NCEA Level 1Time seriesAS 91946

Time series: 7 exam questions solved step by step

What this lesson covers

  • A time series graph shows how one variable changes over time, and its features have names.
  • Trend, seasonal pattern and unusual spikes are read separately and then described together.
Key idea

One data set, 7 questions

  • Guest nights at a holiday park.
  • In hundreds, each quarter, 3 years.
  • Q1 = Jan to Mar (summer).
  • Invented data, for practice.
YearQ1Q2Q3Q4
Year 1159411
Year 21811714
Year 32114216
Your turn

Question 1 · Achieved

  • Guest nights in Q1 of year 2?
  • How many fewer in Q2 of year 2?
  • Careful: the values are hundreds.
Question 1 · Achieved
Worked example

Q1: read, then × 100

  • Values are in hundreds.
  • A change: subtract.
  1. Year 2, Q1: 18 hundred
  2. 18 × 100 = 1800 guest nights
  3. Year 2, Q2: 11 hundred
  4. 11 × 100 = 1100 guest nights
  5. 1800 − 1100 = 700a change
  6. 700 fewer guest nights in Q2
Your turn

Question 2 · Achieved, in context

  • Describe the seasonal pattern.
  • Give the size of the swing.
Question 2 · Achieved, in context
Worked example

Q2: the seasonal pattern

  • When high, when low?
  • Then how big the swing is.
  1. Q1: 15, 18, 21highest every year
  2. Q3: 4, 7, 2lowest every year
  3. Year 1: 15 − 4 = 11peak − trough
  4. Year 2: 18 − 7 = 11peak − trough
  5. swing ≈ 11 hundred = 1100
  6. Peaks in summer (Jan to Mar),
  7. lowest in winter (Jul to Sep),
  8. by about 1100 guest nights.
Your turn

Question 3 · Merit, in context

  • Describe the trend, with a rate.
  • Compare like quarters with like.
Question 3 · Merit, in context
Worked example

Q3: the trend as a rate

  • Same quarter, other years.
  • Leave the odd value out.
  1. Q1: 21 − 15 = 6 hundredover 2 years
  2. 6 ÷ 2 = 3 hundred a year
  3. Q4: 16 − 11 = 5 hundredover 2 years
  4. 5 ÷ 2 = 2.5 hundred a year
  5. Q2: 14 − 9 = 5, 2.5 a year
  6. Guest nights are increasing,
  7. by about 250 to 300 a year.
Your turn

Question 4 · Merit

  • Find the percentage increase in
  • summer (Q1) guest nights,
  • from year 1 to year 3.
Question 4 · Merit
Worked example

Q4: percentage change

  • Change ÷ original × 100.
  • Original = year 1.
  1. Q1, year 1: 1500
  2. Q1, year 3: 2100
  3. change = 2100 − 1500 = 600
  4. 600 ÷ 1500 × 100 = 40%change ÷ original
  5. 600 ÷ 2100 × 100 ≈ 28.6%wrong base
  6. 1500 × 1.4 = 2100
  7. Summer guest nights rose 40%.
Your turn

Question 5 · Merit, in context

  • One value does not fit the pattern.
  • Find it, and how far off it is.
  • Give a possible reason.
Question 5 · Merit, in context
Worked example

Q5: the unusual value

  • Expected minus actual.
  • A reason: say "possibly".
  1. Q3: 4, 7, then 2should keep rising
  2. 7 − 4 = 3 a yearQ3 years 1 to 2
  3. expected ≈ 7 + 3 = 10 hundred
  4. actual = 2 hundred
  5. 10 − 2 = 8 hundred below
  6. Winter, year 3: 200 nights,
  7. about 800 below the pattern.
  8. Possibly a road closure or storm.
Your turn

Question 6 · Excellence, in context

  • Predict the guest nights
  • for Q1 of year 4.
  • Justify it, and give its limits.
Question 6 · Excellence, in context
Worked example

Q6: predict, with limits

  • Latest same quarter,
  • plus one year of trend.
  1. latest Q1: 21 hundredsame season
  2. trend: +3 hundred a yearfrom question 3
  3. 21 + 3 = 24 hundred
  4. ≈ 2400 guest nights
  5. Assumes the pattern carries on.
  6. Only 3 years of data.
  7. A shock (year 3, Q3) can recur.
  8. About 2400, one season ahead.
Your turn

Question 7 · Excellence, in context

  • The owner says year 3 was worse
  • than year 2, as winter was poor.
  • Use the data to evaluate this.
Question 7 · Excellence, in context
Worked example

Q7: test the claim

  • Whole years: add quarters.
  • Then quarter by quarter.
  1. Year 2: 18 + 11 + 7 + 14 = 50
  2. Year 3: 21 + 14 + 2 + 16 = 53
  3. 53 − 50 = 3 hundred more
  4. Q1 +3, Q2 +3, Q4 +2all rose
  5. Q3: 7 → 2, down 5the only fall
  6. Q3 ≈ 10 gives 61 hundredhad it fitted
  7. Year 3: 5300, up 300.
  8. Not supported: only winter fell.
Summary

What answered all seven

  • A number from the data, then a sentence in context.
StepHow
Valuesread, then × 100, with units
Seasonwhen high, when low, how much
Trendlike quarter with like, a rate
Changechange ÷ original × 100
Unusualexpected minus actual, reason
Predictlatest same quarter + trend
Limitsit assumes the pattern holds

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