NCEA Level 1AS 91944Statistical enquiryNCEA Level 1 Maths

Statistical enquiry: 7 questions solved step by step

What this lesson covers

  • A statistical enquiry moves through problem, plan, data, analysis and conclusion, and each stage depends on the one before it.
  • An investigative question names the variable, the group and the kind of answer it wants: a summary, a comparison or a relationship.
  • Data vary for many reasons, and a good plan anticipates the ones it can control.
  • How data are collected or sourced decides what a conclusion can claim about the population.
  • A conclusion answers the investigative question with evidence and says who it applies to.
  • Reflecting on the whole enquiry means naming what limits the conclusion and what would improve it.
Key idea

7 questions, one cycle

  • Problem: a question data can answer.
  • Plan: who, how many, how measured.
  • Data: collect it, then clean it.
  • Analysis: graphs and statistics.
  • Conclusion: answer, then reflect.
Your turn

Question 1 · Achieved

  • "Do teenagers use their phones too much?"
  • Why is this a weak investigative question?
  • Rewrite it.
Worked example

Q1: fix the question

  • Needs a variable.
  • Needs a population.
  1. "Too much" is an opinionno variable
  2. "Teenagers": which ones?no population
  3. What is the typical daily
  4. screen time, in hours, of
  5. Year 11 students at our school?
  6. Variable: daily screen time (h)
  7. Population: Year 11s, our school
  8. Summary question: one group
Your turn

Question 2 · Achieved

  • Do Year 11s at our school who play a
  • team sport tend to have lower resting
  • pulse rates than those who do not?
  • Name type, variables, population, display.
Worked example

Q2: take the question apart

  • Two groups: a comparison.
  • Name every part.
  1. Comparison questiontwo groups
  2. Numerical: resting pulse (bpm)
  3. Categorical: team sport, yes/no
  4. Population: Year 11s, our school
  5. Display: box plots, one scale
  6. Data: 30+ per group, 60 in all
Your turn

Question 3 · Merit

  • Ana wants the typical resting pulse
  • of Year 11 students at her school.
  • Give three problems, and a fix for each.
StepAna's plan
Whoher 12 friends
Whenstraight after PE
Howcount beats for 10 s, then × 6
Worked example

Q3: fix Ana's plan

  • Name the variation.
  • Give a fix for each.
  1. 12 friends: not random, fewsampling variation
  2. Fix: 30 at random from the roll
  3. After PE: pulse still raisedinduced variation
  4. Fix: sit and rest 5 min first
  5. 10 s × 6: 1 missed = 6 bpmmeasurement
  6. Fix: count 30 s, then × 2
Your turn

Question 4 · Merit

  • A school has 184 Year 11 students.
  • How do you choose a random sample of 30?
  • Why are volunteers not good enough?
Worked example

Q4: a random sample

  • Everyone gets a chance.
  • Volunteers pick themselves.
  1. List all 184 Year 11 students
  2. Number them 1 to 184
  3. Calculator: RanInt#(1, 184)
  4. Number repeats? Skip it
  5. Stop at 30 different students
  6. Every student: an equal chance
  7. Volunteers: only keen ones reply
  8. So the sample could be biased
Your turn

Question 5 · Merit, in context

  • Heights of 10 Year 11 students (cm):
  • 158, 1.68, 172, 0, 163,
  • 1650, 181, 175, 199, 170
  • Clean the data, then find the median.
Worked example

Q5: clean, then median

  • Fix slips after checking.
  • Remove only impossibles.
  1. 1.68: in metres, so 168 cmunit slip
  2. 1650: checked, 165 cmtyping slip
  3. 0 cm: impossible, removesay so in the report
  4. 199 cm: tall but possiblekeep it
  5. n = 9 after cleaning
  6. 158, 163, 165, 168, 170,
  7. 172, 175, 181, 199
  8. median = 5th value = 170 cm
Your turn

Question 6 · Excellence

  • The question from Q2, 30 per group,
  • chosen at random from the roll.
  • Write the conclusion, with evidence.
Pulse (bpm)Team sportNo sport
Minimum5458
Q16269
Median6774
Q37179
Maximum8896
Worked example

Q6: the conclusion

  • Evidence, then the call.
  • Population and units.
  1. 74 − 67 = 7 bpmdifference of medians
  2. 74 > 71: outside sport boxso make a call
  3. I think Year 11s at our school
  4. who play a team sport tend to
  5. have lower resting pulse rates
  6. than those who do not.
  7. Medians: 67 bpm vs 74 bpm
  8. Boxes overlap 69 to 71 bpmnot every student
  9. Fitter ones may choose sportnot proof of cause
Your turn

Question 7 · Excellence

  • Each student counted their own pulse,
  • at lunchtime, on one day.
  • Name three limits, with a fix for each,
  • and a question for a new enquiry.
Worked example

Q7: reflect on it

  • Limit, then fix.
  • End with a new question.
  1. Self-counted: beats missedmeasurement
  2. Fix: one trained tester, timer
  3. Lunchtime: some had just runinduced
  4. Fix: 5 min seated rest first
  5. Another 60 would differsampling
  6. Fix: larger random samples
  7. Next: relationship between hours
  8. of exercise a week and resting
  9. pulse, for Year 11s at our school?
Summary

What answered all seven

  • Question, sample, clean, conclude, reflect.
StepHow
Questionvariable, population, type
Samplingrandom, at least 30 a group
Variationname it, then reduce it
Cleaningfix slips, drop impossibles
ConclusionI think, tend to, evidence
Reflectionlimits, fixes, new question

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