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Tables and Graphs

- Calculus
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- Functions
- Fundamental Counting Principle
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- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
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- Integers
- Integrating Polynomials
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- Integration
- Integration Using Partial Fractions
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- Interest
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- Law of Cosines in Algebra
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- Limits of Accuracy
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- Location of Roots
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- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
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- Math formula
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- Matrix Addition and Subtraction
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- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
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- Multiples of Pi
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- Notation
- Number
- Number Line
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- Odd functions
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- Operation with Complex Numbers
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- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
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- Permutations and Combinations
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- Points Lines and Planes
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- Powers Roots And Radicals
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- Prime Numbers
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- Product Rule
- Proof
- Proof and Mathematical Induction
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- Properties of Exponents
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- Quadratic Equations
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- Quadratic functions
- Quadrilaterals
- Quotient Rule
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- Rates of Change
- Ratio
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- Real Numbers
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- Recurrence Relation
- Recursion and Special Sequences
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- Representation of Complex Numbers
- Rewriting Formulas and Equations
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- Rounding
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- Scale Drawings and Maps
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- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
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- Solving Systems of Inequalities
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- Special Products
- Standard Form
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- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
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- Surds
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- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
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- Central Limit Theorem
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- Chi-Square Distribution
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- Conditional Probability
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- Confidence Interval for Population Mean
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- Inferences in Statistics
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- Survey Bias
- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
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- Type I Error
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- Types of Data in Statistics
- Venn Diagrams

It can be very confusing and frustrating to try to understand data when it is not organized in any logical way. Thankfully, there are tools and techniques that you can use to help you to make sense of it, **visualize patterns and trends **and **interpret the information behind the numbers**. In this article, we will show you how you can use tables and different types of graphs to help you achieve this.

Let's start with the basics and define what we mean by data.

**Data** comprise information and knowledge gathered about a specific topic or situation. Data are normally collected through a research and analysis process and presented in the form of numbers, facts, observations, measurements, statistics, and survey results, among others.

In order to help you organize data so that you can analyze them more efficiently, you can use **tables** to represent it.

**Tables **are representations of data organized into different categories by rows and columns.

In tables, you can arrange data in increasing or decreasing order, which makes it easier and quicker for you to locate specific information. Each row and column represents a specific category, typically labeled at the top of each column and at the left-hand side of each row.

Here is an example of a table that contains data about the global revenue of the Unilever Group from 2010 to 2020, by product segment (in million euros):

Revenue of the Unilever Group worldwide 2010-2020, by product segment:

Year | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |

Personal care | 13,767 |
| 18,097 | 18,056 | 17,739 | 20,074 | 20,172 | 20,697 | 20,624 | 21,868 | 21,124 |

Home care | 7,726 |
| 9,057 | 8,946 | 9,164 | 10,159 | 10,009 | 10,574 | 10,131 | 10,825 | 10,460 |

Foods and refreshments | 22,769 |
| 24,170 | 22,795 | 21,533 | 23,039 | 22,532 | 22,444 | 20,227 | 19,287 | 19,140 |

*Source: statista.com*

If you are asked to answer the following questions:

- In what year did the Unilever Group have the highest increase in revenue?
- In what year there was the biggest drop in revenue?

Then you can add a couple of rows to the previous table to give you the information that you need. One row will contain the total revenue per year, and the other one will include the change in revenue between the current year and the previous one.

The values in the T**otal revenue** row in the table below, are the result of adding the revenue for all product segments per year, and the values in the R**evenue change** are the result of subtracting the total revenue from the previous year from the current one. For example, the values corresponding to **Total revenue and Revenue change for the ****year 2011** are calculated as follows:

Let's see the rest of the values in the table below.

Year | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |

Total revenue | 44,262 | 46,467 | 51,324 | 49,797 | 48,436 | 53,272 | 52,713 | 53,715 | 50,982 | 51,980 | 50,724 |

Revenue change | 2,205 | 4,857 | -1,527 | -1,361 | 4,836 | -559 | 1,002 | -2,733 | 998 | -1,256 |

Notice that negative values in the revenue change refer to a decrease in revenue.

Now we can **answer the questions**:

**1. In what year did the Unilever Group have the highest increase in revenue?**

The highest increase in revenue was seen in the year 2012. In comparison to 2011, the revenue in 2012 **increased** by 4,857 million euros. See the table cell highlighted in green.

**2. In what year there was the biggest drop in revenue?**

The biggest drop in revenue occurred in the year 2018. In comparison to the previous year, the revenue **decreased** by 2,733 million euros. See the cell highlighted in yellow.

**Graphs** are graphical representations that provide a more visual way to understand and analyze data, showing the relationship between two or more variables.

Graphs help us analyze the behavior of variables, and can be used to make inferences about them and to facilitate the interpretation of data.

The main types of graphs that you can use to analyze data are as follows:

**Bar graphs**, also known as bar charts, display data using bars of the same width to represent different categories. How tall the bars are is defined by the data that they are associated with, and the scale chosen in each case.

