Core Maths

What should you investigate regarding the source of a study to identify potential bias?

You should check if the source is independent; for example, a study on tooth decay might be biased if it is funded by a sugar company.

What is the difference between Opportunity Sampling and Self-Selection?

Opportunity Sampling only includes people available at a specific moment, which is often biased, while Self-Selection occurs when people with strong opinions are more likely to respond to a survey.

Why is a "truncated" axis a problem in visual data?

If the Y-axis does not start at zero, it can exaggerate data, making small differences appear much larger than they actually are.

How can pictograms create a visual exaggeration of data?

If the height of an image in a pictogram is doubled, its area quadruples, which misleads the viewer's perception of the data's growth.

When is it better to use the Median instead of the Mean?

The Median is better for skewed data (such as salaries) because the Mean is heavily affected by outliers or extreme values.

If an interest rate increases from 2% to 3%, how is this described in terms of percentage points versus percent?

The rate has increased by 1 percentage point, but it represents a 50% increase in value.

Why is it an error to assume Correlation implies Causation?

Correlation is just a mathematical relationship where variables move together; it does not mean one directly influences the other, as a third confounding factor might be affecting both.

What is a common misunderstanding regarding how Tax Bands are applied?

You only pay the higher tax rate on the portion of income that falls above the threshold, rather than the entire amount.

Does increasing a value by 10% and then decreasing it by 10% return it to the original value?

No. Due to compounding, a value of 100 increased by 10% becomes 110, and a subsequent 10% decrease results in 99.

What three-step structure should be used when asked to "Critically evaluate" an error in an exam?

Identify: State exactly what is wrong.

Explain: Describe why this is a problem for the data.

Improve: Suggest a specific way to fix the error.

Think of Correlation like two people walking in the same direction at the same speed; they are moving together, but one isn't necessarily following the other.

Causation is like one person pulling the other on a leash—the movement of the second person is directly caused by the first.

Why should you be skeptical of a study with a small sample size (e.g., n < 30)?

A small sample is rarely representative of a large population, making the results less reliable.

What are two common errors to look for in questionnaire design?

Leading questions that nudge the respondent toward a specific answer (e.g., "Don't you agree that...").

Ambiguous options that overlap, making it unclear which choice a respondent should pick.

Beyond the starting point, what should you check regarding the increments on a graph’s scale?

You must check if the increments are consistent (e.g., 10, 20, 30); if the scale jumps (e.g., 10, 20, 100), it can misleadingly manipulate the visual representation of the data.

What is the primary flaw of using Range as a measure of spread?

It only considers the two most extreme values and fails to provide any information about the data in the "middle".

How do you mathematically remove VAT from a total price?

Rather than simply subtracting a percentage, you should divide the total by 1.2.

Why is inflation a critical factor to check in financial critical analysis?

It is necessary to account for inflation to determine the "real value" of money over a period of time.

Why is a "50% increase" sometimes less significant than it sounds?

Because it depends on the original value; for example, a 50% increase on a value of 2 only results in a new value of 3.