**Introduction**

Finding a relationship between two variables or comparing two sets of data is the main goal of bivariate data. When studying two variables, we have bivariate data. To determine their correlations, these variables are compared as they change.

We will discuss the following in this article: the definition of bivariate data, dependent and independent variables, the difference between univariate and bivariate data, correlation, and scatter diagrams.

**What is Bivariate Data?**

### Definition

In bivariate data, two variables that can change are compared to identify relationships. You will have bivariate data, which consists of an independent and a dependent variable if one variable is impacting the other. This is so that both variables will change if the other one changes.

The data set in an experiment that may be modified or manipulated in an experiment is known as an independent variable. The data set in an experiment known as a dependent variable is one that is subject to external control or influence, usually by the independent variable.

For example, let us look at the table below showing the age and height of a group of children.

Age | Height ( cm ) |

One year | 77.1 |

Two years | 85.5 |

Three years | 95.9 |

Four years | 102.6 |

Five years | 108.9 |

Six years | 113.6 |

Seven years | 120.7 |

Eight years | 125.4 |

Nine years | 131.2 |

Ten years | 139.3 |

Bivariate data is frequently kept in a table with two columns. Between age and height, the independent variable is age, while the dependent variable is height. The height increases when the age increases. The height does not affect age.

**Relationships Between Dependent and Independent Variables**

*Positive Relationship*

The dependent and independent variables may be related in one of two ways:

A positive relationship, also known as positive correlation, indicates that if the independent variable rises, the dependent variable will, too, and the opposite is also true.

Examples:

( a ) You will burn more calories by running on a treadmill for a more extended time.

( b ) The buoyancy of salty water increases with the amount of salt present.

( c ) A child’s clothing size changes as they grow.

( d ) The length of time you stay awake increases as your coffee consumption increases.

( e ) Your car can travel farther the more gas you put in it.

( f ) The likelihood of erosion increases with the number of trees cut down.

( g ) The number of teachers reduces as college enrollment goes down.

( i ) Buoyancy increases as salt in salty water increases.

*Negative Relationship*

When the independent variable rises while the dependent variable falls, or vice versa, there is a negative relationship (negative correlation).

Examples

( a ) As a car gets older, the price goes down.

( b ) The amount of time it takes to go somewhere grows when an automobile loses speed.

( c ) Your debt will decrease as you make more loan payments.

( d ) A biker’s time to cross the finish line gets shorter as their speed rises.

( e ) Fewer clothes are needed to stay warm the warmer the weather is.

( f ) The demand for a given good or service rises as its supply falls.

**Univariate vs. Bivariate Data**

Bivariate refers to two variables, whereas univariate refers to one variable.

*Univariate Data*

The following are the points to remember for univariate data:

( a ) Only uses one variable

( b ) Does not discuss relationships or cause

( c ) The main goal is to describe

*Bivariate Data*

The following are the points to remember for bivariate data:

( a ) Has two variables involved

( b ) Analyses relationships and causation

( c ) The main goal is to explain

Hence, the primary distinction between univariate and bivariate data is that the latter focuses on relationships and causes. In contrast, univariate data describes the single variable that makes up the data.

**Correlation **

Association is what correlation refers to, although it is a measurement of how closely two variables are related. A correlational study can produce one of three outcomes: a positive correlation, a negative correlation, or no correlation at all.

An illustration of a correlation is possible. To accomplish this, create a scatter diagram, also known as a scatterplot, scatter graph, scatter chart, or scattergram.

**No** **Relationship**

A bivariate data set does not exhibit any relationship if the scatterplot is random and with no tilt. The scatterplot with no relationship may show slanting neither downward nor upward as you move from left to right. No relationship is a specific type of linear relationship that has neither increasing nor decreasing. The scatterplot may resemble a round or an oval-shaped cloud.

**Linear Relationship**

The analysis of different types of bivariate data sets varies. The simplest are those that have a linear relationship. Similar to how the normal distribution behaves in the case of univariate data, this connection has a special function in the case of bivariate data. When points appear randomly clustered around a straight line in a scatterplot, it indicates that a bivariate data set contains a linear relationship. The points may be crowded and nearly lined up, or they may be widely spread and appear like a cloud of points. But this one won’t have any extreme outliers, a funnel-shaped or sharply curved relationship.

Positive and negative relationships are the two types of linear relationships that exist. Relationships that are positive have an increasing rightward slope. Points in negative relationships are sloping downward and to the right.

### Correlation Strength

A correlation can be represented numerically as a coefficient, with values ranging from -1 to +1, rather than visually as a scattergram. The correlation coefficient to utilize when working with continuous data is Pearson’s r. The strength of a linear relationship between two variables is indicated by the Pearson correlation coefficient ( r ), but its value typically does not fully characterize their relationship.

The correlation coefficient ( r ) shows how closely the pairs of numbers for two variables lie in a straight line. Values above or below zero denote correlations that are positive or negative.