The **steps to draw a bar graph** from a set of values on a table are as follows:

Choose the scale, depending on the data range (minimum and maximum values), and decide what increments you will use to be able to display all the data;

Draw the axes and label them;

Draw a bar for each category. The length of each bar will depend on the values on the table;

Choose a title for your graph, related to the relationship between the variables that the bar graph is representing.

Bar graphs can be vertical or horizontal.

Going back to the previous example, here is the bar graph corresponding to Unilever's total revenue per year from 2010 to 2020:

Always make sure that the intervals in which the scale increments are consistent and that there are no gaps. Otherwise, the **graphs could be misleading** and lead to misinterpretation of the data.

Read Misleading Graphs to learn more about this topic.

**Line graphs** are especially useful to represent change over time. This allows you to identify trends and patterns in the behavior of a variable.

The **steps to draw a line graph** from a set set of values on a table are:

Choose the scale;

Draw the axes and intervals and label them;

Plot a point on the graph for each value on the table;

Connect each individual point with the one next to it using a straight line;

Choose a title for your line graph.

Let's now represent the same data used in the previous example, but using a line graph.

As you can see, it is easier to identify trends with a line graph. Looking at the line graph above, let's answer the following questions:

**a) In what years did the revenue decrease?**

The years where the revenue decreased were 2013, 2014, 2016, 2018, and 2020. You can identify that these years had a revenue decrease because the line graph has a negative slope (points down) on these particular points.

**b) In what period did the revenue decrease two years in a row?**

The period where the revenue decreased in two consecutive years was 2013 and 2014. As you can see on the line graph, the line has a negative slope in both of these years.

**Pie graphs**, also known as circle graphs or pie charts, are graphical representations that help to visualize how different categories relate to each other and to the whole represented by the circle.

The **steps to draw a pie graph** from data contained in a table are:

Work out the total amount of observations by adding together all of the values per category in the table provided;

Do the following calculation per category in the table to work out the degree measure of each sector in the pie graph:

;

Draw a circle, and use a protractor to draw the angle corresponding to each sector;

Label each sector;

Choose a title for your pie graph.

Let's see this more clearly with an example.

The following table contains the most popular global mobile messenger apps for October 2021, based on monthly active users (in millions). Draw a pie graph to represent the data.

Mobile messenger app | Monthly active users (millions) |

2000 | |

Facebook Messenger | 1300 |

Weixin / WeChat | 1251 |

591 | |

Telegram | 550 |

Snapchat | 538 |

*Source: Statista.com*

As an **example of the calculations** that you need to do to work out the degree measure for each category, let's calculate the one corresponding to WhatsApp:

After calculating the degree measure for each category, you can **draw the pie graph** using a protractor to measure the different angles. After that, you can label each sector and choose a title for your pie graph.

Tables and graphs provide a visual representation of a collection of data presented in an organized way to facilitate interpretation, analysis, and the identification of patterns and trends. Tables and graphs are important resources used in many scenarios, for example:

To facilitate the decision-making process;

To present research findings;

To be used as information to back up a particular argument;

To present the annual results in the sales performance of a company;

To analyze the effectiveness of a particular decision;

To represent the market share of a company in a specific sector, etc.

When we discussed bar graphs, we mentioned that graphs could be misleading and lead to misinterpretation of the data. We identified that this can happen when there are gaps in the intervals used in the scale. Apart from this, there are other **common mistakes that can be made when representing data**, especially in graphs, which you need to keep in mind. Let's mention a few below.

Not starting the scale at zero;

Not including or not labeling the axes;

Presenting incomplete data;

Not plotting the points correctly;

Misinterpreting the information given by the data;

In pie graphs, including percentages that do not add up to 100%, etc.

- Data comprise information and knowledge gathered about a specific topic or situation.
- Tables are representations of data organized into different categories by rows and columns.
- Graphs are graphical representations that provide a more visual way to understand and analyze data, showing the relationship between two or more variables.
- Graphs could be misleading if the intervals in which the scale increments are not consistent and if there are gaps in the data.
- The main types of graphs that you can use to analyze data are bar, line, and pie graphs.

The **key features of tables** include:

- Data are organized in rows and columns in increasing or decreasing order.

- Each row and column represents a specific category, typically labeled at the top of each column and at the left-hand side of each row.

The **key features of graphs** include:

- They are visual representations of data that show the relationship between two or more variables.

- The main types of graphs that you can find are: bar graphs, line graphs and pie graphs.

- Bar and line graphs are represented using an x and a y-axis.

- Pie graphs are graphical representations that help to visualize how different categories relate to each other and to the whole represented by the circle.

**Tables **help you to organize and keep track of data in rows and columns. In tables, data is presented in increasing or decreasing order, making it easier to locate specific information when required. **Graphs or charts** provide a more visual way to represent the behavior of considerably large amounts of data, which helps you to identify trends and patterns that otherwise would be difficult to spot.

An **example of a table** is a table containing data about the number of users of the most popular social media apps from 2010 to 2022.

An** example of a graph** is a line graph representing the sales of a particular product over the past 10 years.

**Tables** organize data in rows and columns in increasing or decreasing order, making it easier to locate specific information when required. **Graphs** are a more visual way to represent the behavior of considerably large amounts of data, helping to identify trends and patterns.

More about Tables and Graphs

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