PHY 231
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 **
30 Minutes
** #$&*Your TIMER data from 20 fast clicks **
Operating the TIMER program
It is easy to operate the Timer program. All you have to do is click on the button labeled Click to Time Event.
Click that button about 10 times and describe what you see.
I see a two column table of ten times. The left-hand column has the original times. And the right-hand column has the added difference between the present column and the previous one, except for the first statistic, which just repeats the first original time.
#$&*
Now click on Initialize Counter, which will clear all the data from the timer window. Click the mouse as fast as you can until the TIMER window fills up. Be sure you get at least 20 time intervals.
If you miss a click, try again. Keep trying until you get at least 20 intervals without a missed or delayed click.
Copy your data starting in the next line:
1 11.94141 11.94141
2 12.125 .1835938
3 12.29883 .1738281
4 12.46582 .1669922
5 12.59473 .1289063
6 12.74512 .1503906
7 12.8916 .1464844
8 13.04004 .1484375
9 13.17676 .1367188
10 13.33496 .1582031
11 13.49707 .1621094
12 13.64355 .1464844
13 13.80664 .1630859
14 13.96289 .15625
15 14.15234 .1894531
16 14.30371 .1513672
17 14.45801 .1542969
18 14.63672 .1787109
19 14.80273 .1660156
20 14.9668 .1640625
21 15.1123 .1455078
22 15.27246 .1601563
#$&*
You got at least 20 time intervals. Based on your data what was the average of the first 20 time intervals? Note that you could get this average by averaging the first 20 intervals. My first few intervals were .15625, .15625, .1875, .171875, etc; I could just add up the first 20 intervals and divide by 20 to get the average. However there is an easier and quicker way to get the result, so use the easier way if you can.
Give your result, number only, in the first line, and starting in the second line explain how you got it.
.1586214286
I obtained my solution by subtracting the first number from the 22nd ( which adds up all of the intervals ); then, I divided it by 21, the number of intervals.
#$&*
When I did this activity the first few lines of my data were as follows:
event number clock time time interval
1 11.67188 11.67188
2 11.875 0.203125
3 12.0625 0.1875
4 12.20313 0.140625
5 12.375 0.171875
6 12.54688 0.171875
7 12.73438 0.1875
8 12.92188 0.1875
9 13.10938 0.1875
10 13.28125 0.171875
11 13.4375 0.15625
It looks like the same intervals keep popping up. For example .1875 seconds occurs 5 times out of the first 10 intervals, .171875 seconds occurs three times, and .203125 seconds, .140625 seconds and .15625 seconds each occur once.
A frequency distribution for my time intervals would be as follows:
time interval frequency
,140625 1
.15625 1
.171875 3
.1875 5
.203125 1
What different time intervals did you observe in your first 20 intervals, and how many times did each occur? List below the different time intervals you observed and the number of times each occurred. List from the shortest to the longest interval, and use a comma between the time interval and its frequency. For example my data above would be listed at
.140625, 1
.1565, 1
.171875, 3
.1875, 5
.203125, 1
Your list should be in exactly this format, with no other symbols or characters.
.1289, 1
.1367, 1
.1455, 1
.1465, 2
.1484, 1
.1504, 1
.1514, 1
.1543, 1
.1563, 1
.1582, 1
.1621, 1
.1631, 1
.1641, 1
.166, 1
.167, 1
.1738, 1
.1787, 1
.1836, 1
.1895, 1
#$&*
You may make any comments or ask any question about the process so far in the box below
#$&*
On the 10 intervals I've shown you, do you really think I managed to get a time of .1875 seconds, accurate to 4 significant figures, on half of the intervals? If you do, I'm grateful for your confidence but I'm just not that good. No human being has that much neurological and muscular control.
So why do you think the TIMER program reported that time so frequently? Why weren't there times like .1830 seconds, or .1769 seconds? Does this mean that the TIMER program is flawed? Does that mean it's useless?
No, I do not believe you were able to repeatedly get a time of .1875 for half of the intervals. The TIMER program reported that time so frequently because it probably cannot capture the exact time that you press the button. It has an error, but the TIMER program probably also rounds to nice neat numbers to four significant decimal places. The probability of me hitting the button to get a number rounded to four decimals exactly or less is highly unlikely. With all machines and humans, there is an error and a loss of accuracy because we are not perfect. The program is naturally flawed, but that does not mean that it is useless; it just means like everything else, it is not perfect. We simply must be aware of this when reporting results. Even stopwatches and clocks have errors. For instance, between the time you think about pressing the button and when you actually do, there is time between that transition, that we often never account for.
