Which of the following graphs easily shows a direct comparison of the set of data

Site navigation menu

• Vertical bar graphs
• Horizontal bar graphs
• Comparing several places or items
• Inappropriate use of bar graphs
• Other bar graphs
• Dot graphs

A bar graph may be either horizontal or vertical. The important point to note about bar graphs is their bar length or height—the greater their length or height, the greater their value.

Bar graphs are one of the many techniques used to present data in a visual form so that the reader may readily recognize patterns or trends.

Bar graphs usually present categorical and numeric variables grouped in class intervals. They consist of an axis and a series or labeled horizontal or vertical bars. The bars depict frequencies of different values of a variable or simply the different values themselves. The numbers on the x-axis of a bar graph or the y-axis of a column graph are called the scale.

When developing bar graphs, draw a vertical or horizontal bar for each category or value. The height or length of the bar will represent the number of units or observations in that category (frequency) or simply the value of the variable. Select an arbitrary but consistent width for each bar as well.

There are three types of graphs used to display time series data:

• horizontal bar graphs,
• vertical bar graphs and
• line graphs.

All three of these types of graphs work well when you need to compare values. However, in general, data comparisons are best represented vertically.

Example 1 – Vertical bar graphs

Bar graphs should be used when you are showing segments of information. From the information given in the section on graph types, you will know that vertical bar graphs are particularly useful for time series data. The space for labels on the x-axis is small, but ideal for years, minutes, hours or months. At a glance you can see from the graph that the scales for both the x- and y-axis increase as they get farther away from the origin. Figure 1 below shows the number of police officers in Crimeville from 1993 to 2001.

In Figure 1 you can see that the number of police officers decreased from 1993 to 1996, but started increasing again in 1996. The graph also makes it easy to compare or contrast the number of police officers for any combination of years. For example, in 2001 there were nine more police officers than in 1998.

The double (or group) vertical bar graph is another effective means of comparing sets of data about the same places or items. This type of vertical bar graph gives two or more pieces of information for each item on the x-axis instead of just one as in Figure 1. This allows you to make direct comparisons on the same graph by age group, sex, race, or anything else you wish to compare. However, if a group vertical bar graph has too many series of data, the graph becomes cluttered and it can be confusing to read.

Figure 2, a double vertical bar graph, compares two series of data: the numbers of boys and girls using the Internet at Redwood Secondary School from 1995 to 2002. One bar represents the number of boys who use the Internet and the other bar represents the girls.

One disadvantage of vertical bar graphs, however, is that they lack space for text labelling at the foot of each bar. When category labels in the graph are too long, you might find a horizontal bar graph better for displaying information.

Example 2 – Horizontal bar graphs

The horizontal bar graph uses the y-axis (vertical line) for labelling. There is more room to fit text labels for categorical variables on the y-axis.

Figure 3 shows the number of students at Diversity College who are immigrants by their last country of permanent residence. The graph shows that 100 students immigrated from China, 380 from France, and 260 from Brazil.

A horizontal bar graph has been used to show a comparison of these data. This graph is the best method to present this type of information because the labels (in this case, the countries' names) are too long to appear clearly on the x-axis.

A double or group horizontal bar graph is similar to a double or group vertical bar graph, and it would be used when the labels are too long to fit on the x-axis.

In Figure 4, more than one piece of information is being delivered to the audience: drug use by 15-year-old boys is being compared with drug use by 15-year-old girls at Jamie's school. Having both pieces of information on the same graph makes it easier to compare. The graph indicates that 32% of boys and 29% of girls have used hashish or marijuana, and 3% of boys and 1% of girls have tried LSD. The graph also shows that the same percent of boys and girls (4%) have used cocaine.

Example 3 – Comparing several places or items

Figure 5 is an example of a double horizontal bar graph. Hillary sampled an equal number of boys and girls at her high school and asked them to pick the one snack food they liked the most from the following list:

• popcorn
• chips
• chocolate bars
• crackers
• pretzels
• cookies
• ice cream
• fruit
• candy
• vegetables.

She created a graph to display the results of her survey. Examine Figure 5, and answer the following questions:

1. What comparison does this graph show?
2. Which snack food was least preferred by girls?
3. Which snack food was preferred by substantially more boys than girls?
4. Which snack foods were preferred by more girls than boys?
5. Which snack food was preferred equally by both boys and girls?

Answers

1. The graph shows a comparison of snack food preferences by sex.
2. Vegetables were the snack food least preferred by girls.
3. A substantial number of more boys than girls preferred chips.
4. Girls preferred candy, crackers, fruit and ice cream more than boys did.
5. The same number of boys and girls preferred popcorn as their snack food choice.

Example 4 – Inappropriate use of bar graphs

Vertical bar graphs are an excellent choice to emphasize a change in magnitude. The best information for a vertical bar graph is data dealing with the description of components, frequency distribution and time-series statistics.

A horizontal bar graph may be more effective than a line graph when there are fewer time periods or segments of data. If you want to compare more than 9 or 10 items, use a line graph instead. Figure 6 is an example of when a line graph should be used instead of a horizontal bar graph.

Example 5 – Other bar graphs

There are several other types of bar graphs that you may encounter. The population pyramid is a special application of a double bar graph. The following examples are rarely used, but can be useful if used correctly.

Stacked bar graphs

The stacked bar graph is a preliminary data analysis tool used to show segments of totals. Statistics Canada rarely uses them, despite the fact that stacked bar graphs can convey a lot of information. The stacked bar graph can be very difficult to analyse if too many items are in each stack. It can contrast values, but not necessarily in the simplest manner.

In Figure 7, it is not difficult to analyse the data presented since there are only three items in each stack: swimming, running and biking. It is easy to see at a glance what percentage of time each woman spent on an event. Had this been a graph representing a decathlon (with 10 events) the data would have been significantly harder to analyse.

Another reason that these graphs are rarely used is that they can represent a picture other than the one that was intended. In the example above, it may have taken Bronwyn two hours to finish the triathlon, and Rosalyn three hours, but they spent almost the same percentage of time on each event. Both women spent 30% of their times swimming, but whereas Rosalyn spent 54 minutes swimming, Bronwyn spent 36 minutes swimming. In other words, this graph does not tell you anything about their ranking, only what percentage of their individual race times were spent on each event. This can be misleading for someone who does not read the graph carefully.

Horizontal, vertical and stacked bar graph guidelines

You should keep the following guidelines in mind when creating your own bar graphs:

• Make bars and columns wider than the space between them.
• Do not allow grid lines to pass through columns or bars.
• Use a single font type on a graph. Try to maintain a consistent font style from graph to graph in a single presentation or document. Simple sans-serif fonts are preferable.
• Order your shade pattern from darkest to lightest on stacked bar graphs.
• Avoid garish colours or patterns.

Dot graphs

A dot graph is one of the simplest ways to represent information pictorially, yet it is the graph that is least used. Figure 8 is an example of a dot graph. As you can see, the message and the information behind the graph are delivered quickly and easily to the reader.

Which graph easily shows a direct comparison of the set of data?

Which graph is best used for comparison of data?

What type of graph represents a comparison between data?

What graph to use when comparing two data sets?