The five-median smoothed value for March 1999 was closest to:

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The task asks us to determine which option is closest to the five-median smoothed value for March 1999, using the provided graph of rooms (%) over time.
First, inspect the plotted data around March 1999. The March 1999 point sits near the mid-60s on the vertical axis, with the surrounding months showing values roughly in the 60s to low 70s range. This places the March 1999 smoothed value in a neighborhood around 66–67 percent rather than at the extremes of 60s or 70s.
Option a: 68. This is a plausible value in the upper 60s, but looking at the exact position of March 1999 on the graph, the point appears slightly below 68, making 68 somewhat higher than the smoothed value at that month.
Option b: 66. This aligns well with the observation that March 1999 sits near the mid-60s, and 66 is a reasonable closest integer in that range given the smoothing.
Option c: 63. While 63 lies in the 60s, the March 1999 point appears higher than 63, closer to mid-60s or slightly above, so 63 is likely too low to be the closest.
Option d: 62. This value is even lower and would be farther from the March 1999 smoothed reading than 63 or 66, making it a poorer match.
To determine closeness, compare the visual distance from the March 1999 mark to each candidate value: 66 sits near the central tendency shown for that period, while 68, 63, and 62 deviate more noticeably from the plotted point. The intention of a five-median smoothing is to reduce month-to-month volatility while preserving overall level, so a value around 66 makes conceptual sense for March 1999.
In summary, among the given options, the one that best matches the March 1999 smoothed value on the graph is the estimate around 66, with 68 being a small overestimate and 63 or 62 being too low for that month.

MUF0142 Fund. Mathematics Unit 2 - Semester 1, 2025 8.6 Time Series: Smoothing Quiz (Formative)

The five-median smoothed value for March 1999 was closest to:

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