#$&*
Here are a few more lines of data, with an added column showing the difference between each time interval and the next.
clock time time interval difference from one time interval to next
9 13.10938 0.1875 -0.01563
10 13.28125 0.171875 -0.01563
11 13.4375 0.15625 0.03125
12 13.625 0.1875 -0.01563
13 13.79688 0.171875 0.015625
14 13.98438 0.1875 0.015625
15 14.1875 0.203125 -0.03125
16 14.35938 0.171875 -0.01563
17 14.51563 0.15625 0.03125
Take a good look at that last column and tell us what you see in those numbers, and what this tells you about the TIMER program
All of the numbers in the last column end in 3 or 5, making them look nice and tidy. The TIMER program has a lack of accuracy. Between intervals, as I have noticed, sometimes, it rounds and other times it does not. It uses significant figures it appears. Thus, the results, when compared against equal interval differences, may not be exactly the same. The TIMER program has a natural error from this, because it is not perfect.
#$&*
Now initialize the TIMER once more, and take a series of 10 relaxed breaths. Every time you start to inhale, hit the TIMER button.
My results for the first 7 complete breaths are as follows:
series of relaxed breaths
event number clock time time interval difference between time interval and next
1 1569.734 1569.734
2 1582.75 13.01563 0.32812
3 1596.094 13.34375 3.90625
4 1613.344 17.25 2.70313
5 1633.297 19.95313 1.35937
6 1654.609 21.3125 4.23438
7 1680.156 25.54688 2.15625
8 1707.859 27.70313
I didn't go on because the time between my breaths kept increasing, and I was afraid if I relaxed any more I might stop breathing altogether. It's going to take either more statistical analysis to determine whether that's a real danger, or a little common sense.
Report your results by just entering your time intervals, one to each line, in the box below. If I was entering my results I would enter
13.01563
13.34375
17.25
19.95313
21.3125
etc.
Enter your results in the same format:
3.70117
2.869141
3.701172
3.056641
3.336914
2.092773
3.665039
3.751953
3.112305
4.680664
#$&*
If you have any comments please insert them here
#$&*
Most likely you did not observe the same exact time interval twice, and if you did it did not happen nearly as often as when you did the fast clicks.
Why do you think this is exactly what we would expect?
The probability for identical clicks is half as great, because you have only clicked half as many times. But, factoring in how TIMER accounts for the results, the probability is slightly greater, which is maybe why I got one interval twice. Ironically, this is the same number I got during the fast clicks. However; in general, the probability for identical clicks would increase with the greater number of clicks.
#$&*
Which of the following statements do you think is the most accurate?
a. The TIMER program is capable of determining the time between two events accurately to within about .1 second.
b. The TIMER program is capable of determining the time between two events accurately to within about .01 second.
c. The TIMER program is capable of determining the time between two events accurately to within about .001 second.
d. The TIMER program is capable of determining the time between two events accurately to within about .0001 second.
Enter your answer and your reasoning below:
The TIMER program is capable of recording D., accurately within .0001 seconds of two events. Sometimes, the program goes further, but not consistently enough. That is to the most decimal places recorded within differences in my results. For the most part, it used up to four significant figures, when concerning decimal places.
#$&*
Note that the TIMER.exe program can save your data in a format that can be read by a spreadsheet (the TIMER applet cannot do so). This will be very handy in the future, so take a minute and do the following:
1. Click on the button at the lower right of the TIMER form, entitled Click to File Data.
2. A box will pop up allowing you to include an identifying message. You should generally choose to include such a message; for the data presently on your timer that might be 'series of regular breaths time at beginning of inhalation' or something similar. Type in whatever you think would serve as a good identifier for this data and OK that box.
3. A typical Save As window will appear. Decide where to save your data and what to call it, and proceed to save it. The program will save the file as a comma-delimited text file.
4. Open your spreadsheet program (typically Excel) and choose File > Open. Browse to the folder in which you just saved your data. Below the File Name line will be a File Type line; set this either to Text Files or All Files so your file will appear. Open it.
5. A series of windows will typically appear. In the first window make sure the file type chosen is Delimited, the proceed to the next window.
6. In the second window you will see a series of checkboxes; check the one entitled Comma, in order to select the comma-delimited file, then just click on Finish.
Your data should appear in your spreadsheet, and can be manipulated as in any spreadsheet.
Copy a few lines of the data from your spreadsheet below:
Series of Breaths
event number, clock time ,time interval
1 , 2274.72 , 2274.72
2 , 2278.421 , 3.701172
3 , 2281.29 , 2.869141
#$&*
&#Your work looks very good. Let me know if you have any questions. &#