A perfect positive correlation, or correlation of 1, means that as one variable rise, the other rises as well.

A perfect negative correlation, or correlation of -1, means that when one measure rises, the other falls.

**Scatter Diagrams and Data**

The relationships or associations between the two numerical variables (or co-variables) are visually represented as points (or dots) for each pair of numerical data in a scattergram.

The essential relationship between the two measurements is deciphered using the scatter diagram. Despite the widespread usage of bar charts and line plots, the scatter diagram continues to rule in both business and science. People can quickly determine the relationship between points on a scale by simply looking at them.

Scatter diagrams display the degree and direction of the correlation between the variables. A scatter diagram graphs them with one variable on each axis to find a relationship between two pairs of numerical data. If the variables are correlated, a line or curve will be formed by the points. The points will hug the line closer the better the association.

*Positive Correlation*

The near proximity of the points to a straight line demonstrates that as one variable rise, the other rises.

*Negative Correlation*

The close proximity of the points to a straight line demonstrates how one variable decreases as the other increases.

*No correlation*

There is no pattern to the point, which shows no connection between the two variables.

**Example**

Maria surveyed her classmates to learn how long they spent studying and how well they did on the math exam. Create a scatter diagram for the data below to see whether there is a correlation between the time spent studying for the exam and the math scores.

Student | Studying Hours | Math Scores |

1 | 1.5 | 90 |

2 | 2 | 87 |

3 | 1 | 83 |

4 | 2.5 | 94 |

5 | 0.50 | 75 |

6 | 3 | 95 |

7 | 0.50 | 72 |

8 | 1 | 80 |

9 | 2 | 91 |

10 | 2 | 90 |

11 | 3 | 100 |

12 | 4 | 98 |

13 | 1 | 85 |

14 | 1.5 | 89 |

15 | 2.5 | 93 |

**Solution**

In the example, the independent variable is the time spent studying, while the dependent variable is the math score.

To construct the scatter diagram, we must first identify the x – axis and the y -axis and define the scale for each axis. Then, plot the points in the scatter diagram based on their values. The image shows a scatter diagram for this example.

The above scatter diagram shows that math exam scores increase as study time increases. Hence, there is a positive relationship between the two variables.

**Bivariate Analysis**

In statistics, we frequently interpret the given collection of data and make statements and predictions. An analysis is conducted during the research in an effort to pinpoint the cause and influence of the given factors.

According to the definition, the bivariate analysis examines any concurrent relationship between two variables or qualities. This study examines the relationship between the variables as well as the strength of this relationship to establish if there are any differences between the two variables and the potential causes of these differences. Examples include scatter plots and percentage tables, among others.

*Bivariate Analysis Types*

The kinds of variables we will employ for analysis will determine the kinds of bivariate analyses we can perform. A variable could be categorical, ordinal, or numerical.

Numerical and Numerical: Both the independent and dependent variables are numerical

Categorical and Categorical: Both the independent and the dependent variables are categorical

Numerical and Categorical: One variable is numerical, and the other is categorical

**Summary**

*Bivariate Data*

In bivariate data, two variables that can change are compared in order to identify relationships. You will have bivariate data, which consists of an independent and a dependent variable if one variable is impacting the other. This is so that both variables will change if the other one changes.

*Independent Variable*

The data set in an experiment that may be modified or manipulated in an experiment is known as an independent variable.

*Dependent Variable*

The data set in an experiment known as a dependent variable is one that is subject to external control or influence, usually by the independent variable.

*Univariate and Bivariate Data*

The table below shows the comparison between univariate data and bivariate data.

Univariate Data | Bivariate Data |

Only uses one variableDoes not discuss relationships or cause The main goal is to describe | Have two variables involvedAnalyses relationships and causationThe main goal is to explain |

*Correlation *

Association is what correlation refers to, although it is actually a measurement of how closely two variables are related. A correlational study can produce one of three outcomes: a positive correlation, a negative correlation, or no correlation at all. An illustration of a correlation is possible. To accomplish this, create a scatter diagram, also known as a scatterplot, scatter graph, scatter chart, or scattergram.

*Correlation Coefficient*

A perfect positive correlation, or correlation of 1, means that as one variable rise, the other rises as well.

A perfect negative correlation, or correlation of -1, means that when one measure rises, the other falls.

*Scatter Diagrams*

The relationships or associations between the two numerical variables (or co-variables) are visually represented as points (or dots) for each pair of numerical data in a scattergram. On scatter diagrams, the strength and direction of the correlation between the variables are displayed.

Positive Relation | Negative Relation | No Relation |

The near proximity of the points to a straight line demonstrates that as one variable rise, the other rises. | The close proximity of the points to a straight line demonstrates how one variable decreases as the other increases. | There is no pattern to the point, which shows no connection between the two variables. |

*Bivariate Analysis*

An analysis is conducted during the research in an effort to pinpoint the cause and influence of the given factors. According to the definition, the bivariate analysis examines any concurrent relationship between two variables or qualities. To determine whether there are any differences between the two variables and the potential causes of these differences, this study examines the relationship between the two variables as well as the depth of this relationship. Examples include scatter plots and percentage tables, among others.

