The five-median smoothed value for September 1998 was closest to:

Question

BlackTom AI · Accepted Answer

We start by identifying the target time point: September 1998 on the plotted series.

Option by option comparison:
- Option a (62): If the September 1998 smoothed value were exactly 62, the line would need to sit at or near 62 on the vertical axis. Looking at the graph, the September 1998 data point sits somewhat above 60 but does not reach 62 in a way that aligns with a five-month median smoothing peak around that month. The discrepancy appears larger than with other nearby values.
- Option b (68): The five-month smoothed value around September 1998 tends to pull upward from previous months due to the recent rise in the line. The smoothed value sits closer to the upper mid-60s, around 68, which matches the observed trend of a rising sequence entering September. This makes 68 a plausible closest value after considering the smoothing effect.
- Option c (66): A smoothed value of 66 would be plausible if the month-to-month data were centered a bit lower; however, the recent uptick in the window around September 1998 typically yields a value a notch higher than 66, making 66 a less accurate fit than 68 when the five-month median is computed.
- Option d (64): While 64 is near the mid-60s, the smoothing window around September 1998 leans toward a higher figure due to the preceding increases. Thus 64 underestimates the smoothed value relative to the observed smoothing trajectory for that period.

Synthesis: The five-month median smoothing around September 1998 combines the recent rise from prior months and the influence of adjacent observations. The resulting smoothed value lies in the upper mid-60s, making 68 the closest match among the given options when compared to the other nearby candidates. The other choices (62, 66, 64) are all farther from this smoothed estimate given the observed trend in the window.

The five-median smoothed value for September 1998 was closest to:

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