course phy 201
ph1 query 1*********************************************
Question: `qExplain in your own words how the standard deviation of a set of numbers is calculated.
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Your solution:
Standard deviation of a set of numbers is calculated by following the steps below:
1. Determine the mean (average) number of your set of numbers
2. Determine the deviations from the mean for each number by taking the abs. value of the difference of the number and the mean.
3. Square each deviation
4. Determine the deviated average: add the set of deviations and divide the deviations by the number of deviations -1
5. Find the Square root of this deviated average
Example
Five numbers:
11, 12, 13, 14, 15
the mean of these numbers is 13
Find the deviations:
|11-13| = 2
|12-13|=1
|13-13|=0
|14-13|=1
|15-13|=2
Square each deviation
4, 1, 0, 1, 4
Average = 4+1+0+1+4/4 = 10/4 = 2.5
Take the square root of 2.5 = 1.5811388
The standard deviation is 1.5811388 for this set of numbers.
Confidence Assessment: 3 Confident
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Question: Explain in your own words the process of fitting a straight line to a graph of y vs. x data, and briefly discuss the nature of the uncertainties encountered in the process. For example, you might address the question of how two different people, given the same graph, might obtain different results for the slope and the vertical intercept.
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Your solution:
The purpose of finding the Best fit line for a graph of y vs x data is to find a straight line that will mark the trend of the data as accurately as possible by coming close to the mean distances of the point distribution. This line may be different based on how the observer looks at the distribution of the data and the relationship between the vertical intercept. Two points at the left of the spectrum might seem to provide a plausible best fit line to one person while on the same set of points another person sees that another set of points in the upper right spectrum will provide a better best fit line. I’ve learned to try to look at the set of points in a plane and fold the plane in half to find the best fit line. It’s helped me visualize best fit lines better.
Confidence Assessment: 3 Confident
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Question: Briefly state what you think velocity is and how you think it is an example of a rate.
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Your solution: Velocity is displacement (amount moved) over time. I have learned that rate is distance over time. To solve for rate you use the formula, Rate = distance/time Thus if we substitute rate with velocity and distance with displacement you can use the same formula to solve for velocity.
Confidence Assessment: 3
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Given Solution:
A rate is a change in something divided by a change in something else.
This question concerns velocity, which is the rate of change of position: change in position divided by change in clock time. **
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Self-critique (if necessary):
I included this, but went a little further.
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Question: Given average speed and time interval how do you find distance moved?
Your solution:
D istance = rate * time
Distance = speed * time
For example: If you traveled 70 mph for 1.5 hours, how far did you go?
distance = 70 mph * 1.5 hrs
Distance = 105 miles
Confidence Assessment: 3
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Given Solution:
** You multiply average speed * time interval to find distance moved.
For example, 50 miles / hour * 3 hours = 150 miles. **
Self-critique (if necessary):
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Question: Given average speed and distance moved how do you find the corresponding time interval?
Your solution:
T = D/S
For example If you traveled 105 miles at 70 mph how long would it take?
T = 105miles / 70 mph
T = 1.5 hours
Confidence Assessment: 3
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Given Solution:
** time interval = distance / average speed. For example if we travel 100 miles at 50 mph it takes 2 hours--we divide the distance by the speed.
In symbols, if `ds = vAve * `dt then `dt = `ds/vAve.
Also note that (cm/s ) / s = cm/s^2, not sec, whereas cm / (cm/s) = cm * s / cm = s, as appropriate in a calculation of `dt. **
Self-critique (if necessary):
******Is the equation above stated correctly? Should it be:
vAve = `ds * `dt then `dt = vAve/`ds
vAve = `ds / `dt, not `ds * `dt. For example to figure out the average velocity when you travel 300 miles in 5 hours, you wouldn't multiply the two quantities, you would divide.
Question: Given time interval and distance moved how do you get average speed?
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Your solution:
vAve = `ds * `dt then `ds = vAve/`dt
For example If you traveled 105 miles at 1.5 hours how fast were you traveling?
`ds =105 miles/1.5hours
`ds = 70 mph
Confidence Assessment: 3
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Given Solution:
** Average speed = distance / change in clock time. This is the definition of average speed.
For example if we travel 300 miles in 5 hours we have been traveling at an average speed of 300 miles / 5 hours = 60 miles / hour. **
&#This looks good. Let me know if you have any questions. &#