Welcome to Data Analysis!
In the world of Problem Solving, data isn't just a bunch of boring numbers—it's a story waiting to be told. Whether you're looking at a graph of climate change or a table of high scores in a video game, "Analyse data" is about two main things: changing how data looks so it’s easier to understand, and figuring out the "why" behind the numbers. Don't worry if you aren't a math genius; this chapter is more about logic and "detective work" than complex arithmetic!
3.1 Transform data
Sometimes, data is presented in a way that is hard to read. Transforming data means taking that information and seeing it in a different, equivalent way. It’s like translating a sentence from one language to another—the meaning stays the same, but the form changes.
Recognising Alternative Representations
You need to be able to see that a pie chart, a bar chart, and a data table can all show the exact same information. For example, if a table shows that 50% of students like apples and 50% like bananas, you should be able to spot the pie chart that is split exactly in half.
Quick Tip: When comparing different charts, look for the "extremes" first. Which category is the biggest? Which is the smallest? If the bar chart shows "Blue" is the tallest bar, the pie chart must show "Blue" as the biggest slice!
Identifying Features of a Model
A "model" is just a rule or a graph that explains how something works. One of the most important features to understand is the gradient (the slope) of a graph.
Example: If you have a graph showing the cost of a taxi ride, the "steepness" of the line represents the price per kilometre.
If the line is:
1. Steep: The price per km is high.
2. Flat: The price per km is low.
3. Horizontal: There is no extra charge for more distance.
Spatial Transformations (Tiles and Patterns)
Data isn't always numbers; sometimes it's visual. You might be asked to identify a pattern or a "tile" after it has been rotated or flipped (transformations).
Analogy: Think of a patterned floor tile. If you rotate it 90 degrees, the shapes in the corners move. To solve these, pick one specific "feature" (like a red dot in the top-left corner) and track where it goes after the turn.
Key Takeaway: Data can change its "outfit" (how it looks), but the "body" (the facts) stays the same. Look for the biggest and smallest values to match different charts quickly.
3.2 Explain trends in data
Once you can see what the data is, you need to explain what is happening. Why is the line going up? Why did it suddenly drop in June?
Suggesting Explanations for Trends
A trend is a general direction in which something is developing or changing. Your job is to suggest a logical reason for that change.
Example: If a graph shows ice cream sales suddenly doubling in July, a logical explanation is the weather getting hotter. If sales of umbrellas spike at the same time, it might be a very rainy summer instead!
Did you know? Sometimes a trend changes at a specific "threshold." For example, a phone plan might cost \( \$10 \) per month for the first 500MB, but the "trend" changes and becomes much steeper (more expensive) once you go over that limit.
Fitting a Model to Information
This sounds fancy, but it just means "finding the hidden rule." If you are given a few pieces of data, can you figure out the formula being used?
Step-by-Step Example:
1. A 2km taxi ride costs \( \$5 \).
2. A 5km taxi ride costs \( \$11 \).
3. The difference in distance is \( 3km \).
4. The difference in price is \( \$6 \).
5. Therefore, the "model" or rule is: The price is \( \$2 \) per kilometre (plus a \( \$1 \) starting fee).
Memory Aid: Use the "Change in Y / Change in X" trick from math to find the rate of change! In Thinking Skills, we call this "fitting a parameter."
Key Takeaway: Trends usually have a logical cause. To find the "rule" behind the numbers, look at the difference between two points in the data.
Quick Review: Avoiding Common Mistakes
1. Don't confuse "Correlation" with "Cause": Just because two things happen at the same time (like shark attacks and ice cream sales both rising in summer), it doesn't mean one caused the other (ice cream doesn't make sharks hungry—it's just that more people go in the water when it's hot!).
2. Watch the Scales: Always check the numbers on the side (y-axis) and bottom (x-axis) of a graph. Some graphs are drawn to look "scarier" or "steeper" by changing the scale.
3. Check for "Fixed Costs": In many models, there is a starting value before anything even happens (like a \( \$3 \) "connection fee" for a phone call before you even speak for one minute).
Don't worry if this seems tricky at first! Data analysis is a skill that gets much easier with practice. Start by looking at the charts in news articles or sports stats and ask yourself: "How else could they have shown this data?" and "What is the rule that explains these numbers?"