Aggregating percentiles by averaging them, whether weighted or not, does not provide an accurate representation of the overall percentile for the aggregated time period.
Percentiles, by definition, represent the value below which a certain percentage of observations fall. In your example, the 100th percentile (maximum value) for each minute interval is given, and attempting to average these values does not yield the correct 100th percentile for the entire 15-minute period.
The reason for this is that percentiles are not additive or linearly combinable. Each percentile value represents a specific point in the distribution of the data, and averaging them does not consider the underlying distribution of the data points.
In your example, the correct 100th percentile for the 15-minute period is indeed 601, which is the maximum value observed across all the minute intervals. No matter how you average the individual 100th percentiles, you cannot arrive at this value.
Similarly, aggregating other percentiles, such as the 95th percentile, by averaging them would not provide an accurate representation of the overall percentile for the aggregated time period.
To correctly aggregate percentiles, you would need to collect and consider the entire set of raw data points for the desired time period (e.g., last day, week, or month) and then calculate the percentile directly from that combined dataset. This ensures that the distribution of the data is taken into account when determining the aggregated percentile value.
In summary, aggregating percentiles by averaging them is not a valid approach. To obtain accurate aggregated percentiles, you need to consider the entire dataset for the desired time period and calculate the percentiles directly from that combined data.