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Can you determine the impact a sub-set of data has on the overall nth percentile?

For example, imagine I am studying the time it takes to deliver a baby. I have data from hospitals spanning the month of September 1972, and the delivery time in the 60th percentile for the entire month's worth of data was 4 hours. However, on September 24 1972 I know that hospital workers were working slowly - sneaking away from their posts to watch sports coverage of game 6 in the Canada versus Soviet Union Summit Series. For that one day's worth of data, the delivery time 60th percentile is notably higher than the rest of the month's - 7 hours.

How can I determine what impact (in hours/minutes) the game had on the delivery time 60th percentile for the month? Can I determine it at all? What data would I need?

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