.
- Mode: The mode is the most frequently occurring value of the data set.
2. Measures of Dispersion (or Variability)
- Range: The range is the difference between the highest and lowest value of the dataset.
- Variance: The Variance measures how far a data point is from the mean.
- Standard Deviation: The standard deviation is the square root of the variance. The standard deviation also indicates how far values deviate from the mean.
3. Measures of Shape (Distribution)
Descriptive statistics also describe the shape and symmetry of the distribution of the dataset. The measures of shape include:
- Skewness: Skewness indicates the extent to which the data is skewed left or right, with positively skewed data having a longer right tail. When there is no skewness, which means the distribution is symmetrical, it indicates that mean = median = mode.
- Kurtosis: Kurtosis measures the “tail” of the graph of distribution of the data. Using this metric, we can comment on the nature of the distribution of the data. The distribution with shorter tail has negative kurtosis, whereas the distribution with longer tail has positive kurtosis.
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Types of Inferential Statistics
Making accurate predictions or inferences about the whole population is tricky. Inferential Statistics enables you to analyse sample data and draw conclusions about a population with as much accuracy as possible.
1. Hypothesis Testing
Hypothesis Testing is a statistical method used to make decisions or inferences about a population based on a sample of that population. The process to perform hypothesis testing is as follows.
- First, you will assume a null hypothesis and an alternative hypothesis.
- Then, using statistical tests such as t-tests, chi-square tests, and ANOVA, you calculate the p-value. This will tell you whether the data is close to the null hypothesis or the alternate hypothesis.
- Based on this result, you will either reject the null hypothesis or fail to reject the null hypothesis.
2. Confidence Intervals
Confidence intervals allows statisticians to make predictions about the parameters like mean, median, mode of the population with some “confidence”. It is range of values between which the population parameters are most likely to lie with a probability of certainty. For example, a statistician might predict the average height of women in India lies between 155 cm to 163 cm with 95% confidence level. This means that they are 95% sure that the average height of women of whole population of India lies in that range.
3. Regression Analysis
Regression analysis expresses the relationship between the dependent variable and one or more independent variables. It accurately quantifies the relationship between the variables. Regression is widely used for identifying trends and patterns, making predictions, and categorization the factors of interest.
4. Analysis of Variance (ANOVA)
ANOVA is used to test whether the individual means of three or more groups are significantly different. ANOVA helps to clarify whether the variability you find in the data is due to real differences among the groups or just random chance. ANOVA only indicates that the means are different; it does not specify which groups have significantly different means.
5. Correlation Analysis
Correlation measures the degree and direction of association between two variables. It tells how a variable A will change with respect to changes in variable B. The direction is indicated by the sign of the value, whether it is positive or negative. The value describes the degree of association. The value lies between 0 and 1. Therefore, the correlation value, r, has a range of -1 to +1 to accommodate both types of associations.
When to Use Descriptive or Inferential Statistics: Real-Life Scenario Explained
Consider an Ed Tech company that launched a new online course. After some time, 10,000 students have enrolled in the course. The company wants to perform a study to understand how well students are performing. Let us look at the scenarios where descriptive statistics and inferential statistics should be used and where they should be avoided.
- You should use Descriptive Statistics when you want to summarise the actual data collected. For example, the company might calculate:
- The average score of all students.The highest and lowest scores.
- The distribution of grades (how many students scored between 80–90%, etc.).
These statistics measures help you develop a strong understanding of how this specific batch of students performed. Once you have a solid grasp of the “what is” in the dataset, you can move forward to make informed estimates about future outcomes and decide on the next steps to improve the course, and even influence broader decisions at the Ed Tech company level.
- Then, you can use Inferential Statistics when the company wants to generalize from a larger group to make future decisions. Let us say the company only has access to data from 1,000 randomly selected students using sampling techniques. They can use inferential methods like hypothesis testing or confidence intervals to:
Estimate the average score of all 10,000 students. - Predict future performance for upcoming course batches.
- Determine whether a new teaching technique will significantly alter the scores from the old teaching technique.
These statistics will give you insights about “what could be,” and help you make informed predictions and decisions based on the inferential statistics results of the data.
Conclusion
When analyzing data, it is important to be aware of the differences between descriptive and inferential statistics before making data-based decisions. Descriptive statistics summarize data based on summary statistics such as mean, median, mode, standard deviation, and so on. In contrast, inferential statistics allow the analyst to make predictions, test hypotheses, and make decisions about a population based on a sample from that population. Regardless of your experience in the field of data science, understanding descriptive and inferential statistical techniques will aid you in making better decisions in any situation.
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Descriptive vs Inferential Statistics – FAQs
Q1. What is the difference between descriptive statistics and inferential statistics?
You can think of descriptive statistics as summarizing data (e.g., mean, median), while inferential statistics helps you draw conclusions or predictions about a population based on a sample.
Q2. What is a descriptive statistic example?
You can use the average test score of a class as an example of descriptive statistics—it summarizes the overall performance without predicting future outcomes or generalizing beyond that group.
Q3. What is inferential statistics with an example?
You can see inferential statistics in action when you survey 100 people and use the results to estimate how a larger population might behave or think.
Q4. What is the difference between statistical inference and inferential statistics?
You can consider statistical inference as the process, and inferential statistics as the tools or methods (like confidence intervals, hypothesis testing) used to make those inferences about populations.
Q5. Is t-test descriptive or inferential?
t-test is inferential statistics because it helps you determine if the difference between group means is statistically significant, generalizing from the sample to the population.