Welcome to the "Data Detective" Phase!
In CP2 (Modelling Practice), you are often handed a large, messy spreadsheet of raw data. Before you start building complex formulas or models, you need to understand exactly what you are working with. Think of this chapter as the "Meet and Greet" with your data.
Summarising data is about turning thousands of rows of numbers into a few key insights. It’s important because it helps you spot errors, identify trends, and decide which modelling approach is best. If your data is "garbage," your model will be "garbage" (the famous GIGO principle: Garbage In, Garbage Out!).
Don't worry if you aren't a stats genius—we are going to break this down into simple, manageable steps that will help you ace the exam.
1. Descriptive Statistics: The "Big Three" Measures
When we look at a column of data, we want to know where the "middle" is. We call this Central Tendency. Here are the three ways we measure it:
A. The Mean (Average)
This is the sum of all values divided by the number of values.
Formula: \( \bar{x} = \frac{\sum x_i}{n} \)
When to use it: Use it when data is symmetrical (evenly spread).
The Trap: The Mean is very sensitive to outliers (extreme values). For example, if you have five people earning \$20,000 and one person earning \$1,000,000, the "average" will look very high, even though it doesn't represent most people.
B. The Median (The Middle Man)
This is the middle value when you line everything up from smallest to largest.
When to use it: Use it when your data is skewed or has extreme outliers (like house prices or salaries). It gives a better "typical" value than the mean in these cases.
C. The Mode (The Most Popular)
The value that appears most frequently.
When to use it: Great for categorical data (e.g., "What is the most common claim type?").
Quick Review Box:
• Mean: Sensitive to extremes.
• Median: Robust against extremes.
• Mode: Good for categories.
2. Measuring the "Spread": How Messy is the Data?
Knowing the average isn't enough. Imagine a river with an average depth of 4 feet—you could still drown if one part is 10 feet deep! We need to know the dispersion.
Standard Deviation and Variance
These tell us how far, on average, the data points sit from the mean.
Formula for Standard Deviation: \( \sigma = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n}} \)
Simple Analogy: If everyone in a class gets 70% on a test, the Standard Deviation is zero. If half get 40% and half get 100%, the average is still 70%, but the Standard Deviation will be very high!
Range and Interquartile Range (IQR)
• Range: The difference between the Maximum and Minimum value. Simple, but easily ruined by one single outlier.
• IQR: The difference between the 75th percentile (Upper Quartile) and the 25th percentile (Lower Quartile). It tells you where the middle 50% of your data lives.
Did you know? In CP2, calculating these stats is often the first step in Data Validation. If your "Minimum Age" is -5 or your "Maximum Age" is 250, you've found a data error!
3. Graphical Representation: Visualising the Story
Sometimes a picture is worth a thousand rows of Excel. In CP2, you must choose the right graph for the right purpose.
Histograms
What it is: A bar chart where the x-axis represents ranges (bins) of values.
Purpose: To see the distribution (shape) of the data. Is it bell-shaped (Normal), or is it leaning to one side (Skewed)?
Box Plots (Box and Whisker)
What it is: A box showing the IQR, a line for the median, and "whiskers" showing the range.
Purpose: Excellent for spotting outliers and comparing different groups side-by-side.
Scatter Plots
What it is: Dots on an X and Y axis.
Purpose: To see if there is a correlation between two variables. For example: "Does the claim amount increase as the age of the driver increases?"
Line Graphs
What it is: Data points connected by a line.
Purpose: Best for Time Series data. Use this to show how a value changes over months or years.
Key Takeaway: Don't just make a graph because it looks pretty. In your CP2 summary document, you must explain why you chose that graph and what it shows (e.g., "The scatter plot shows a weak positive correlation between weight and cost").
4. Data Reasonability and Quality Checks
This is a core part of the "Preparation and analysis of data" section. You must prove to the examiners that you checked if the data makes sense.
Common Checks to Perform:
1. Completeness: Are there any blank cells or "N/A" values?
2. Uniqueness: Are there duplicate records (e.g., the same policy number twice)?
3. Range Checks: Are dates in the past/future where they shouldn't be? Are values negative that should be positive?
4. Consistency: If a policy is marked as "Lapsed," is the "Premium Received" column zero?
Mnemonics for Data Quality: Try "ACCURATE"
• Accurate
• Complete
• Consistent
• Up-to-date
• Relevant
• Authoritative
• Timely
• Extended (Easy to understand)
5. Common Mistakes to Avoid
• Ignoring the "Zeroes": Sometimes a "0" means "Data not collected," and sometimes it actually means "Zero." Don't treat them the same without checking!
• Over-summarising: If you only look at the mean, you might miss the fact that your data is split into two very different groups (bimodal).
• Bad Binning: In histograms, if your bins are too wide, you lose detail. If they are too narrow, the graph looks like a mess of sticks.
• Not Labeling: In CP2, a graph without a title and axis labels is a quick way to lose easy marks.
Summary: The CP2 Workflow
1. Clean: Find the blanks and errors.
2. Calculate: Get the Mean, Median, SD, and Range.
3. Visualise: Create a Histogram or Box Plot to see the shape.
4. Verify: Ask "Does this data look reasonable for an actuarial model?"
5. Document: Write down what you found. If you deleted 10 rows of bad data, you must state that in your audit trail!
Don't worry if this seems like a lot of work before you even start "modelling." Understanding your data is 50% of the battle in CP2. Once you know your data, the formulas become much easier to write!