KBAT Problems
KBAT Problem: Making a Decision with Statistics
A KBAT-style problem where you compare two data sets and justify a decision, testing whether you can interpret spread, not just calculate it.
Compare centre and spread
Two machines produce parts with the same mean length but different standard deviations. You are asked which is more reliable.
The mean alone does not answer it, the smaller standard deviation means more consistent parts, so it is the more reliable machine.
Justify the decision
A full-mark answer computes both standard deviations, states which is smaller, and explains in words why a smaller spread means more consistent output. The maths and the interpretation both earn marks.
Understand the problem
A canteen weighs five oranges from each of two suppliers (grams). Supplier A: 118, 120, 122, 120, 120.
Supplier B: 110, 130, 120, 125, 115. Which supplier is more consistent?
Both look similar until you notice the real question is about spread, not average, so the mean alone cannot settle it.
Plan and solve
- Find each mean. A: (118+120+122+120+120)/5 = 600/5 = 120 g. B: (110+130+120+125+115)/5 = 600/5 = 120 g. The means are equal, so they cannot decide it.
- For A, the squared deviations from 120 are 4, 0, 4, 0, 0, totalling 8. Variance = 8/5 = 1.6, so σ_A = √1.6 ≈ 1.26 g.
- For B, the squared deviations are 100, 100, 0, 25, 25, totalling 250. Variance = 250/5 = 50, so σ_B = √50 ≈ 7.07 g.
- Since σ_A ≈ 1.26 < σ_B ≈ 7.07, Supplier A's oranges vary far less. Choose Supplier A for consistent weight.
Check and a variant
Check with the range: A spans 122 − 118 = 4 g, B spans 130 − 110 = 20 g, agreeing that A is tighter. A variant the examiner could add: Supplier B is cheaper per kilogram.
Now decide with a trade-off, B costs less but is less consistent, so state which matters more for the use and justify it. A full-mark answer always ends with a reasoned decision, not just the smaller number.
Frequently asked questions
If two data sets have the same mean, is the question always about standard deviation?
Very often, yes. When the means match, the examiner is steering you to compare spread, usually standard deviation or range.
That is the KBAT signal: it wants interpretation, not just a repeated mean calculation. State clearly that the means are equal, then let the spread decide.
Can I use my calculator's statistics mode instead of the table?
Use it to check, not to replace your working. Paper 2 gives method marks for the deviations and the formula, so show them.
Enter the data in statistics mode to confirm your standard deviation quickly, then write the steps a marker can follow. The mode is a safety net, not a shortcut past the marks.
How do I write the justification so it earns the interpretation mark?
Name the smaller standard deviation, then say in one plain sentence what it means in the situation: smaller spread means more consistent output, so that option is more reliable. Link the number back to the real decision.
Markers reward the sentence that connects the maths to the choice, not the value alone.