Bike-Share Data Interpretation
A city publishes bike-share usage for four quarters. Riders: Q1 = 1,200; Q2 = 1,800; Q3 = 2,700; Q4 = 1,500. A council member says, 'Usage grew 125% from Q1 to Q3 and then fell, so the program is declining.' A staffer counters that the pattern is seasonal and that year-over-year data is needed. The council has ridership goals of 2,000 average per quarter. They ask you to interpret the numbers honestly before the next budget vote.
1. Compute the percent change from Q1 to Q2, Q2 to Q3, and Q3 to Q4. Then compute the average quarterly ridership for the year and state whether the 2,000 goal was met.
Read the worked answer
Q1→Q2: (1800 − 1200)/1200 = 600/1200 = 50% increase. Q2→Q3: (2700 − 1800)/1800 = 900/1800 = 50% increase. Q3→Q4: (1500 − 2700)/2700 = −1200/2700 ≈ −44.4% (a decrease).
Average = (1200 + 1800 + 2700 + 1500)/4 = 7200/4 = 1,800 per quarter.
The 2,000 goal was not met; the average fell 200 short, about 10% below goal.
2. Evaluate the council member's claim that 'the program is declining.' What does the data actually support, and what additional data would settle the question?
Read the worked answer
The claim overstates the evidence. The Q3→Q4 drop is real (−44%), but Q4 (1,500) is still 25% above Q1 (1,200), and the year's average (1,800) exceeds Q1 by 50%. A single quarter-over-quarter decline after a summer peak is consistent with seasonality, not necessarily a downward trend.
To settle it, compare the same quarter across years (e.g., Q4 this year vs. Q4 last year). If Q4 is up year-over-year, the drop is seasonal; if down, the decline claim gains support. Two data points (a peak and a dip) cannot establish a trend.