Subjects
Grades
Types of Graphs in Statistics - Secondary 1 and 2
| Mathematics
In statistics, graphs are very useful for looking at how data is distributed.
Horizontal or Vertical Bar Graphs
A bar graph is used to represent observed frequencies. It can represent both qualitative data and discrete quantitative data. The characteristics of the bar graph are the following:
-
Each bar is associated with a value and a category.
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The length of the bar is proportional to its frequency.
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The distance between each bar must be the same and the first bar must not be directly attached to the parallel axis.
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The width of the bars should be uniform.
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The graph should have a title and the axes should be labelled with what they represent.
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The bars can be vertical or horizontal.
Here is a table of values, along with a horizontal bar graph, representing the number of points accumulated during the soccer season by four different teams.
|
Soccer teams |
A |
B |
C |
D |
|---|---|---|---|---|
|
Number of points accumulated |
|35| |
|22| |
|27| |
|43| |
The same rules must be followed with vertical bar graphs. Essentially, only the orientation of the bars will be different.
A survey was conducted to determine the favourite pet of the residents in a municipality. Here is a table of values and a vertical bar graph displaying the results.
|
Favourite Pet |
Bird |
Cat |
Dog |
Fish |
|---|---|---|---|---|
|
Number of people |
|10| |
|20| |
|25| |
|30| |
Broken-Line Graphs
The broken-line graph is used to show discrete quantitative and continuous quantitative data that changes over time. The characteristics of the broken-line graph are the following:
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Each point is plotted according to the |x|- and |y|-axis.
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Usually, this kind of graph represents a situation that changes over time (years, months, days, etc.).
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Starting from the first point, connect each consecutive point using straight lines.
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The graph must have a title and the axes must be labelled with what they represent.
This winter, Charles, a middle school student, experienced serious health problems. His mass fluctuation is shown in a table of values and a broken-line graph.
|
Month |
Nov. |
Dec. |
Jan. |
Feb. |
Mar. |
Apr. |
|---|---|---|---|---|---|---|
|
Mass (kg) |
|44| |
|42| |
|43| |
|46| |
|44| |
|41| |
Pictographs
Frequencies can also be represented in the form of pictographs. In contrast to other diagrams, these consist of drawings that are associated with quantities.
On a beautiful summer evening, Marie and Simon count all the stars they see. Marie sees |65,| while Simon sees |70.| The situation can be represented as follows.
|
Number of stars observed by Marie |
 |
|---|---|
|
Number of stars observed by Simon |
 |
Legend: each star in the pictograph represents |10| stars.
Interpreting pictographs requires first reading and understanding the legend. In this case, a star represents |10| real stars. From this, it can also be deduced that a half-star represents half of |10| stars, which is |5| stars.
In the pictograph above, there are |6.5| stars, which correspond to the |65| stars observed by Mary.
Pie Charts
The pie chart is useful for showing a whole divided into parts. It is used to represent qualitative data. The characteristics of a pie chart are the following:
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Each circle sector is linked to a category that is usually presented as a percentage.
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The central angle of each section of the circle represents the proportion of a category with respect to the whole |(360^\circ).|
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There must be a title and a legend describing the category of each section.
|160| high school students are asked which season is their favourite. Here is the frequency table illustrating the results.
|
Season |
Students |
Relative frequency |(\%)| |
Central angle |(^\circ)| |
|---|---|---|---|
|
Winter |
|48| |
|30| |
|108| |
|
Fall |
|24| |
|15| |
|54| |
|
Spring |
|16| |
|10| |
|36| |
|
Summer |
|72| |
|45| |
|162| |
|
Total |
|160| |
|100| |
|360| |
The relative frequency of a data value can be calculated using the following proportion.||\dfrac{\text{Relative frequency}}{100}=\dfrac{\text{Frequency}}{\text{Total frequency}}||The central angle can be calculated using one of the 2 following proportions.
||\dfrac{\text{Central angle of a section}}{360^\circ}=\dfrac{\text{Frequency}}{\text{Total frequency}}||
||\dfrac{\text{Central angle of a section}}{360^\circ}=\dfrac{\text{Relative frequency}}{100}||
Since the pie chart is made by drawing a circle, we can use certain properties of the circle to find missing quantities.
Here is the incomplete data table of a pie chart.
|
Season |
Students |
Relative frequency |(\%)| |
Central angle |(^\circ)| |
|---|---|---|---|
|
Winter |
|48| |
|30| |
|108| |
|
Fall |
|
|
|
|
Spring |
|16| |
|
|36| |
|
Summer |
|
|45| |
|
|
Total |
|
|100| |
|360| |
To find the value of the green box, use the following proportion.||\begin{align}\dfrac{30}{15}&=\dfrac{108}{\color{#3a9a38}{\text{green box}}}\\\\\color{#3a9a38}{\text{green box}}&=15\times108\div30\\&=54\end{align}||