Special Topics in Bar Graphs
Negative Frequency
Values
Objectives
After completing this unit, you should be able to:
- Read and analyze bar graphs that have both positive and negative
values.
Bar Graphs with both Positive and Negative Bars
Some bar graphs display negative values. For instance, if we spend
more than we earn, we actually lose money. This loss is represented
as a negative number. This fact has implications for how we read
and construct this type of bar graph. (NOTE: The unit titled Constructing
Bar Graphs provides a review of constructing bar graphs.
|
If we look at the table below, Net Exports of Selected Nations,
we notice that two of these countries, Britain and United States,
have net exports that are negative. If we construct a bar graph
for this data we must take that into account.
What does it mean to have a negative net export level? Does
it mean that the US and Britain do not export any goods? Certainly
not! What it does imply is that the US and Britain do not export
more than they import. |
Net Exports of Selected
Nations
|
County |
Net Exports
(in billions of dollars) |
|
Canada |
10 |
|
France |
12 |
|
Italy |
36 |
|
Japan |
142 |
|
Britain |
-22 |
|
United States |
-132 |
|
When constructing a bar graph with negative
values, you follow the steps outlined in the last unit on Constructing Bar Graphs, paying close attention to the scale of the
frequency axis. Since there are negative values, the scale
of this axis will not start at zero. The bar graph for this table
of information is shown below:
Net Exports of Selected
Nations
Drawing the bars beginning at zero on the frequency axis, allows
us to easily visualize which countries have a negative net export.
Also note the placement of the country names. This is done to
make the graph easier to read. (NOTE: If you wish to see the detailed
construction of this bar graph you can click here, [constructing a bar
graph with negative frequency values].) Now let's look
at example of the kind of information that can be drawn from these
sorts of bar graphs.
Example
Using the bar graph of Net
Exports of Selected Nations which is shown above, answer
the following questions.
- Which nation has the highest level of net exports? Approximate this level, in billions of
dollars.
- What is the largest difference in net exports between two
nations shown on the graph?
- Britain's net export level is closest to which other county's
level of net exports?
Answers to Example
- Which nation has the highest level
of net exports? Approximate this level, in billions of dollars.
The nation with the highest
level of exports will be the one that corresponds to the biggest
bar on the right (positive) side of the graph. Since Japan's export level is obviously the
most positive, it is the largest. We can approximate this to
be around 140 billion dollars worth of exports. (An estimate
that is within the range of 135-145 billion is acceptable.)
- What is the largest difference in
net exports between two nations shown on the graph?
To answer this question, we must estimate the export levels of
the two nations having corresponding bars which are furthest
apart at their tips. Since the United States' export level is
approximately -135 billion dollars and Japan's has been found
to be around 140 billion dollars, the difference can be found
by subtracting the two numbers.
140 - (-135) = 275 billion dollars.
- Britain's net export level is closest
to which other county's level of net exports?
We must be careful when answering this question. Keep in mind
that, although Britain's net export level is negative, the next
closest nation may be positive. Realizing this, we can see that
Canada, having a net export of approximately
10 billion dollars, is closest to Britain's net export level
of -25 billion dollars.
Now try a practice on analyzing bar graphs with negative frequencies.
