Spring is in the air, and Easter is coming up soon! Easter occurs relatively late this year, on April 21. Some years it seems early and some it seems late. So I started wondering about the distribution of Easter dates. Which dates are more common and which are less common?
Even after reading the official definition of when Easter occurs, I still wasn’t clear about the date range. Easter occurs on the Sunday that follows the Paschal Full Moon date for the year. The Paschal Full Moon is the Ecclesiastical Full Moon that occurs after March 20. Huh? So, I’m going to use Minitab Statistical Software to help find the answers!
The Gregorian calendar starts in 1582 and is accurate up until 4099. For once, we won’t be looking at a sample but rather the entire population of the 2,517 Easters that fall within the Gregorian calendar! You can get the Minitab worksheet here.
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Graphing the Distribution of the Easter Dates: 1583 to 4099
When you want to get a quick feel for the data, it’s a good idea to graph the distribution. Below is a bar chart that displays the number of times that Easter falls on any given date. The graph uses codes for the dates on the X-axis. For example, M31 is March 31 and A1 is April 1.
By looking at the range of the X-axis, we can see that Easter occurs from March 22 to April 25, or 35 possible dates. The broad middle of the distribution bubbles up and down around the average of 72 occurrences per date. The most common date is April 10, with 102 occurrences (4.05%). The least common day is March 23, with only 14 occurrences (0.56%).
You only start to get extremely rare dates for Easter with the earliest three (March 22 – 24) and latest three (April 23 – 25) possible dates. The right tail of the distribution is thicker than the left tail. This indicates that last three dates occur a bit more often than the earliest 3 dates.
To illustrate this, Easter falls on the earliest date of March 22 only 0.60% of the time. The last time was in 1818 and the next time will be 2285, which is a span of 467 years! On the other hand, Easter falls on the latest date (April 25) 1.03% of the time. The last such occurrence was in 1943, and the next is 2038, or a span of 95 years.
Is April 21 or After Unusual for Easter?
Well, April 21 certainly isn't, relatively speaking. Easter Sunday has fallen on this date 14 times in the past 500 years and it will fall on this date over 70 more times in the next 2,080 years of our calendar. The last time Easter fell on this date was 1957, and we will see it again after this year in 2030, 2041 and 2052.
Let’s use our friend the probability distribution plot to determine how often Easter occurs April 21 or later.
The shaded area indicates that Easter occurs April 21 or later about 10% of the time.
Are There Patterns in the Easter Dates?
After assessing the distribution of Easter dates, I wondered if patterns exist. Specifically, if Easter occurs on date X in one year, when does it first occur on date X again? I’ll graph the frequency of the first recurrences below.
The first thing that stands out in this graph is that large spike at 11 years. This bar indicates that for 1,141 Easters (45%), the date that Easter occurs in one year will first repeat in 11 years.
We are in a time period now that is pretty representative of that trend — four the next 10 Easters (including this one) repeat in the following 11 years.
|April 21, 2019||April 21, 2030|
|April 12, 2020||April 12, 2093|
|April 4, 2021||April 4, 2083|
|April 17, 2022||April 17, 2033|
|April 9, 2023||April 9, 2034|
|March 31, 2024||March 31, 2086|
|April 20, 2025||April 20, 2087|
|April 5, 2026||April 5, 2037|
|March 28, 2027||March 28, 2032|
|April 16, 2028||April 16, 2090|
The other thing that stands out for me is the relative handful of years in which an Easter date can first repeat. For example, an Easter date cannot repeat in 2 years or 7 years, or any of the other large number of possibilities that are not on the graph. It’s definitely not a random distribution!
While the official definition for Easter really didn’t help clarify things for me, I found that normal data analysis methodology provides a very clear picture of when Easter occurs, and what is truly unusual.