What statistics to use? beginner question.

Hello, I have 24 hour continuous heart rate information for patients with various heart diseases. I have created a matlab script that pulls 5 minute average heart rates for the 24 hour period. The ultimate goal is to find the shortest duration of the recording to get average heart rate that falls with in the 5+- of the 24 hour heart rate(true heart rate). If I try continuous cumulative recording it take at least 6 hours of recording to get heart rate that is similar to true heart rate due to unpredictability in high and low heart rate periods through the day. Now I am trying to find out how many of the random 5 minute recording at various times of the day is needed to get a mean heart rate similar to 24 hour mean heart rate. My understanding of the statistics is not great and i am hoping to get some inputs what would be best statistical method to use for sampling. ? Any inputs or ideal will be greatly appreciated.