Comparing Data Sets
Compare typical value and spread using contextual interpretations of interquartile range and standard deviation.
How to study National 5 Mathematics
Secure one operational skill at a time, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and a checked conclusion.
Core concepts
Concept 1
Interquartile range is upper quartile minus lower quartile and describes the spread of the middle half of ordered data.
Exam cue: Order data before locating quartiles.
Concept 2
Sample standard deviation measures spread around the mean and is supplied in two equivalent formula forms.
Exam cue: Use mean with standard deviation or median with interquartile range coherently.
Concept 3
A valid comparison addresses both centre and spread and names what the values measure in the context.
Exam cue: Translate higher or lower spread into consistency in the named variable.
Risk pitfalls and guardrails
Calculating the semi-interquartile range.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Calling a lower mean more consistent.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Comparing numbers without their contextual meaning.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Memory anchors
Interquartile range
Q3 − Q1.
IQR meaning
Spread of the middle 50% of ordered values.
Standard deviation
Typical spread of values around the mean.
Lower spread
Greater consistency in the measured variable.
Centre comparison
State which group has the higher typical value and what it means.
Full comparison
Contextual centre plus contextual spread.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
A data set has lower quartile 12 and upper quartile 28. Find its interquartile range.
For the ordered data 2, 4, 5, 7, 8, 10, 12, find the median and IQR, in that order.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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