Use SQL to Calculate Median Values

In this puzzle, we’re going to learn how to find the person whose birthday, among others, is in the middle. Knowing how to calculate the median value is a good skill to have. As you start to explore business intelligence, you’ll come across similar problems to solve.

Also, be sure to check out the bonus question. We’ll work with date from colonial times. The calendar was different, and you see that the standard DATETIME datatype falls short of our challenge.

Solving puzzles is a great way to learn SQL. Nothing beats practicing what you’ve learned. Once you have figured out the puzzle, post your answer in the comments so we all can learn from one another. We also discuss puzzle and more in Essential SQL Learning Group on Facebook. Be sure to find us there!

Calculate the Median Date Among a List of Dates

Here is today’s puzzle written by Chris Huntley.

You have a list of people with birth dates and want to find the person who has the middle birth date?

In other words, who has the median birth date?

Are you up to the challenge? Can you write a single SQL statement to find this person?

To get started, be sure to download the code samples. You’ll find sample data for this and the bonus question here.

Beware of Date Conversion Issues

The first Idea might be to convert it to an integer and then use that in a sort or to calculate median values. However, depending on how you convert it you may end up with something you don’t want. For example, converting it to a numeric looking string and then into an integer value

Here is one way to convert date to an INT, but not the right way!

SELECT personid,
       personname,
       birthdate,
       CAST(CONVERT(NVARCHAR(10), birthdate,112)as INT) as BirthINT,
       CAST(CONVERT(NVARCHAR(10), birthdate,112)as INT)+1 as BirthINTIncremented,
       CAST(CONVERT(NVARCHAR(10), birthdate,112)as INT)+30 as BirthINTIncrementedMore
FROM   @datetable

A disadvantage of this conversion is shown below. You can increment it like any other integer but it isn’t a date anymore so you get dates that don’t really exist. Incrementing dates should be done with appropriate datatypes and possibly appropriate functions.

Continuing with this idea, we just calculate the median value of this integer and get the following.

-- calculating the median using the converted String
-- using a CTE to reference the conversion
;WITH ctedateconversion AS (
   SELECT personid,
          personname,
          birthdate,
          CONVERT( INT, Birthdate) as BirthINT
   FROM   @datetable
)
SELECT CONVERT(DATETIME,
               SUM(birthint)/(SELECT COUNT(*) FROM cteDateconversion)) As meanbirthdate
FROM ctedateconversion 

We do get the median date but it’s not a date on our list meaning it doesn’t represent a person in our table.
If we remove the outside conversion back into a date

SUM(birthint)/(SELECT COUNT(*) FROM cteDateconversion) As meanbirthdate

we would have received the value 29438

Which is the number of days since 1/1/1900.

If you want to confirm this, use the following code:

SELECT DATEDIFF(dd, '1900-01-01 00:00:00','1980-08-07 00:00:00.000')

Answer to Calculating the Median Date

To get the median birth date, I decided to use (2) PERCENTILE_DISC. PERCENTILE_DISC computes a specific percentile for a distribution, which in our example, is a list of dates. Specifying PERCENTILE_DISC (.5) calculates the 50^th percentile, which happens to be the median.

;with ctedateconversion as(
   SELECT personid,
          PersonName,
          Birthdate,
          Percentile_Disc(0.5) within group (order by Birthdate) OVER() as MedianBirthDate
   FROM   @datetable
)
SELECT personname,
       birthdate
FROM   ctedateconversion
WHERE  Birthdate = MedianBirthDate

This gives us the answer.

There’s more than one way to get the answer you seek. How did you accomplish this task?

Bonus Question

Find the specific presidents that were the mean age of all presidents when they entered or left the presidency. Specifically, either they were the mean age of all presidents when they entered or the mean age of all presidents when they left This requires you to consider the datatypes you use carefully. The analyst who collected this data for you gave it to you in a denormalized format with everything in a string datatype since they couldn’t get DATETIME to work.

To get started, be sure to download the code samples. You’ll find sample data for the bonus question here.

Sample Data

The first thought might be convert it to a DATETIME then just do the math. If you try that, you’ll find an error.

SELECT President,
       Convert(DATETIME, Birthdate) as Birthdate,
       Convert(DATETIME, TermStart) TermStart,
       Convert(DATETIME, TermEnd) as TermEnd
FROM   Presidents

Why?

DATETIME has a history and the dates it can hold are limited to dates greater than 1/1/1753. The history is that Pope Gregory, for whom the calendar is named, in 1582 enacted reform to change from the Julian to Gregorian calendar.

It took Britain and the Colonies quite a while to get around to it and they finally decided that 1752 would be the change over. In order to make the change over, they had to drop 11 days from September 1752.

Way back when they were designing SQL server, they chose to just ignore this period and support from 1753 onward using the Gregorian Calendar.

An option might be convert to DATETIME2 which is Gregorian and supports all dates down to 00/00/0001 which makes it compatible with other DBMS.

SELECT President,
       Convert(DATETIME2, Birthdate) as Birthdate,
       Convert(DATETIME2, TermStart) TermStart,
       Convert(DATETIME2, TermEnd) as TermEnd
FROM   Presidents

How do we want to get this data? We can use chained CTEs (Common Table Expression) so we can convert and then perform the calculations as follows:

; with ctepresidents as(
   SELECT President,
          Convert(DATETIME2, Birthdate) as Birthdate,
          Convert(DATETIME2, TermStart) TermStart,
          Convert(DATETIME2, TermEnd) as TermEnd
   FROM Presidents
)
,
CTESTEP2 as(
   SELECT President,
          CAST(DATEDIFF(dd, birthdate, termstart)/365.0 as INT) as startage,
          CAST(DATEDIFF(dd, birthdate, termend)/365.0 as INT) as endage
   FROM ctepresidents
)
,<span style="color: #339966;">ctefinal as(
   SELECT   CAST(SUM(startage)/(select COUNT(*) FROM Ctestep2)as INT) as meanStartAge,
            CAST(SUM(endage)/(select COUNT(*) FROM Ctestep2)as INT )as meanendAge
   FROM CTESTEP2)
,cteconnectingitall as(
   SELECT President
   FROM   CTESTEP2 c
          INNER JOIN <span style="color: #339966;">CTEFINAL f
          on c.startage = f.meanStartAge
   UNION ALL
   SELECT President
   FROM   <span style="color: #339966;">ctefinal ff
          INNER JOIN CTESTEP2 cc
          ON cc.endage = ff.meanendAge
)
SELECT * FROM cteconnectingitall

Giving us:

• The mean age of start of a presidential term is: 54
• The mean age of the end of a presidential term is: 59

Just to make confirmation easier, here’s the code:

;with ctepresidents as(
   SELECT President,
          Convert(DATETIME2, Birthdate) as Birthdate,
          Convert(DATETIME2, TermStart) TermStart,
          Convert(DATETIME2, TermEnd) as TermEnd
   FROM   Presidents
)
,
CTESTEP2 as(
   SELECT President,
          CAST(DATEDIFF(dd, birthdate, termstart)/365.0 as INT) as startage,
          CAST(DATEDIFF(dd, birthdate, termend)/365.0 as INT) as endage
   FROM ctepresidents
)
SELECT * FROM CTESTEP2
WHERE  startage = 54
       OR endage = 59

How did you get the answer? Did you have a flatter and easier way?

Bio

This blog was authored by Chris Huntley. He is a Business Intelligence Developer living in Dallas Fort Worth. He loves data, the Microsoft Bi Stack and tacos not necessarily in that order.

Chris frequently helps fellow SQL coders.