Exploring Binary and Categorical Data
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The mode is the value — or values in case of a tie — that appears most often in the data. For example, the mode of the cause of delay at Dallas/Fort Worth airport is “Inbound.” As another example, in most parts of the United States, the mode for religious preference would be Christian. The mode is a simple summary statistic for categorical data, and it is generally not used for numeric data.
A special type of categorical data is data in which the categories represent or can be mapped to discrete values on the same scale. A marketer for a new cloud technology, for example, offers two levels of service, one priced at $300/month and another at $50/month. The marketer offers free webinars to generate leads, and the firm figures that 5% of the attendees will sign up for the $300 service, 15% for the $50 service, and 80% will not sign up for anything. This data can be summed up, for financial purposes, in a single “expected value,” which is a form of weighted mean in which the weights are probabilities. The expected value is calculated as follows: 1. Multiply each outcome by its probability of occurring. 2. Sum these values. In the cloud service example, the expected value of a webinar attendee is thus $22.50 per month, calculated as follows:
The expected value is really a form of weighted mean: it adds the ideas of future expectations and probability weights, often based on subjective judgment. Expected value is a fundamental concept in business valuation and capital budgeting — for example, the expected value of five years of profits from a new acquisition, or the expected cost savings from new patient management software at a clinic.
The frequency or proportion for each category plotted as bars.
The frequency or proportion for each category plotted as wedges in a pie.
