In the previous lesson, we talked about what data is and the different kinds of data that people who work with insurance and numbers use. Now let us say you have a set of information like a lot of insurance claims. There may be hundreds of observations. When you look at all this information it can be really hard to understand what it means. So how do people who work with numbers and insurance make sense of all the data from insurance claims?
Unorganized (raw) data is usually messy and hard to understand.
Example: Claim amounts ($): 200, 500, 200, 450, 500, 200.
From the above example it is hard to draw any conclusion or quickly see patterns. However, organizing data enables us to easily identify trends and patterns, summarize information, and make better decisions.
A frequency table helps us organize data by representing each value and how frequently it appears. The number of times a data value appears is known as its frequency. This way it becomes easier to compare data, understand common values, and prepare it for further analysis. In actuarial science, frequency tables are usually used in analyzing the number of claims, types of policies, and customer groups.
| Claim Amount ($) | Frequency |
|---|---|
| 200 | 3 |
| 450 | 1 |
| 500 | 2 |
We term data as ungrouped data when raw individual values are listed exactly as they are.
Example: Ages of policyholders: 23, 27, 30, 27, 50.
Frequency Table for Age Data
| Age | Frequency |
|---|---|
| 23 | 1 |
| 27 | 2 |
| 30 | 1 |
| 50 | 1 |
However, it is difficult to get useful insights from ungrouped data, especially when dealing with bigger datasets.
Grouped data is organized into class intervals or categories. Instead of showing every individual value, grouped data summarizes observations within ranges.
| Age Group | Frequency |
|---|---|
| 20 – 29 | 3 |
| 30 – 39 | 1 |
| 40 – 49 | 0 |
| 50 – 59 | 1 |
Grouped data is especially useful for large datasets because it makes the distribution of data easier to observe. It helps identify concentrations, gaps, and general trends more efficiently than a long list of raw values.
Example: In actuarial science, grouped data is often used to classify policyholders by age bands, claim sizes, or risk categories. This allows actuaries to study patterns in risk more effectively and supports pricing, reserving, and decision-making.
Data can also be classified according to its level of measurement. The level of measurement tells us how a variable is recorded and what kinds of comparisons or calculations are meaningful. Here are two simple kinds of data that you should know about: nominal data and ordinal data.
Categories have no natural order. When the data for a variable consists of labels or names used to identify an attribute.
Example: Type of insurance (Health insurance, Life insurance or Motor insurance)
Ordinal data exhibits the properties of nominal data and in addition, the order or rank of the data is meaningful.
Example: Risk Level (Low, Medium or High)
These kinds of data help actuaries understand and analyze information in a better way.
You did an excellent job with this lesson. You learned how to organize data using frequency tables. You also learned about grouped and ungrouped data. These tools allow you to better understand and examine datasets.
In the following lesson, we will go over more data summarization techniques. We will discuss the mean, median, and mode, which are all highly essential statistical tools.