Estimating the world sleeping population required:
Determining the world population by time zone: Country populations and time zone data was sourced from Wikipedia. For the approximately 2 dozen countries with multiple time zones, further analysis was undertaken to determine the split of population by time zone.
Adjusting population for daylight savings: Population / time zone data was further adjusted for daylight savings time where applicable. This resulted in the estimate of world poulation by time zone below.
Estimating peak sleep time: Based on data published by Sleep Cycle, an app used by millions worldwide to track sleep, an estimate of peak sleep time (the time the greatest proportion of the population is asleep) was estimated at 03:56 local time.
Assumption on peak and trough people sleeping: In many developed countries, roughly 15% of the workforce works night shifts. Adjusting for the young and elderly, it was assumed that 90% of the population was asleep at peak times and that at any given time at least 10% of the population would be sleeping.
Assumption on amount of sleep: For the purposes of this anaylis, it was assumed that the population sleeps on average 8 hours.
Distribution of sleeping population: A normal distribution was applied to determine the proportion of the population sleeping such that the average over a day was 8 hours and that the peak and trough would be 90% and 10% respectively. This resulted in the distribution below.
World Population by Time Zone (UTC)
Note: Chart does not show +5.75 time zone which comprises approximately 0.39% of world population
Indvidual Time Zone Sleep Distribution by Local Time