Statistics is at the heart of data analytics. It is the branch of mathematics that helps us spot trends and patterns in the bulk of numerical data. Statistical techniques can be categorized as Descriptive Statistics and Inferential Statistics. In this post, we explore the differences in descriptive vs. inferential statistics, how they impact the field of data analytics. Interestingly, some of the measurement techniques are similar, but the objectives are different. So, let’s understand the major differences.

## What is Descriptive Statistics?

Descriptive Statistics describes the characteristics of a data set. It is a simple technique to describe, show and summarize data in a meaningful way. You simply choose a group you’re interested in, record data about the group, and then use summary statistics and graphs to describe the group properties. There is no uncertainty involved because you’re just describing the people or items that you actually measure. You’re not aiming to infer properties about a large data set.

Descriptive statistics involves taking a potentially sizeable number of data points in the sample data and reducing them to certain meaningful summary values and graphs. The process allows you to obtain insights and visualize the data rather than simply pouring through sets of raw numbers. With descriptive statistics, you can describe both an entire population and an individual sample.

## What is Inferential Statistics?

In Inferential Statistics, the focus is on making predictions about a large group of data based on a representative sample of the population. A random sample of data is considered from a population to describe and make inferences about the population. This technique allows you to work with a small sample rather than the whole population. Since inferential statistics make predictions rather than stating facts, the results are often in the form of probability.

The accuracy of inferential statistics depends largely on the accuracy of sample data and how it represents the larger population. This can be effectively done by obtaining a random sample. Results that are based on non-random samples are usually discarded. Random sampling - though not very straightforward always – is extremely important for carrying out inferential techniques.

## Types of Descriptive Statistics

There are three major types of Descriptive Statistics.

### 1. Frequency Distribution

Frequency distribution is used to show how often a response is given for quantitative as well as qualitative data. It shows the count, percent, or frequency of different outcomes occurring in a given data set. Frequency distribution is usually represented in a table or graph. Bar charts, histograms, pie charts, and line charts are commonly used to present frequency distribution. Each entry in the graph or table is accompanied by how many times the value occurs in a specific interval, range, or group.

These tables of graphs are a structured way to depict a summary of grouped data classified on the basis of mutually exclusive classes and the frequency of occurrence in each respective class.

### 2. Central Tendency

Central tendency includes the descriptive summary of a dataset using a single value that reflects the center of the data distribution. It locates the distribution by various points and is used to show average or most commonly indicated responses in a data set. Measures of central tendency or measures of central location include the mean, median, and mode. Mean refers to the average or most common value in a data set, while the median is the middle score for the data set in increasing order, and mode is the most frequent value.

### 3. Variability or Dispersion

A measure of variability identifies the range, variance, and standard deviation of scores in a sample. This measure denotes the range and width of distribution values in a data set and determines how to spread apart the data points are from the center.

The range shows the degree of dispersion or the difference between the highest and lowest values within the data set. The variance refers to the degree of the spread and is measured as an average of the squared deviations. The standard deviation determines the difference between the observed score in the data set and the mean value. This descriptive statistic is useful when you want to show how to spread out your data is and how it affects the mean.

Descriptive Statistics is also used to determine measures of position, which describes how a score ranks in relation to another. This statistic is used to compare scores to a normalized score like determining percentile ranks and quartile ranks.

## Types of Inferential Statistics

Inferential Statistics helps to draw conclusions and make predictions based on a data set. It is done using several techniques, methods, and types of calculations. Some of the most important types of inferential statistics calculations are:

### 1. Regression Analysis

Regression models show the relationship between a set of independent variables and a dependent variable. This statistical method lets you predict the value of the dependent variable based on different values of the independent variables. Hypothesis tests are incorporated to determine whether the relationships observed in sample data actually exist in the data set.

### 2. Hypothesis Tests

Hypothesis testing is used to compare entire populations or assess relationships between variables using samples. Hypotheses or predictions are tested using statistical tests so as to draw valid inferences.

### 3. Confidence Intervals

The main goal of inferential statistics is to estimate population parameters, which are mostly unknown or unknowable values. A confidence interval observes the variability in a statistic to draw an interval estimate for a parameter. Confidence intervals take uncertainty and sampling error into account to create a range of values within which the actual population value is estimated to fall.

Each confidence interval is associated with a confidence level that indicates the probability in the percentage of the interval to contain the parameter estimate if you repeat the study.

## Example of Descriptive Statistics

Examples of descriptive statistics are used to enumerate and explain a dataset's key characteristics. Measures like mean, median, mode, range, variance, and standard deviation are some examples. For instance, you could use descriptive statistics to determine the average age, the age distribution, and the age standard deviation of a group of individuals if you wanted to summarize their ages.

## Example of Inferential Statistics

Using a sample of data, inferential statistics is used to draw conclusions or generalizations about a broader population. Examples include regression analysis, confidence ranges, and hypothesis testing. For instance, you could use inferential statistics to assess whether there is a significant difference in the outcomes of patients who receive the drug compared to those who receive a placebo if you want to know if a new drug is effective.

## Tools of Descriptive Statistics

Measures of centre tendency (mean, median, mode), measures of variability (range, variance, standard deviation), frequency distributions, histograms, scatterplots, and box plots are examples of descriptive statistics tools.

## Tools of Inferential Statistics

Hypothesis testing, confidence intervals, regression analysis, analysis of variance (ANOVA), and chi-square tests are examples of inferential statistics tools.

## Similarities Between Descriptive and Inferential Statistics

Descriptive and inferential statistics are both used to analyze and comprehend data, which is a similar function to that of descriptive statistics. They both employ statistical techniques and instruments to make judgements about a community. The same fundamental ideas in probability, such as selection, randomization, and probability distributions, are also used by both of them. Last but not least, they both employ the same kinds of statistical programs, including SPSS, SAS, and R.

## Difference Between Descriptive and Inferential statistics

As you can see, Descriptive statistics summarize the features or characteristics of a data set, while Inferential statistics enables the user to test a hypothesis to check if the data is generalizable to the wider population. Now, how can we go from descriptive to inferential statistics? The difference lies in finding the answer to “What is?” vs. “What else it might be?”.

The differences between descriptive statistics vs inferential statistics lie as much in the process as in the statistics reported. Given below are the key points of difference in descriptive vs inferential statistics.

- Descriptive Statistics gives information about raw data regarding its description or features. Inferential statistics, on the other hand, draw inferences about the population by using data extracted from the population.
- We use descriptive statistics to describe a situation, while we use inferential statistics to explain the probability of occurrence of an event.
- As for descriptive statistics, it helps to organize, analyze and present data in a meaningful manner. Inferential statistics helps to compare data, make hypotheses and predictions.
- Descriptive statistics explains already known data related to a particular sample or population of a small size. Inferential statistics, however, aims to draw inferences or conclusions about a whole population.
- We use charts, graphs, and tables to represent descriptive statistics, while we use probability methods for inferential statistics.
- It is simpler to perform a study using descriptive statistics rather than inferential statistics, where you need to establish a relationship between variables in an entire population.

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