Question

Holes-R-Us, an Internet company that sells piercing jewelry, keeps transaction records on its sales. At a recent sales meeting, one of the staff presented a histogram of the zip codes of the last 500 customers, so that the staff might understand where sales are coming from. Comment on the usefulness and appropriateness of the display.

Short answer

A histogram is inappropriate; use a bar chart or map.

Step-by-step solution

Understanding the Objective

The company wants to identify where its sales are geographically concentrated by examining the zip codes of recent customers. This could help tailor marketing strategies and allocate resources more effectively.

Evaluating the Histogram as a Tool

A histogram is a graphical representation showing the distribution of numerical data. It groups data into 'bins' or intervals, making it suitable for understanding the frequency distribution of continuous data. However, zip codes are categorical, not continuous.

Identifying the Misalignment

Since zip codes are categorical and not numerical, using a histogram may not accurately represent the information. Each zip code is a distinct category, meaning a vertical bar for each specific location would be more appropriate.

Suggesting an Alternative Display

A bar chart or a map would be more suitable for displaying zip code data. A bar chart would show counts of transactions per zip code, while a map could visualize the geographical distribution of the customers.

Conclusion

The histogram is not an appropriate method of displaying zip code data because it assumes numerical continuity, which zip codes do not have. A bar chart or map would provide clearer insights into customer distribution by location.

Key concepts

Categorical Data

When dealing with data like zip codes, it's important to understand that they represent categorical data. This means each zip code is a distinct category, having no inherent order or numerical value like numbers do. Categorical data can be sorted into qualitative categories, often without a specific order. For example, zip codes stand simply as labels for specific regions, not measurements or quantities. Understanding the nature of categorical data helps in selecting the right tools for visual representation. This discernment ensures that data is presented accurately and comprehensibly.

Geographical Distribution

Understanding where sales come from helps businesses target their efforts and optimize resources. Analyzing geographical distribution involves observing how data points like zip codes are spread across different locations. Geographical distribution can indicate market trends and consumer behavior. For example, a cluster of transactions in specific areas might suggest higher demand in those regions. Visual tools such as maps can greatly aid in interpreting geographical distribution. Maps make it easier to see patterns and clusters, offering valuable insights into customer demographics and potential markets.

Bar Chart Usage

Bar charts are a popular choice for representing categorical data like zip codes. They display information using rectangular bars, where each bar represents a category. In the context of sales data, a bar chart makes it easy to compare the number of transactions across different zip codes. Each category (zip code) is shown with a separate bar, clearly communicating frequency without implying a numerical relationship. Bar charts help viewers quickly grasp the distribution of categorical data. They are especially useful for illustrating comparisons because the length of the bars instantly highlights differences in data.

Appropriate Graphical Representations

Choosing the right graphical representation is crucial for clear communication of data. Misrepresentation can lead to misunderstandings, potentially leading to misguided decisions. For instance, using a histogram for zip code data, as discussed earlier, misrepresents the nature of the data. This is because histograms imply a sequence and continuity that doesn't exist in categorical data like zip codes. Instead, selecting visual tools like bar charts or geographical maps aligns the presentation of data with its underlying nature. This alignment ensures that stakeholders can accurately interpret the data, making informed business decisions.