Your 'timer program' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
Your General Comment
Describe what you see on your first 10 clicks
The timer program created three columns. The first column is just a list from 1-10, everytime I clicked the button. The second column is a the total amount of time that has passed since the program was opened. The third column is the time since I last clicked the button for each event. This program serves as a timer like a stopwatch.
Your TIMER data from 20 fast clicks
1 163.4355 163.4355
2 163.5879 .1523438
3 163.7461 .1582031
4 163.8965 .1503906
5 164.0371 .140625
6 164.1973 .1601563
7 164.3477 .1503906
8 164.5176 .1699219
9 164.6582 .140625
10 164.8281 .1699219
11 164.9883 .1601563
12 165.1094 .1210938
13 165.2695 .1601563
14 165.418 .1484375
15 165.5781 .1601563
16 165.7207 .1425781
17 165.8691 .1484375
18 166.0293 .1601563
19 166.1895 .1601563
20 166.3496 .1601563
21 166.541 .1914063
Your average time interval for 20 time intervals
0.1552735
I got this number by adding up all 20 intervals and then dividing by 20. I couldn't think of a faster way to get the average.
Your frequency distribution for the 20 time intervals (interval, number of times it was observed)
0.1210938, 1
0.1406250, 2
0.1425781, 1
0.1484375, 2
0.1503906, 2
0.1523438, 1
0.1582031, 1
0.1601563, 7
0.1699219, 2
0.1914063, 1
Your general comment to this point
Why did you observe only certain time intervals?
No, the TIMER program isn't flawed or useless. It has certain numbers programmed into it and when you hit the button, it spits out the number it has that's nearest when you hit it. It's still a fairly valid way of taking timed measurements.
What did you see when you looked at the differences between time successive time intervals?
The TIMER only contains values that are multiples of 0.01563.
Your time intervals for 7 complete breaths:
7.492188
7.046875
7.851563
7.503906
7.359375
6.6875
6.703125
8.03125
6.808594
7.703125
Your general comment to this point:
Why did you rarely, if ever, observe that same time interval twice?
Maybe because breathing does not produce as exact a pattern as clicking as fast as possible. If you click as fast as you can, it's likely that you will be able to get a higher frequency because of the time lapsing per click. With breathing, you are letting so much time go by that it will be extremely difficult to hit the same number when the numbers are changing by .01563 with each moment.
Excellent observation.
Note that 1/64 = .015625. Every number is exactly a multiply of this number.
64 being a power of 2, and computers being based on binary coding, this is not surprising.
Do you think this program is accurate to .1 or .01 ...
The program is probably accurate to at least 0.01 seconds (b), and maybe even one more decimal. Since it is increasing by a specified interval, it cannot be infinitely accurate and 0.01 seems the most reasonable.
.015 is greater than .01, which is the resolution of the timer. The program can't be accurate to more than the resolution, but the degree of accuracy is closer to .01 than to .1.
Copy of a few lines of your spreadsheet from the TIMER program.
fast click
event number clock time time interval
1 8.28125 8.28125
2 8.464844 0.1835938
3 8.632813 0.1679688
4 8.804688 0.171875
5 8.953125 0.1484375
It took me about 20 minutes to complete this experiment, but I was interrupted several times.
Good work. See my notes.