NCEA Level 1Interpreting displaysAS 91946

Interpreting displays: 7 exam questions solved step by step

What this lesson covers

  • A claim about two groups needs evidence from the whole distribution, not from single values.
  • A relationship shown in a display supports a claim only as far as its direction and strength go.
Key idea

7 displays, one method

  • 1. Read the values, with units.
  • 2. Work out the % or difference.
  • 3. Say it in context: name the group.
  • 4. Check the scale and the total.
Your turn

Question 1 · Achieved

  • A survey of 200 students at a school:
  • do you play a sport for the school?
  • What percentage of the Year 11
  • students play sport?
Year levelSportNo sportTotal
Year 9543690
Year 114466110
Total98102200
Worked example

Q1: Year 11 who play sport

  • Find the right row.
  • Divide by its row total.
  1. Year 11 who play sport: 44
  2. Year 11 total: 110the row total
  3. 44 ÷ 110 = 0.4part ÷ whole
  4. 0.4 × 100 = 40%
  5. 44 ÷ 200 = 22%200 is everyone
  6. 40% of Year 11 play sport
Your turn

Question 2 · Achieved, in context

  • Same survey, same table.
  • Compare the percentages of Year 9
  • and Year 11 students who play sport.
  • Write the comparison in context.
Year levelSportNo sportTotal
Year 9543690
Year 114466110
Total98102200
Worked example

Q2: Year 9 against Year 11

  • Groups differ in size.
  • So compare percentages.
  1. Year 9: 54 ÷ 90 = 0.6 = 60%
  2. Year 11: 44 ÷ 110 = 40%from question 1
  3. 60 − 40 = 20 percentage points
  4. 54 − 44 = 10 studentsgroup sizes differ
  5. Year 9 60%, Year 11 40%
Your turn

Question 3 · Merit

  • 20 Year 11 students: days last week
  • they bought canteen lunch.
  • Claim: "Most bought lunch on 3+ days."
  • Find the median. Is the claim right?
Question 3 · Merit
Worked example

Q3: canteen lunches

  • Count every dot.
  • Most means over half.
  1. 0: 3, 1: 4, 2: 5, 3: 4, 4: 2, 5: 2
  2. 3 + 4 + 5 + 4 + 2 + 2 = 20
  3. median: 10th and 11th values
  4. 3 + 4 = 7, 7 + 5 = 12counting up
  5. median = 2 days
  6. 3 or more days: 4 + 2 + 2 = 8
  7. 8 ÷ 20 = 0.4 = 40%
  8. Not supported: only 40%under half
Your turn

Question 4 · Merit

  • 2 km time trial, in minutes:
  • 20 Year 9 and 20 Year 11 students.
  • Find each median and IQR.
  • Call "Year 11 tend to be faster"?
Question 4 · Merit
Worked example

Q4: read the box plots

  • Read off the scale.
  • IQR = Q3 − Q1.
  1. Year 9: Q1 11, median 13, Q3 15
  2. IQR = 15 − 11 = 4 minQ3 − Q1
  3. Year 11: Q1 9, median 10, Q3 12
  4. IQR = 12 − 9 = 3 minQ3 − Q1
  5. medians: 13 − 10 = 3 min
Worked example

Q4: can we make a call?

  • Lower time = faster.
  • Median outside the box?
  1. medians: 13 − 10 = 3 min
  2. Year 11 median 10 < Year 9 Q1 11
  3. outside the Year 9 boxso we can make a call
  4. shorter time = faster
  5. IQR 3 < 4: less spread
  6. Year 11 tend to be faster
Your turn

Question 5 · Merit, in context

  • Library visits a week:
  • Term 1: 240, Term 2: 260.
  • The newsletter graph starts at 230.
  • Headline: "Visits have tripled!"
  • Check the scale first.
Question 5 · Merit, in context
Worked example

Q5: has it tripled?

  • The bars start at 230.
  • Compare the real values.
  1. Term 1 bar: 240 − 230 = 10
  2. Term 2 bar: 260 − 230 = 30
  3. 30 ÷ 10 = 3why it looks tripled
  4. increase: 260 − 240 = 20
  5. 20 ÷ 240 × 100 ≈ 8.3%compared with Term 1
  6. 3 × 240 = 720, not 260
  7. "tripled"axis does not start at 0
  8. Up 20 visits a week, about 8%
Your turn

Question 6 · Excellence

  • 20 Year 11 students: paid work
  • (hours a week), sleep (hours a night).
  • Describe the relationship. Estimate
  • sleep for 10 hours of work a week.
Question 6 · Excellence
Worked example

Q6: describe the relationship

  • Direction, strength, rate.
  • Read the trend line.
  1. direction: negativemore work, less sleep
  2. strength: moderateclear, but scattered
  3. trend: 8.5 h at 0, 6.5 h at 20
  4. drop = 8.5 − 6.5 = 2 hover 20 hours of work
  5. 2 ÷ 20 = 0.1 h per hourthe rate
  6. 0.1 × 60 = 6 minuteshours to minutes
Worked example

Q6: estimate, then the caution

  • Use the trend line.
  • A link is not a cause.
  1. 0.1 × 60 = 6 minutes
  2. at 10 h: 8.5 − 0.1 × 10trend line
  3. = 8.5 − 1 = 7.5 hours
  4. 1 hour less than at 0 hours
  5. work causes less sleeplinked, not proven
  6. about 7.5 hours a night
Your turn

Question 7 · Excellence

  • A coach claims Year 11 students run
  • faster because more of them play sport.
  • Use the table and the box plots.
  • Does the evidence support the claim?
FindingYear 9Year 11
Play sport (Q1, Q2)60%40%
Median 2 km time (Q4)13 min10 min
Worked example

Q7: test each part of the claim

  • Two parts, two displays.
  • Does the reason fit?
  1. Year 11 faster? 10 < 13 min
  2. more Year 11 play sport40%, against 60%
  3. so the "because" fails
  4. more likely: older, stronger
  5. two samples, one schoola limitation
  6. Faster: yes. Because sport: no.
Summary

What solved all seven

  • Read, calculate, compare, then say it in context.
StepHow
Readthe values, with units
Right totalpart ÷ that group's total
Comparepercentages, not counts
Box plotsmedian outside box: a call
Scaledoes the axis start at 0?
Scatterdirection, strength, rate
In contextname the group, no "proves"

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