The kinds of variables we will employ for analysis will determine the kinds of bivariate analyses we can perform. A variable could be categorical, ordinal, or numerical.

Numerical and Numerical: Both the independent and dependent variables are numerical

Categorical and Categorical: Both the independent and the dependent variables are categorical

Numerical and Categorical: One variable is numerical, and the other is categorical

**Frequently Asked Questions on Bivariate Data ( FAQs )**

### How do you differentiate univariate data from bivariate data?

In contrast to univariate, which refers to one variable, bivariate refers to two variables. The main difference between univariate and bivariate data is that the latter emphasizes relationships and causes. The univariate data only describes the one variable that constitutes the data.

*Univariate Data*

When using univariate data, keep the following in mind:

(a) Uses a single variable

(b) Does not discuss relationships or cause

(c) To describe is the primary objective.

*Bivariate Data*

The following should be kept in mind while using bivariate data:

(a) Involves two variables.

(a) Examines connections and causes

(c) The main objective is to explain

### What are examples of positive correlations in real life?

A positive correlation, often known as a positive relationship, shows that if the independent variable increases, the dependent variable will increase as well. If the independent variable decreases, the dependent variable will decrease too.

*Examples:*

( a ) You can drive further with more gas in your car.

( b ) As kids become older, their clothing sizes change.

( c ) As more trees are cut down, erosion is more likely to occur.

( d ) The buoyancy of salty water rises with the concentration of salt.

( e ) As the age of the children increases, their height increases as well.

( f ) As college enrollment declines, the number of teachers reduces.

( g ) As your coffee intake increases, the amount of time you stay awake increases.

( h ) Running on a treadmill for a more extended time will result in more significant calorie burn.

( i ) Buoyancy increases as salt in salty water increases.

### What are examples of negative correlations in real life?

A negative relationship exists when the independent variable increases while the dependent variable decreases, or vice versa (negative correlation).

Examples

( a ) The cost of a car decreases as it ages.

( b ) As you make more loan payments, your debt will decrease.

( c ) As an item or service’s supply declines, so does consumer demand.

( d ) As the temperature rises, fewer layers of clothing are required to stay warm.

( e ) As bikers increase their pace, it takes them less time to cross the finish line.

( f ) As an automobile loses speed, the amount of time it takes to get somewhere increases.

### What is the correlation coefficient?

A correlation can be represented numerically as a coefficient, with values ranging from -1 to +1, rather than visually as a scattergram. The correlation coefficient to utilize when working with continuous data is Pearson’s r. The extent to which the pairs of numbers for two variables lie on a straight line is indicated by the correlation coefficient (r). Values above or below zero denote correlations that are positive or negative.

### What is a perfect positive correlation on a scatter diagram?

A perfect positive correlation, or correlation of 1, means that as one variable rise, the other rises as well.

Perfect Positive Correlation

### What is a perfect negative correlation on a scatter diagram?

A perfect negative correlation, or correlation of -1, means that when one measure rises, the other falls.

Perfect Negative Correlation

### What makes up a scatter diagram, and how to construct it?

An x-axis (the horizontal axis), a y-axis (the vertical axis), and a collection of dots make up a scatter diagram. Each dot on the scatter diagram represents one item from a data set. Its location on the scatter diagram represents the X and Y values of a dot.

To construct a scatter diagram, the following steps are followed:

Step 1: Identify the horizontal axis ( x-axis ) and the vertical axis ( y-axis ).

Step 2: Establish the scale for each axis.

Step 3: Plot the points.

### What is the difference between dependent and independent variables?

Two variables that can change are compared in bivariate data in order to find relationships. If one variable influences the other, you will have bivariate data consisting of an independent and a dependent variable. This ensures that if either variable changes, both will as well.

*Independent Variable*

The data set in an experiment that may be modified or manipulated in an experiment is known as an independent variable.

*Dependent Variable*

The data set in an experiment known as a dependent variable is one that is subject to external control or influence, usually by the independent variable.

### What is meant by linear relationships?

The most straightforward analysis for bivariate data is those that have a linear relationship. Similar to how the normal distribution behaves in the case of univariate data, this connection has a special function in the case of bivariate data.

When points appear randomly clustered around a straight line in a scatterplot, it indicates that a bivariate data set contains a linear relationship. The points may be crowded and nearly lined up, or they may be widely spread and appear like a cloud of points. But this one won’t have any extreme outliers, a funnel-shaped or sharply curved relationship.

Positive and negative relationships are the two types of linear relationships that exist. Relationships that are positive have an increasing rightward slope. Points in negative relationships are sloping downward and to the right.

## Recommended Worksheets

Bivariate Data (Earth Day Themed) Math Worksheets

Data (World War II Themed) Math Worksheets

Primary and Secondary Data (Summer Solstice Themed) Math Worksheets