Continuous data has an uncountable number of values between any two values. You should use continuous data when you want to make inference about a population mean, median, standard deviation, or variance.
When you measure a characteristic of a part or process, such as length, weight, or temperature, you usually obtain continuous data. Continuous data often includes fractional (or decimal) values. For example, a quality engineer wants to determine whether the mean weight differs from the value stated on the package label (500 g). The engineer samples cereal boxes and records their weights.
You should use Bernoulli data to make inference about proportions or percentages. Bernoulli data is often referred to as binomial data because a Bernoulli population can be interpreted as a binomial population.
When you classify an item, event, or person into one of two categories you obtain binomial data. The two categories should be mutually exclusive, such as yes/no, pass/fail, or defective/nondefective. For example, engineers examine a sample of bolts for severe cracks that make the bolts unusable. They record the number of bolts that are inspected and the number of bolts that are rejected. The engineers want to determine whether the percentage of defective bolts is less than 0.2%.