Bar Charts
Section 2.1 introduced some of the basic tools for describing numerical variables, both dis- crete and continuous, when the data are in their raw form. However, in many instances, you will be working with categorical data or data that have already been summarized to some extent. In these cases, an effective presentation tool is often a bar chart.
2.2
o u tc o m e 4
Bar Chart
A graphical representation of a categorical data set in which a rectangle or bar is drawn over each category or class. The length or height of each bar represents the frequency or percentage of observations or some other measure associated with the category. The bars may be vertical or horizontal. The bars may all be the same color or they may be different colors depicting different categories.
Additionally, multiple variables can be graphed on the same bar chart.
BUSINESS APPLICATION
Developing Bar Charts
New Car Sales The automobile industry is a significant part of the U.S economy. When car sales are up, the economy is up, and vice versa. Table 2.8 displays data showing the total number of cars sold in the United States in 2015 by the ten largest automobile companies in the world. Although the table format is informative, a graphical presentation is often desira- ble. Because the car sales data are given by car company, a bar chart would work well in this instance. The bars on a bar chart can be vertical (called a column bar chart) or horizontal (called a horizontal bar chart). Figure 2.7 is an example of a column bar chart. The height of the bars corresponds to the number of cars sold by each company. This gives you an idea of the sales advantage held by General Motors and Ford in 2015.
One strength of the bar chart is its capability of displaying multiple variables on the same chart. For instance, a bar chart can conveniently compare new car sales data for 2015 and sales for the previous year. Figure 2.8 is a horizontal bar chart that does just that. Notice that all com- panies posted gains between 2014 and 2015, with Fiat Chrysler highest at 7.22%.
TABLE 2.8 2015 New Car Sales for the Top Ten Automobile Companies (United States)
Car Company 2015 Sales
Daimler 380,461
BMW 405,377
Volkswagen 606,840
Hyundai Kia 1,387,528
Nissan 1,484,918
Honda 1,586,551
Fiat Chrysler 2,257,728
Toyota 2,499,313
Ford 2,603,082
General Motors 3,082,366 Source: www.goodcarbadcar.net
3,500,000
2,500,000
1,500,000
500,000 0 3,000,000
2,000,000
1,000,000
General
Motors Ford Honda Nissan Hyundai Daimler
Kia Volks- wagen BMW Toyota Fiat
Chrysler
Automobile Company
2015 New Cars Sold
FIGURE 2.7 Bar Chart Showing 2015 New Car Sales (Source: www.goodcarbadcar.net )
M02_GROE0383_10_GE_C02.indd 74 05/09/17 2:08 PM
2.2 Bar Charts, Pie Charts, and Stem and Leaf Diagrams
|
Chapter 2 75People sometimes confuse histograms and bar charts. Although there are some similari- ties, they are two very different graphical tools. Histograms are used to represent a frequency distribution associated with a single quantitative (ratio- or interval-level) variable. Refer to the histograms in Section 2.1. In every case, the variable on the horizontal axis was numeri- cal, with values moving from low to high. The vertical axis shows the frequency count, or relative frequency, for each numerical value or range of values. There are no gaps between the histogram bars. On the other hand, bar charts are used when one or more variables of interest are categorical, as in this case in which the category is “car company.”
2,000,000 3,000,000 3,500,000 1,000,000 1,500,000 2,500,000
500,000 0
Automobile Company
New Cars Sold General
Motors
Volks- wagen BMW Daimler Hyundai Kia Nissan Honda ChryslerFiat Toyota Ford
2014 Sales 2015 Up 5.02%
2015 Up 5.33%
2015 Up 5.29%
2015 Up 7.22%
2015 Up 7.07%
2015 Up 6.25%
2015 Up 2.20%
2015 Up 3.78%
2015 Up 1.19%
2015 Up 2.96%
2015 Sales FIGURE 2.8 Bar Chart
Comparing 2014 and 2015 New Cars Sold
(Source: www.goodcarbadcar.net)
EXAMPLE 2-7
Bar Charts
Price/Earnings Ratios The S&P 500, or the Standard & Poor’s 500, is an American stock market index based on the market capitalizations of 500 large companies that have common stock listed on the NYSE or NASDAQ. A key measure of importance to investors is the price earnings (PE) ratio. The PE ratio is computed by dividing a stock’s price by the earnings of the company. Companies with high PE ratios may be overpriced, while companies with low PE ratios may be underpriced. Each year on January 1, Standard & Poor’s computes the combined PE ratio for all 500 companies in the S&P 500 Index. We are interested in devel- oping a bar chart that displays the S&P 500 PE ratios for the years 2010 through 2016.
s t e p 1 Define the categories.
