## Use MEDIAN function to calculate overlapping ranges

I found an old post that I think is interesting to write about today. Think of two overlapping ranges, it may be dates, times or whatever, the formula demonstrated here works with everything.

This picture shows two time ranges, 06:00-13:00 (yellow) and 11:00-18:00 (green).

It is obvious that there are two overlapping hours but how do we calculate it in excel?

The MEDIAN function comes to rescue, but first let me explain the function. It returns a value that separates the higher half of a data set from the lower half. Example, MEDIAN(1,2,3) returns 2. 1 is the lower half and 3 is the higher half.

MEDIAN(1,2,3,4,5,6) returns 3.5 because there are two values (3, 4) separating the higher half (5,6) from the lower half (1,2). The average of these two values is 3.5.

### Calculate overlapping hours

We have 4 times here to remember, the start and end of time range 1 and 2.

Let see what happens if we use the MEDIAN function with the start and end value of time range 1 and only the start value of time range 2.

MEDIAN("06:00", "13:00", "11:00") returns 11:00.

And then the end of time range 2.

MEDIAN("06:00", "13:00", "18:00") returns 13:00

13:00 - 11:00 is 02:00. Two hours are overlapping.

The formula becomes

and returns 02:00.

### Lets do something more complicated

Between 00:00 and 08:00 the rate is 8, 08:00-18:00 the rate is 5 and 18:00 to 24:00 the rate is 10.

How do we **calculate total cost** if the time range is 06:00-20:00?

Count overlapping hours for the first range 00:00-08:00 and multiply with rate 8.

returns 16.

Count overlapping hours for the second range 08:00-18:00 and multiply with rate 5.

returns 50

Count overlapping hours for the second range 18:00-24:00 and multiply with rate 10.

returns 20

Combining all formulas gives

returns 86.

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### Download *.xlsx file

Median - overlapping ranges.xlsx

### I have a question for you

It would be great to build an array formula to shrink the formula above, like this one:

But it won´t work, you can´t use the MEDIAN function to do that. Do you know a workaround?

### 8 Responses to “Use MEDIAN function to calculate overlapping ranges”

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Great post! Here's a solution, which uses a couple of (changeable) assumptions:

=SUMPRODUCT(FREQUENCY(ROW(INDIRECT("A"&HOUR(A7)+ 1&":A"&HOUR(B7))), HOUR(C2:C3)), D2:D4)

By quantizing the time (into hours in this case), and then counting the quantity in each rate bucket, we can then do a SUMPRODUCT against the rates. Remember that the FREQUENCY function returns one more item than the number of buckets passed to it, so I left out the final bucket time to compensate.

-Alex

Alex,

fantastic, why didn´t I think of that.

Thank you for your valuable comment!

I'm willing to take my medicine if there's something simple in here that I should have seen, but here goes...

How do I find overlapping ranges (using the MEDIAN function) for three to six time ranges? Or do I have to figure each range separately, then combine it into one IF statement using AND statements?

Forgot to add something to my previous post:

There are a variable number of time range(s) within each day - anywhere from 0 to 4 time ranges - and the number of ranges may change from day to day. Any formula must be able to handle this.

Henry Dishington,

Do you want to find overlapping ranges? Read this:

http://www.get-digital-help.com/2013/11/26/identify-overlapping-records/

Or do you want to count overlapping days?

Another solution at your quest, with CSE formula:B2:B4,$A$7,B2:B4)>0,IF($B$7 B2:B4,$A$7,B2:B4),0)*D2:D4*24)

=SUM(IF(IF($B$7

for some unknown reason, previous paste was an error.

Correct formula is:

{=SUM(IF(IF($B$7A2:A4,$A$7,A2:A4)>0,IF($B$7A2:A4,$A$7,A2:A4),0)*C2:C4*24)}

O, no, not again!

I try to upload a file.