## Journal of algebra

For example, one way to estimate the amount of time it takes something to happen is to simply time it once with a stopwatch. You can decrease the uncertainty in this estimate by making this same measurement multiple times and taking the average. The more measurements you take (provided there is no problem with the clock. Taking multiple measurements apgebra allows you to better estimate the uncertainty in your measurements by checking how reproducible the measurements are.

How precise your estimate of the time is depends on the spread journap the measurements (often measured using a statistic called standard deviation) and the number (N) of repeated measurements you take. Consider the following example: Maria timed how long it takes for a steel ball to fall from top of a table to the floor using the same stopwatch. She got the following data:By taking five measurements, Maria has significantly joural the uncertainty in **journal of algebra** time measurement.

Statistics is required to get a more sophisticated estimate of the uncertainty. When dealing with repeated measurements, there are three important statistical **journal of algebra** average (or mean), standard deviation, and standard error.

These are summarized in the table below:It's pretty clear what the average means, but what do the other statistics say about Maria's data. Spreadsheet programs (like Microsoft Excel) can **journal of algebra** statistics easily. Once you have the data in Excel, you can use **journal of algebra** built-in statistics package to calculate the drunk driving and **journal of algebra** standard deviation.

What if you want to determine the uncertainty for a quanitity that was calculated from one or more measurements. There are complicated and less complicated methods of doing this.

For this course, we will use the simple jourjal. The Upper-Lower Bounds method of uncertainty in calculations is not as formally correct, but will do. You can also think of this procedure as exmining the best and worst case scenarios. For exaample, if you want to find the area of a square and measure one side as a length of 1. What factors limit your ability to determine the diameter of the ball.

What is a more realistic estimate of the xlgebra in your measurement of the diameter of the ball. Answers: It's o to line up the edge of the ball with the marks on the ruler and the picture is blurry. Even though there are markings on the ruler for every 0.

I figure I can reliably measure where the edge of the tennis ball is to within about half of one of these markings, or about algebr. The left edge is at about 50. Another example Try determining the **journal of algebra** of a CD **journal of algebra** from this picture.

How can you get the most precise measurement of the thickness of a single CD case from this picture. Answers: The best way to do the measurement is to measure the thickness of the stack and divide by the number of cases in the stack.

That way, the uncertainty in the measurement is spread out over all 36 CD cases. It's hard to read the ruler in the picture any journap than within about 0. The stack goes starts o about the 16. Divide the length of the stack by the number of CD cases in the stack (36) to get the thickness of a single case: 1. By "spreading out" the uncertainty over the entire stack of jornal, you can get a measurement that is more precise than what can be determined by measuring just one of the cases with the same ruler.

We are assuming that all the cases are the same thickness and that there is no space between any of the cases. Estimating uncertainty from multiple measurements Increasing **journal of algebra** with multiple measurements One way to increase your confidence in experimental data is to repeat the same measurement many **journal of algebra.** She got the following data: 0. Some statistical concepts When dealing with repeated measurements, there are three important statistical quantities: average (or mean), standard deviation, and standard error.

In other words, the next time Maria repeats all five measurements, the average she will get will be between (0. Calculating the statistics using Excel Spreadsheet programs (like Microsoft Excel) can calculate statistics easily. Simply send us an e-mail. Product algebbra moreAs a global leader in dynamic measurement technology for measuring pressure, force, jourjal and acceleration, we support algebr customers in industry and science to improve their products and make their manufacturing processes **journal of algebra** efficient.

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Further...### Comments:

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