To determine the most appropriate type of graph for the given data on annual salaries, let's analyze the nature and range of the data:
The data includes the following annual salaries (in dollars):
- 13,000
- 15,000
- 19,000
- 23,000
- 23,000
- 255,000
- 32,000
- 16,000
- 17,000
- 22,000
- 21,000
- 18,000
Let's consider the options:
1. Histogram: A histogram is useful for showing the frequency distribution of numerical data over a continuous interval or certain range. It helps to see the shape of the data distribution.
2. Pie chart: A pie chart is designed to show proportions of a whole and is generally used for categorical data rather than continuous numerical data such as salaries.
3. Box-and-whisker plot: A box-and-whisker plot (also known as a box plot) is excellent for displaying the spread and skewness of data. It shows the median, quartiles, and potential outliers. Given that annual salaries can vary widely, this type of plot is useful for identifying the overall distribution and detecting any extreme outliers (such as a very high salary in this dataset).
4. Stem-and-leaf plot: A stem-and-leaf plot is a method for displaying quantitative data in a graphic format, similar to a histogram. It's generally more useful for small data sets and gives a quick view of the distribution.
Given the wide range of salaries, with one exceptionally high salary ($255,000) as a potential outlier, the box-and-whisker plot is the most appropriate choice. It will effectively highlight the spread of the data and the presence of any outliers.
Therefore, the correct answer is:
- a box-and-whisker plot
