The time series plot below shows the number of hours of sunshine in a day for 16 days in a month.The 5-median smoothed value for the seventh day is closest to

Question

BlackTom AI · Accepted Answer

To answer, we need to consider a 5-day window centered on day 7 and find the median of the sunshine hours in that window.
Option A: 9.0. If the days in the window (days 5–9) have values approximately 8, 9, 10.5, 9, and 6, the sorted order is 6, 8, 9, 9, 10.5, giving a median of 9.0. This makes A a plausible match.
Option B: 8.0. If the median were 8.0, at least two middle values would need to be at or below 8, which isn’t consistent with the central values around day 7 (which include a value near 9–10). Thus 8.0 is unlikely.
Option C: 10.0. The middle of the five values would be 10 only if the sorted middle value were 10, but with the observed days 5–9, the middle value is closer to 9, not 10.0. So this is not supported by the data.
Option D: 6.5. This would require the middle value to be around 6.5, which would imply several small values in days 5–9, but the window includes values around 8–10, making 6.5 too low for the median.
In summary, the 5-day window around day 7 yields a set roughly like (8, 9, 10.5, 9, 6), whose median is 9.0, making option A the closest value.

The time series plot below shows the number of hours of sunshine in a day for 16 days in a month.The 5-median smoothed value for the seventh day is closest to

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