📍 The Situation
Maria has run Coastal Café for two years. Business looks good on a busy Saturday, but with seasonal dips in winter she's unsure whether the underlying trend is actually growing, or if she's just riding the good seasons.
She's been offered the lease on the empty shop next door. Before she signs, she needs to crunch the numbers. You're her data analyst. Six steps stand between her and that second cup.
📊 Coastal Café, Quarterly Sales Data
Quarter
Season
Sales ($'000)
Q1
Summer (Yr 1)
80
Q2
Autumn (Yr 1)
60
Q3
Winter (Yr 1)
50
Q4
Spring (Yr 1)
70
Q5
Summer (Yr 2)
90
Q6
Autumn (Yr 2)
70
Q7
Winter (Yr 2)
60
Q8
Spring (Yr 2)
80
Reminder: 4-pt MA = (add 4 consecutive values) ÷ 4. Centred MA = average of two consecutive 4-pt MAs.
1
Step 1 · First 4-Point MA
Calculate the 4-point moving average for the window Q1, Q4 (Summer, Autumn, Winter, Spring of Year 1).
Add the four sales values and divide by 4. This smooths out all four seasons equally.
💡 (80 + 60 + 50 + 70) ÷ 4 = ? ÷ 4
✅ MA(Q1, Q4) = 65. One season worth of smoothing done.
2
Step 2 · Next 4-Point MA
Calculate the 4-point moving average for the window Q2, Q5. The window shifts one quarter forward.
This time you're averaging Q2, Q3, Q4 and Q5, the window "moves" one step along the data.
💡 (60 + 50 + 70 + 90) ÷ 4 = ? ÷ 4
✅ MA(Q2, Q5) = 67.5. The average is rising, promising sign.
3
Step 3 · Centre the Moving Averages
MA(Q1, Q4) = 65 and MA(Q2, Q5) = 67.5. These two averages sit on either side of Q3. Calculate the centred moving average at Q3.
CMA = average of the two consecutive 4-pt MAs. This "centres" the value so it aligns with an actual quarter.
💡 CMA = (65 + 67.5) ÷ 2. Average the two 4-pt MAs.
✅ CMA at Q3 = 66.25. Now the trend value aligns with a real quarter.
4
Step 4 · Peak Season Finder
Looking at the raw data, which quarter number (1 to 8) had the highest sales?
Just scan the table, which single quarter sold the most? Enter the quarter number.
💡 Look at the Sales column: 80, 60, 50, 70, 90, 70, 60, 80. Which is largest?
✅ Q5 (Summer, Year 2) had the highest sales at $90,000, the second summer beat the first!
5
Step 5 · Read the Trend
The full set of 4-point centred moving averages for this dataset are: 66.25, 68.75, 71.25, 73.75.
What is the trend? Enter 1 for increasing, 2 for decreasing, 3 for no clear trend.
Compare the CMA values from first to last, are they going up, down, or staying roughly the same?
💡 66.25 → 68.75 → 71.25 → 73.75. Is each number bigger or smaller than the last?
✅ The trend is increasing! The CMAs grow by exactly 2.5 each quarter, consistent upward trend.
6
Step 6 · Predict the Pattern
The 4-point moving averages form this sequence: 65.0 → 67.5 → 70.0 → 72.5 → 75.0 → ?
If this pattern continues, what would the next 4-point moving average be?
Spot the pattern in consecutive MAs. What is the common difference? What comes after 75.0?
💡 65, 67.5, 70, 72.5, 75, what is the difference between each consecutive pair? Add that to 75.
✅ The next MA = 77.5. The sequence increases by 2.5 each time, an arithmetic pattern.
☕
Second Cup: Approved!
The analysis is done. Maria's centred moving averages show a clear, consistent upward trend of $2,500 per quarter, even after removing the seasonal summer spikes. The underlying business is genuinely growing.
She signs the lease. Second Cup opens in spring. ☕☕
4-pt MA = sum of 4 consecutive values ÷ 4 ·
CMA = average of consecutive 4-pt MAs ·
rising CMAs = upward trend