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 **
I see the numbers from 1 to 10 in the first column, and in the second column I see numbers increasing in value and in the third column I see the difference between the numbers in the second column.
** Your TIMER data from 20 fast clicks **
1 588.6875 588.6875
2 588.8281 .140625
3 588.9531 .125
4 589.0625 .109375
5 589.1875 .125
6 589.2969 .109375
7 589.4219 .125
8 589.5469 .125
9 589.6563 .109375
10 589.7969 .140625
11 589.9063 .109375
12 590.0313 .125
13 590.1563 .125
14 590.2813 .125
15 590.4375 .15625
16 590.5781 .140625
17 590.7344 .15625
18 590.875 .140625
19 591.0156 .140625
20 591.1563 .140625
21 591.2813 .125
** Your average time interval for 20 time intervals **
0.129688
I added up all the numbers and divided by 20.
&#If you divide the difference between the 1st and 20th time clock times by the 20 - 1 = 19 time intervals you would get the average time interval, and this will agree with the average you obtained by adding the 19 intervals and dividing by 19.
More generally, if you take the difference between two clock times and the difference between their numberings, i.e., subtract the second-column numbers, subtract the first-column numbers and divide, you will get the average of the time intervals between those clock times. &#
** Your frequency distribution for the 20 time intervals (interval, number of times it was observed) **
0.14063, 6
0.125, 8
0.15625, 2
0.10938, 4
** Your general comment to this point **
I understand the process so far.
** Why did you observe only certain time intervals? **
The timer program is not necessarily flawed, it just does not detect times accurately at such small intervals. Maybe if the intervals were farther apart they would be more accurate.
** What did you see when you looked at the differences between time successive time intervals? **
This tells you that there is sometimes a negative difference from one time interval to the next and sometimes a positive difference. This means that the time intervals are increasing and decreasing around a certain number. It is not always exactly on that number everytime, but it is very very close to that number every time.
** Your time intervals for 7 complete breaths: **
5.484375
4.265625
3.765625
3.34375
4.09375
3.90625
4.078125
** Your general comment to this point: **
** Why did you rarely, if ever, observe that same time interval twice? **
Because the time intervals were farther apart.
** Do you think this program is accurate to .1 or .01 ... **
I think the answer is a, because once the difference between the number starts getting smaller (.01 or less) you start seeing the same numbers more and more often.
** Copy of a few lines of your spreadsheet from the TIMER program. **
Breathing exercise
event number clock time time interval
1 2490.578 2490.578
2 2496.063 5.484375
3 2500.328 4.265625
4 2504.094 3.765625
** **
Thiry minutes
** **
&#Veryood work. Let me know if you have questions. &#