Descriptive statistics and inferential statistics are two fundamental branches of data analysis, each serving distinct purposes.

Unlike inferential statistics, descriptive statistics help you summarise and describe the main characteristics of a data set.

Understanding the differences between these two types of statistics is crucial for effectively analyzing data and making informed decisions. This article explores what is descriptive statistics, its unique applications, and how it differs from inferential statistics.

## Main Purpose Of Descriptive Statistics

Descriptive statistics refers to a branch of statistics that helps you understand and summarise data in a meaningful way.

Descriptive statistics focuses solely on describing the collected data without drawing conclusions.

One key aspect of descriptive statistics is the measure of central tendency, which includes the mean, median, and mode.

If you have the test scores of five students (85, 90, 78, 92, and 88), you can calculate the mean by adding all the scores and dividing by the total number of scores, resulting in an average of 86.6.

The median, the middle value when the scores are arranged in ascending order, is 88. The mode is the most frequently occurring score, but in this case, each score is unique.

Descriptive statistics also involves measures of dispersion, such as the:

- range,
- variance, and
- standard deviation.

The range is the difference between the highest and lowest values in a data set. The variance measures the average squared deviation from the mean, while the standard deviation, the square root of the variance, indicates how spread out the data points are.

If you calculate the standard deviation for the test scores, you’ll get an idea of the variability within the data set.

Another essential tool in descriptive statistics is the frequency distribution, which shows how often each value appears.

Let’s say if a company surveys its employees about their mode of transport, and the results show that:

- 11 employees prefer cars,
- 9 use public transport,
- 5 walk, and
- 5 cycle,

You can create a frequency table to summarise this data. This helps in understanding the transportation preferences of the employees.

Descriptive statistics can also use charts like:

- histograms,
- bar charts, and
- pie charts to
- visualise data.

These visual tools make it easier to grasp the shape of the data and identify patterns or outliers.

By using descriptive statistics, you can describe the data from a sample, understand its central tendency and variability, and present it in a clear, concise manner.

This is crucial for anyone new to quantitative data analysis, as it provides a solid foundation for further statistical and data analysis.

## Descriptive Statistics vs Inferential Statistics

Descriptive statistics is not the only way to approach statistics. There’s also another – inferential statistics.

They are two fundamental branches of statistics, each with its own unique purpose and methods.

Understanding how descriptive and inferential statistics differ can help you effectively analyze data and make informed decisions. Here’s how they are different:

**Purpose and Scope**

Descriptive statistics aim to summarise and describe the main features of a data set. They focus on presenting quantitative descriptions in a manageable form.

You use descriptive statistics to provide a snapshot of your data, which includes calculating measures of central tendency like the:

- mean,
- median, and
- mode.

For example, if you have the test scores of students, you can calculate the mean score to understand the average performance.

Inferential statistics, on the other hand, go beyond merely describing the data. Inferential statistics allow you to make predictions or inferences about a larger population based on a sample.

If you survey 100 people in a city about their car preferences, you can use inferential statistics to predict how the entire city’s population might respond. This involves using techniques like:

- hypothesis testing,
- confidence intervals, and
- regression analysis.

**Data Handling**

Descriptive statistics handle the data you have, summarising it to make it understandable. You might use a bar graph to show the frequency distribution of different categories, or a scatter plot to visualise relationships between two variables.

Suppose you are trying to summarise how many employees in a company prefer different modes of transport—car, bike, or public transport. The idea here is to get a clear picture of commuting habits.

Inferential statistics take the sample data and make generalizations about a larger population. You don’t just stop at the data you have; you use it to make predictions.

In this case, if 20 out of 100 surveyed people prefer blue cars, inferential statistics can help you estimate the percentage of the entire city’s population that might prefer blue cars, accounting for a margin of error.

**Measures Used**

In descriptive statistics, you frequently use measures of central tendency and measures of dispersion. Measures of central tendency, like the mean, median, and mode, help describe the central point of your data.

Measures of dispersion, such as:

- range,
- variance, and
- standard deviation,

tell you about the variability or spread of your data. The standard deviation shows how much individual data points differ from the mean.

Inferential statistics use sample data to make estimates or test hypotheses about a population. This involves calculating confidence intervals and p-values to determine the probability that your findings are due to chance.

In inferential analysis, the larger the sample size, the more accurate your inferences will be.

**Visual Tools**

Descriptive statistics often use visual tools to present data in an understandable way. Histograms, pie charts, and frequency tables are common. These tools help you quickly see:

- patterns,
- trends, and
- outliers within the data set.

A pie chart could show the percentage distribution of transportation methods used by employees, making it easy to grasp at a glance.

Inferential statistics might also use visual tools, but their purpose is to illustrate the inferences or predictions.

A confidence interval might be represented graphically to show the range within which you expect a population parameter to fall, based on your sample data.

**Data Interpretation**

Descriptive statistics provide a straightforward interpretation of the data at hand. They give you specific numbers and visualisations that describe your data set.

You may say in descriptive statistics that:

*“the average test score is 85 directly describes the data you collected.”*

Inferential statistics involve interpreting the data to make broader conclusions. When performing inferential statistics with a data set, you might say:

*“Based on our sample, we are 95% confident that between 18% and 22% of the city’s population prefer blue cars.”*

This interpretation uses probability to express confidence in your predictions.

## Types Of Descriptive Statistics

There are 3 main types of descriptive statistics. They are:

- univariate,
- bivariate, and
- multivariate.

Each of these three type focus on different numbers of variables and uses various measures to describe the data. They can also be performed with much automation, with AI’s help.