Data for the PE ratios for the seven years are shown as follows:
Year S&P 500 PE Ratio
2016 21.21
2015 20.02
2014 18.15
2013 17.03
2012 14.87
2011 16.3
2010 20.07
The category to be displayed is the year.
s t e p 2 Determine the appropriate measure to be displayed.
The measure of interest is the PE ratio.
HOW TO DO IT (Example 2-7)
Constructing Bar Charts 1. Define the categories for the variable of interest.
2. For each category, determine the appropriate measure or value.
3. For a column bar chart, locate the categories on the hor- izontal axis. The vertical axis is set to a scale corresponding to the values in the categories. For a horizontal bar chart, place the categories on the vertical axis and set the scale of the horizon- tal axis in accordance with the values in the categories. Then construct bars, either vertical or horizontal, for each category such that the length or height corresponds to the value for the category.
M02_GROE0383_10_GE_C02.indd 75 05/09/17 2:08 PM
76 Chapter 2
|
Graphs, Charts, and Tables—Describing Your DataBUSINESS APPLICATION
Constructing Bar Charts
Bach, Lombard, & Wilson One of the most useful features of bar charts is that they can display multiple issues. Consider Bach, Lombard, & Wilson, a New England law firm.
Recently, the firm handled a case in which a woman was suing her employer, a major elec- tronics firm, claiming the company gave higher starting salaries to men than to women. Con- sequently, she stated, even though the company tended to give equal-percentage raises to women and men, the gap between the two groups widened.
Attorneys at Bach, Lombard, & Wilson had their staff assemble massive amounts of data. Table 2.9 provides an example of the type of data they collected. A bar chart is a more effective way to convey this information, as Figure 2.9 shows. From this graph we can quickly see that in all years except 2013, the starting salaries for males did exceed those for females. The bar chart also illustrates that the general trend in starting salaries for both groups has been increasing, though with a slight downturn in 2015. Do you think the infor- mation in Figure 2.9 alone is sufficient to rule in favor of the claimant in this lawsuit? Bar charts like the one in Figure 2.9 that display two or more variables are referred to as cluster bar charts.
Excel Tutorial
TABLE 2.9 Starting Salary Data Year Males: Average
Starting Salaries Females: Average Starting Salaries
2010 $45,000 $41,000
2011 $48,000 $46,000
2012 $53,000 $51,000
2013 $58,000 $59,000
2014 $62,000 $59,000
2015 $59,000 $54,000
2016 $64,000 $62,000
s t e p 3 Develop the bar chart.
A column bar chart is developed by placing the seven years on the horizontal axis and constructing bars whose heights correspond to the values of the S&P PE ratio. Each year is assigned a different-colored bar. The resulting bar chart is
Year
PE Ratio
S&P 500 PE Ratios
2010 15
5 20
10
0 2011 2012 2013 2014 2015 2016
20.07 20.02 21.21
16.3 14.87
17.03 18.15
s t e p 4 Interpret the results.
The bar chart shows that the S&P PE ratio computed on January 1, 2016, was the highest of the seven years, while the 2012 PE ratio was the lowest.
TRY EXERCISE 2-26 (pg. 80)
M02_GROE0383_10_GE_C02.indd 76 05/09/17 2:08 PM
2.2 Bar Charts, Pie Charts, and Stem and Leaf Diagrams
|
Chapter 2 77$70,000
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000 0
Starting Salaries
Female Male
2010 2011 2012 2013 2014 2015 2016
Year
Starting Salaries — Males and Females FIGURE 2.9 Bar Chart of
Starting Salaries