# Graphs, Charts, Plots and Tables | Les diagrammes et les tableaux

Data needs to be organized to produce useful information. Charts, graphs, plots and tables are effective visual tools that accurately present facts or information quickly. Data representation tools are useful ways of displaying, analyzing or reporting data which facilitate understanding of the data and highlight important facts. Data display formats may show:

• visible patterns and trends

• relationships and comparisons

• frequencies and shape distributions

• time series

Charts, graphs, plots and tables may be used to solve problems and/or to communicate about situations. It is important to choose a format that suits the data.

Listed below are examples of some common forms of data representation tools as well as their function.

Data representation tools | Des outils de représentation des données Concrete Graph | Le diagramme concret

A concrete graph is a graph on which real objects are used to represent data.

Using real objects help younger students understand graphing. Older students may use concrete models that represent real objects.

A concrete graph allows for easy comparisons and answering simple questions.

Pictograph | Le diagramme à pictogrammes  A pictograph is a graph that uses pictures or symbols to represent data. It shows the number of an object or value of data by the use of full or partial pictures/graphics/ illustrations.

A scale is used to tell the reader what the picture represents

(for example: each cookie represents 2 students, each note represents 1 student).

The same picture or symbol is usually used throughout the pictograph. A consistent baseline or the need for equally spaced items on the line is important when creating concrete graphs.

A pictograph compares frequencies of data in different categories. Circle Graph / Pie Chart | Le diagramme circulaire

A circle graph is a circular chart divided into sectors. Each sector shows categorical data (specific categories) of a single variable, in proportion to the quantity it represents. It uses fractions or percentages to compare information.

A pie chart compares parts to a whole, shows relationships among the parts of a whole and between each part and the whole.

Venn Diagram | Le diagramme de Venn A Venn diagram consists of overlapping and/or nested shapes1. Each data set is represented by a shape (usually circles). The amount of overlap between the data sets is shown by the overlap between the shapes.

A Venn diagram shows what two or more data sets have and do not have in common as well as overlaps between sets of data.

##### 1. From: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

Carroll Diagram | Le diagramme de Carroll A Carroll diagram is a chart that displays yes/no categorical data (specific categories). It is used for grouping data in a yes/no fashion.

A Carroll diagram shows numbers or objects categorized as either having an attribute or not having an attribute.

Parts of a graph | Les parties d’un diagramme A graph usually consists of two axes: the x-axis| l’axe des x (horizontal) and y-axis | l’axe des y (vertical). Each axis corresponds to one variable.

The origin| l’origine is where the two axes intersect.

Tips to preparing a graph | Conseils pour préparer un graphique

 It is important to keep in mind when preparing graphs to include: Il est important de se rappeler lors de l'élaboration des diagrammes d’y inclure: a meaningful title to help the reader understand the graph un titre significatif pour aider le lecteur à comprendre le diagramme carefully labelled x-axis and y-axis titles des titres à l’axe des x et à l'axe des y qui sont soigneusement étiqueter an appropriate scale for each axis une échelle appropriée pour chaque axe a legend to identify each data set une légende pour identifier chaque ensemble de données

Tally Marks | Le pointage avec les traits Tally marks are used for counting sets of data. They are small vertical lines, each one representing one unit. The 5th tally mark in a group is always drawn across the first four.

Tally marks make it easier to count the total in groups of five.

Tally Chart| Le tableau des effectifs A tally chart is a simple type of data display that uses tally marks to present the frequency of responses or items in different categories.

A tally chart is useful to count collected data.

Frequency Table | Le tableau de distribution de fréquence A frequency table can be an extension of a tally chart. It presents data by putting together the values of a characteristic along with the number of times each value appears in the data set. A frequency table shows the recorded number of responses or items in each category.

In a frequency table, the data is recorded in the form of a numeral instead of tally marks and the totals of the tally marks are recorded at the bottom.

A frequency table is useful as a summary table after the data have been collected and counted.

Bar Graph | Diagramme à bandes

A bar graph is graph consisting of horizontal or vertical bars1.

The bars are separated with a gap to indicate that the data is categorical (specific categories) or discrete (numerical variables).

##### 1. From: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

A Vertical Bar Graph| Un diagramme à bandes verticales The height or length of the bars represents measured values or frequencies. The higher or longer the bar is, the greater the value.

A bar graph represents the frequency of an event or outcome, compares a set of individual items or several sets of related items at one point in time or shows relationships between different data sets.

A Horizontal Bar Graph | Un diagramme à bandes horizontales Double-Bar Graph (Comparative Bar Graph) | Diagramme à bandes doubles (diagramme comparatif)

A double-bar graph is a graph that combines two bar graphs. It displays two sets of data simultaneously.

A legend is used to help the reader understand or interpret a double-bar graph. A double-bar graph compares two aspects of the data in related contexts.

Line Plot | La ligne de dénombrement

A line plot is a graph that shows a mark (usually an X) above a value on the number line for each entry in the data set1. A line plot shows the frequency of data by organizing the information along a number line.

##### 1. From: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

Histogram | L’histogramme A histogram is a type of bar graph in which each bar represents a range of values in a data set1. It divides the range of possible values into classes or groups.

In a histogram the bars touch. This is to indicate that the data intervals are continuous (can take on any value).

A histogram is used to summarize discrete or continuous data that are measured on an interval scale.

##### 1. From: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

Stem-and-Leaf Plot | Le diagramme à tiges et à feuilles A stem-and-leaf plot is a source of raw data as well as a data display. It is used to organize and display data into categories based on place values. The data values themselves create the shape of the graph. This tool is useful when organizing a lot of data values.

This stem-and-leaf plot shows the scores for a golf tournament. A stem-and-leaf plot shows the frequency of data in each interval as well as each individual piece of data. It allows easy identification of the greatest, least and median values in a set of data1.

##### 1. From: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

Continuous Line Graph| Le diagramme linéaire A continuous line graph is a graph that consists of an unbroken line in which both axes represent continuous quantities1. It is used to plot a set of data usually over an amount of time.The slope of the line tells the reader in a glance the direction of the trends.

A continuous line graph shows trends in data, usually over time.

##### 1. From: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

Broken-line Graph | Le diagramme à ligne brisée A broken-line graph is a graph that represents data by plotting points on the graph and connecting them with line segments. It is an effective way to display large amounts of data.

The horizontal axis (x-axis) represents discrete quantities (can only have certain values). The vertical axis (y- axis) represents continuous quantities (can take on any value)1.

Broken-line graphs are useful for showing trends, for identifying relationships between two variables or showing changes, usually over time.

##### 1. From: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

Scatter Plot | Le nuage de points A scatter plot is a graph that has data points plotted but not joined. It is used to show a relationship between corresponding numbers from two sets of data of a single object or event.

A scatter plot is useful for showing trends and determining relationships between two variables.

Coordinate Graph | Le diagramme de dispersion A coordinate graph is a graph that has data points represented as ordered pairs on a coordinate grid1.

A coordinate graph is used to show a relationship between variables, descriptions or trends over time.

##### 1. From: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

Tree Diagram | Le diagramme en arbre A tree diagram is a branching diagram. It is a way of representing a sequence of events.

A tree diagram shows all possible combinations or outcomes for two or more independent events.