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 **
There are a list of 10 rows, each row with 2 columns of numbers. The row on the right seems to be the differences in seconds between each click.
** Your TIMER data from 20 fast clicks **
1 141.4023 141.4023
2 141.543 .140625
3 141.6719 .1289063
4 141.8164 .1445313
5 141.9531 .1367188
6 142.1055 .1523438
7 142.2344 .1289063
8 142.3867 .1523438
9 142.5156 .1289063
10 142.6641 .1484375
11 142.8047 .140625
12 142.9453 .140625
13 143.0977 .1523438
14 143.2461 .1484375
15 143.3984 .1523438
16 143.5273 .1289063
17 143.6758 .1484375
18 143.8281 .1523438
19 143.9883 .1601563
20 144.1367 .1484375
21 144.2969 .1601563
22 144.4492 .1523438
23 144.5898 .140625
24 144.7383 .1484375
** Your average time interval for 20 time intervals **
0.144726595
Excel, using the avg function.
How would you calculate that without Excel? What does the average really mean?
&#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) **
0.1289063, 4
0.1367188, 1
0.140625, 3
0.1445313, 1
0.1484375, 4
0.1523438, 5
0.1601563, 2
** Your general comment to this point **
none
** Why did you observe only certain time intervals? **
I think that the program has some predetermined times and when you click the button, your time falls into a specific time interval which is assigned to one of the predetermined times (whichever one it's closer to). So in reality the program is more of an interval estimator. It's not useless, but past probably 2 significant digits, it should not be too heavily relied upon.
** What did you see when you looked at the differences between time successive time intervals? **
It supports my theory that there are a predetermined list of times that are evenly spaced apart.
** Your time intervals for 7 complete breaths: **
4.976563
4.996094
5.269531
5.617188
5.367188
5.007813
5.378906
5.957031
5.648438
5.417969
** Your general comment to this point: **
none
** Why did you rarely, if ever, observe that same time interval twice? **
The predetermined times I previously mentioned are probably all very close together (as in, maybe only .001 seconds apart). When we increased the time between clicks using breathing, it lessens the chance of having clicks being near the same time.
** Do you think this program is accurate to .1 or .01 ... **
c.
&#What is the basis for your answer? You need to include details.
&#
** Copy of a few lines of your spreadsheet from the TIMER program. **
clicks between 10 relaxed breaths
event number clock time time interval
1 977.1758 977.1758
2 982.1523 4.976563
3 987.1484 4.996094
4 992.418 5.269531
5 998.0352 5.617188
6 1003.402 5.367188
** **
20 minutes
** **
none
&#Good work. See my notes and let me know if you have questions. &#