Need to visualise some statistical data you have just collected? Bar graphs are an extremely helpful way to achieve this goal; they allow you to graph quantitative data on one of the axes with a qualitative or quantitative dependent variable on the other axis.
What is a Bar Graph?
A bar graph (or bar chart or bar diagram) is a pictorial representation of data through the use of vertical or horizontal bars, whose length is proportional to the represented data.
The most significant aspect of a bar graph is the length of the bars it contains, as these represent the data illustrated through the graph.
The independent variable in a bar graph is the characteristics or the categories studied, and the dependent variable is the frequency of each category, that is, the length of the bar which represents this category.
What does a Bar Graph look like?
Below is an example of a vertical bar graph, for the data contained in the following table:
Table for favourite movie type in a friendship group (www.word.com)
Bar graph for favourite movie type in a friend group (www.mathiscool.com)
As is now visible, the above vertical bar graph helps to distinguish between the popularity of different movie types with much more ease than through observing the table.
Since these are very information-dense and simple to understand, it is not surprising that they are used in a plethora of presentations.
What are the different types of Bar Graphs?
There are four main types of bar charts:
Vertical bar graphs
This is any bar chart where the bars are directed upwards. An example of such a graph is shown above.
Horizontal bar graphs
This is any bar chart where the bars are directed sideways. They are the same as vertical bar graphs, but they have inverted axes.
Horizontal bar graph (www.depictdatastudio.com)
Stacked bar graphs
A stacked, or divided, bar graph is a chart where each bar represents is separated between two or more sections. An example of this is shown below:
Instruments played by girls and boys (Study.com)
This graph shows the number of girls and boys playing their respective instruments. The height of a section represents the number of girls or boys who play that specific instrument. The colour of a section determines whether that bar represents boys or girls.
Grouped bar graphs
A grouped bar graph is a chart where there is one independent variable but more than one dependent variable, that is, the graph measures the frequency of more than one characteristic. A grouped bar graph containing the information from the following table is shown below:
Products sold by a tech company at different months in a calendar year (www.word.com)
Products sold by a tech company at different months in a calendar year (www.word.com)
It is important to make the gaps between the independent variables (the months of the year) noticeably bigger than the spacing between the measured variables (the products sold). There are grouped bar graphs that have no space between the bars of each category.
It is important to notice that vertical and horizontal bar charts are mutually exclusive, that is, there is no such thing as a vertical horizontal bar chart. This is also the case for grouped and stacked bar charts. However, whether a bar graph is grouped or stacked does not affect whether it will be vertical or horizontal. In fact, every bar chart must be vertical or horizontal and grouped or stacked.
How is a Bar Graph Drawn?
Below is a list of steps needed to draw a bar graph:
1. Identify the type of graph you intend to use;
2. Draw the axes;
3. Label the axes with an appropriate measure;
4. Draw the scale for your graph;
5. Draw the bars for each section according to the represented data.
Bar Graph Statistics
Bar graphs have statistical parameters that can be uncovered through the characteristics of the bar chart directly or by performing certain calculations from the data the chart contains.
Mode
The mode is the statistic defined as the most common data point. When we apply this to a bar chart, we see that the mode is the longest bar in its respective category.
Find the mode height in the maths class below:
Height of students in a maths class (www.word.com)
Solution
The mode height will be the highest bar. Thus, it will be the height of 179cm as it has 4 students in it (the highest of any of the categories).
Total
The total is the sum of the height of all the bars in the diagram. This gives the total number of people participating in the first diagram.
Find the total number of students in the maths class from the diagram above.
Solution
The total number of students will be the sum of the height of all bars. Thus, the number of students is:
.
Median
This only works for quantitative categories. The median will lie where the "middle" is, that is, it will be the value in the quantitative characteristic in which half the total data set lies.
Find the median height of the maths class above.
Solution
The median will be between the tenth and the eleventh students, as there are twenty students in the class.
Remember that when the total number of data points is an even number, the median will be the average of the middle two numbers, after data points are listed from the least to the greatest.
Counting progressively from the first height bracket, the tenth student is in the 175 cm bracket. And the eleventh student is also in the 175 cm bracket. Thus, the median height is cm.
Mean
The mean length of a bar graph refers to the average length of the bars in the graph, it is the total value of the data set divided by the number of bars.
If the mean is asked with regards to the characteristic being measured, it is the sum of the length of the first bar multiplied by the value of its category, added to the length of the second bar multiplied by the value of its independent variable, and so on, divided by the total.
Find the mean height of students in the following maths class in the diagram above:
Height of students in a maths class (www.word.com)
The total number of students is:
Now we must multiply the number of students in each category by their respective height category:
Dividing this by the total number of students:
The average height in the class is 175.2 cm.
Bar Graphs - Key takeaways
- There are multiple types of bar charts: vertical and horizontal bar charts, and grouped or stacked bar charts
- Vertical and horizontal bar charts refer to the direction in which the bar is drawn
- Grouped and stacked bar charts represent a single or multiple dependent variables and one independent variable; that is, a stacked bar chart illustrates more than one variable
- Bar charts are helpful in representing dense information at a glance, and allow one to observe trends easily
- However, stacked bar charts can complicate the interpretation of data of lower orders of magnitude, and they do not justify or explain the cause of trends in the data they display
- The mode is the longest bar
- The total is the sum of the length of all bars
- The median is the bar in which the "middle" variable is
- The mean is either the average bar length or the average independent variable
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