Frequency distribution

[initial response deleted]

After looking at your data, I don't think your question is well-formulated. You have activities with a Start and Stop time. For a given interval, what you do want to count?

The number of activities that start in that interval
The number of activities that end in that interval
The number of activities that have any portion of time in that interval

For questions like this it's always helpful to include a sample of what you want the result to be.

In the spirit of divide and conquer, here's how I developed what appears to be a workable solution:

1) As much as I might have liked to use the FREQUENCY() function, with some of the anticipated other steps along the way, I decided that the COUNTIFS() function would be more useful. Can I assume you are familiar with the COUNTIFS() function (https://support.office.com/en-us/art...c-aa8c2a866842 )? Once I had chosen the COUNTIFS() function as my desired function, everything else seemed like the underneath problem (not necessarily Excel specific) of figuring out the logic needed to correctly count each entry.
2) First step seemed to be to count how many start times are after each time interval. COUNTIFS(start_times,"<="&time_interval) (replace text with appropriate references, and pay attention to relative and absolute references so that the formula will be easy to copy).
3) The other half of the count is determining how many end times are before a given time interval (a similar COUNTIFS() function to the previous).
4) The actual count you want is to count all of those that start after the time interval, and then remove those that ended before the time interval -- effectively (result of step 2)-(result of step 3).
5) That will fail to capture the "partial" time intervals, so I thought, if I can get the start_times to round down to the nearest 15 minutes and the end-times to round up to the nearest 15 minutes, I should be able to capture the partial intervals as well. The functions for these are the FLOOR() and CEILING() functions, so I added a couple of helper columns adjacent to the start and end times to perform these calculations. help file for FLOOR() function https://support.office.com/en-us/art...7-b0b4de5a8886 Ceiling function similar.
6) Then, using these helper columns, instead of the original, as the inputs to steps 2 and 3, I think I got pretty close to what you want.

It will be valuable to take joeu2004's comment about floating point rounding errors into consideration, as they could cause something to be miscounted.

As one who hates trying to cram a lot into a single cell, I spread that calculation over several cells, and did not bother trying to nest it all into a single function. I expect it can be done, if needed, but I was too lazy to do it.

Does that work? What part do you get stuck on?

On edit: initially I think I had the inequality inverted in step 2. I think it is correct now, though, as soon as I start second guessing myself, I get lost in trying to decide. You may need to double check that part of the logic and make sure the inequality is pointed the right way.