# Special Topics in Bar Graphs

## 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)

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.

1. Which nation has the highest level of net exports? Approximate this level, in billions of dollars.
2. What is the largest difference in net exports between two nations shown on the graph?
3. Britain's net export level is closest to which other county's level of net exports?

1. 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.)
2. 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.

3. 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.