**Univariate Descriptive Statistics**

Univariate descriptive statistics analyze one variable at a time. This type of analysis includes measures of:

- central tendency,
- measures of dispersion, and
- measures of shape.

When you have a data set of student test scores, you might calculate the mean, median, and mode to understand the central tendency. These measures describe data by pinpointing the center of the data distribution.

Consider a data set with test scores of 100 students. You might find that the mean score is 75, the median is 78, and the mode is 80.

These measures give you different perspectives on the data’s central point. Measures of dispersion like range, variance, and standard deviation help you understand the spread of scores.

If the range is 50, variance is 100, and the standard deviation is 10, you can infer the variability within the data set. A histogram or frequency distribution table can visually summarise these statistics.

**Bivariate Descriptive Statistics**

Bivariate descriptive statistics analyze two variables simultaneously. This analysis helps you explore relationships and correlations between variables.

You might study the relationship between students’ heights and weights. A scatter plot can visually represent this relationship, showing you how one variable changes with the other.

Imagine you have data on 100 students’ heights and weights. By plotting these on a scatter plot, you might notice a trend indicating that taller students tend to weigh more. You can calculate the correlation coefficient to quantify this relationship.

If the correlation coefficient is 0.8, it suggests a strong positive relationship between height and weight. This type of analysis is essential for identifying patterns and making predictions based on two variables.

**Multivariate Descriptive Statistics**

Multivariate descriptive statistics analyse more than two variables. This type of analysis is more complex and involves exploring interactions between multiple variables.

You might study students’ test scores, study hours, and sleep duration to understand how these factors collectively impact performance.

Using a data set of 100 students, you can create a multivariate analysis using techniques like multiple regression analysis or factor analysis. A 3D scatter plot can help visualise the relationships between the three variables.

By analyzing the interactions, you might discover that students who study more and sleep adequately tend to score higher.

## Common Measures Used In Descriptive Statistics

These common measures in descriptive statistics include measures of central tendency and measures of dispersion, each providing unique insights.

**Measures of Central Tendency**

Measures of central tendency describe the center or typical value of your data set.

The most common measures are the:

- mean,
- median, and
- mode.

The mean, or average, is calculated by summing all data points and dividing by the total number. If you have test scores of 80, 85, 90, 75, and 95, the mean score is 85.

The median is the middle value when the data points are arranged in ascending order. In the test scores example, the median is also 85.

If the number of data points is even, the median is the average of the two middle values. The mode is the most frequently occurring value in the data set.

If the scores were 80, 85, 85, 90, and 95, the mode would be 85.

**Measures of Dispersion**

Measures of dispersion describe the spread or variability of your data.

Common measures include:

- range,
- variance, and
- standard deviation.

The range is the difference between the highest and lowest values. For the test scores (80, 85, 90, 75, 95), the range is 20 (95-75).

Variance measures how much each data point differs from the mean. A higher variance indicates more spread out data.

Standard deviation, the square root of the variance, gives a measure of spread in the same unit as the data. If the standard deviation is high, the data points are widely spread around the mean.

If your test scores have a standard deviation of 5, most scores are within 5 points of the mean (85).

## Descriptive Statistics Examples

Descriptive statistics may sound hard, but they can come quite naturally when used in actual research. Let’s look at two specific examples.

**Example 1: Employee Commuting Patterns**

Imagine you work for a company that wants to understand how its employees commute to work. A survey reveals that out of 100 employees:

- 50 drive,
- 30 use public transport,
- 15 bike, and
- 5 walk.

Using descriptive statistics, you can summarise this data effectively.

First, you calculate the frequency distribution. This shows that:

- 50% of employees drive,
- 30% use public transport,
- 15% bike, and
- 5% walk.

You can also create a pie chart to visualise these commuting patterns. The pie chart quickly communicates that driving is the most common mode of transport among employees.

Next, you might want to understand the central tendency of commuting distances. Suppose the commuting distances (in miles) are collected and you find

- the mean distance is 10 miles,
- the median is 8 miles, and
- the mode is 5 miles.

These measures of central tendency describe the average, middle, and most frequent commuting distances, respectively.

**Example 2: Student Test Scores**

Consider a data set of test scores from a class of 30 students. The scores range from 50 to 100. You can use descriptive statistics to summarise this data and understand student performance.

First, calculate the mean and median, as well as mode. If the mean score is 75, the median is 78, and the mode is 80, you get a sense of:

- the average performance,
- the middle score, and
- the most frequent score.

This helps in identifying how well the students are doing overall.

Next, examine the measures of dispersion. The range is 50 (100 – 50), the variance is 200, and the standard deviation is 14.14 (the square root of the variance).

These measures of dispersion tell you how spread out the scores are. A high standard deviation indicates that the scores vary widely from the mean.

To visualise this data, you can create a histogram. If the histogram shows a bell curve, it indicates a normal distribution of scores.

This insight is crucial for making inferences about the class performance and planning further educational interventions.

Using these examples of descriptive statistics, you can see how they provide a snapshot of the data, helping to summarise and describe the main characteristics. This foundational analysis is essential before moving on to more complex inferential statistics.

## Descriptive Statistics and Interferential Statistics Explained

Descriptive statistics and inferential statistics serve complementary yet distinct roles in data analysis. Descriptive statistics focus on summarising and describing data sets, providing a clear snapshot of what the data reveals.

Inferential statistics, on the other hand, use sample data to make predictions and draw conclusions about a larger population.

Understanding these differences is crucial for effectively interpreting data and making informed decisions in your research. Mastery of both types of statistics enhances your ability to analyze and utilize data comprehensively.