Contents

# Discrete Data|Definition & Meaning

## Definition

Discrete Data is also known as **discrete values** which is the type of data statistic that can only have** certain values** in it. Data in this form is **finite** and countable like whole numbers or integers.

## Explanation of Discrete Data

**Data** is known as the **raw information** that has been collected through various processes. For our ease, we have categorized data into branches and subbranches as well. When the data has been analyzed then it is known as **statistics** of the information that was provided.

From the figure above, we can say that data has been divided into 4 parts

- Nominal
- Ordinal
- Continuous
- Discrete

Discrete Data is one of the types of **quantitative data,** which is a collection of images and statistics of whole number data type which lies in the finite range because discrete data has to be countable. It is a data type that is based on the proportions or occurrence of any events. All the data included in this category are counted as **positive integers**.

For a better understanding, let us take a look at an example. A pizza store has recently introduced 5 new toppings, which is why there is a particularly long queue of 500 people outside. The most common order includes these 2 toppings: honey-laced pepperoni and pineapple onions.

From this example, the data that we can collect is:

**500 people**queue outside of the store**2 flavors**which are the most common among customers.

### Difference Between Discrete and Continuous Data

Discrete data is the set that only includes certain values or **single-point data**. There are no fractional values or negative integers in it. All this data exists in the **finite range**, making it **countable**. Such data can not be divided into smaller parts. Some examples of discrete data are as given below:

- The number of students on a bus
- The number of new paint boxes in a store
- The number of agreements signed between two companies

Continuous data is the type of data which is needed to be **measured**. It includes values that are not fixed and lie in the infinite range. Such measurements can be divided into smaller parts no matter how small the numbers get. The values are placed in a particular range and are **measured continuously** over time. We use continuous data in **histograms** as the change over time makes it easy to visualize data. Some examples of continuous data are given below:

- The age of a person
- The weather in any area
- The range of frequencies in the radio

Discrete and continuous data are considered the same due to having **numerical data**, but they are actually **complete opposites** of each other. One of the basic differences is the range of these numbers. Discrete data is countable, meaning it is a f**inite set of data**, whereas continuous data has an** infinite range**. Moreover, continuous data can be **measured**, whereas discrete data is **fixed** and can not be divided into smaller parts.

### Drawbacks of Discrete Data

Discrete data has fixed values, so it requires many samples for **graphical **and** statistical analysis**. This process not only becomes time taking but is also quite expensive. To visualize** discrete data**, you need to be more **comprehensive**, whereas **continuous data** requires clear instructions and is** easy to use**.

To **collect** and** generate** discrete data, the** categories** must be defined properly. To get **accurate** data, a data analyst must **check** and **correct** any mistakes made by humans and the machine collecting the data. All such issues must be resolved **before data collection**, making it a tricky task.

### Real-life Examples of Discrete Data

Some real-life examples of discrete data are given below:

- Number of movie ticket sales
- Frequency counts of eye color
- Result of students in 10th grade
- Probability of dice rolls
- Number of books in the library
- Total food items on the menu
- Number of plants in the garden
- Number of cars in the garage
- Total number of patients in the hospital
- Population analysis of a country

## Methods of Concept Illustration

To understand and process information, sometimes we need to use **graphical tools** to assist us in **presenting data** so that it becomes easy for the viewer. By doing so, we can check the** performance**, resolve any issues or debug a problem that might occur. Some of the ways by which we can graphically represent discrete data are as below:

**Bar Graphs**

Bar graphs are used to plot data for **comparison purposes** (mainly). Data must be **categorized** first.

**Frequency Tables**

It is a **basic chart** that has been divided into a** category** **side** and a **numerals side**. Due to the numeric side, it helps to visualize the** in-demand product** or most **popular option**.

**Plotted Points**

A plotted points graph is the **conventional** form of a graph where we have an** x-axis** and a **y-axis** in which **data has been plotted**. It is used when the data samples are **limited**, and the **goal** is to find **general trends**.

## Solved Examples of Discrete Data

**Example 1**

The following data shows 10 students’ ages. Compile the data and find out whether it is discrete data or not.

- John, 8
- Ella, 10
- Kevin, 9
- Troy, 12
- Nicole,12
- Ted, 9
- James, 9
- Lily, 10
- Ryan, 9
- Hannah, 9

**Solution **

First, we will categorize data according to age:

Age 8: **1** student

Age 9: **5** students

Age 10: **2** students

Age 12: **2** students

From the data that has been given, we can conclude it to be **discrete data** as it has **whole numbers** and is **countable**.

**Example 2 **

From the variables given below, identify discrete data.

- Shoe size of men
- Number of books in the library
- Weight of students in a class

**Solution **

- The shoe size of men is
**discrete data**because the range of shoe size is**fixed and finite**. We can easily**count**it. - The number of books in a library is also
**discrete data**because we can**count them,**and the amount exists in a**whole number**format. - The weight of students is
**continuous data**, not discrete data as there is an**infinite number of weights**that can exist and all of these weights must be measured.

*All images/mathematical drawings are created with GeoGebra.*