Can you accurately determine

Do about 10 measurement for each equipment. By statistics, this condition will minimize your measurement error for sure! Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. How can you accurately determine your own mass? Ask Question. Asked 7 years, 1 month ago. Active 7 years, 1 month ago. Viewed 1k times. It doesn't matter how many samples you take, theoretically we don't know the relationship between the real weight and the shown weight, nor do we know the distribution in the case of inaccuracies. It could be the case that old scales will always show a higher value, or that certain manufacturers skew their results down to make overweight people happier.

First of all, it is not so easy to find objects with accurate weights. Weightlifting plates can be a few percent off. Also, the error will accumulate. For example, if you calibrate with water and you want your curve to go up to 80kg, you need 80 liters of water. Improve this question. CaptainCodeman CaptainCodeman 1, 2 2 gold badges 11 11 silver badges 17 17 bronze badges. Whatever method you use, the answer always comes back to "calibration".

You need a standard that you trust - whether it be mass, frequency, force, If you have some weightlifting weights you can create a calibration curve for your scales at a particular location, flat surface. But now you need to know if your weights are accurate.

Maybe you can use equivalent volume of water - if you have a means of measuring that I know that it is possible to buy or rent or otherwise access highly accurate equipment, however I'm curious as to whether or not it's possible to do it from home. But you need to have some standard that you trust.

Essentially, you need a way to trace your measurement to the definition of the kg with better than 0. That is quite a challenge. Differential measurements are always easier than absolute ones. You would definitely need "point attachment" or knife edge to both sides of your beam and you would want to confirm they are equal length by swapping the weights and confirming you are still in balance.

There is an uncertainty in anything calculated from measured quantities. For example, the area of a floor calculated from measurements of its length and width has an uncertainty because the length and width have uncertainties.

How big is the uncertainty in something you calculate by multiplication or division? If the measurements going into the calculation have small uncertainties a few percent or less , then the method of adding percents can be used for multiplication or division. This method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation.

For example, if a floor has a length of 4. Expressed as an area this is 0. A high school track coach has just purchased a new stopwatch. Why or why not? An important factor in the accuracy and precision of measurements involves the precision of the measuring tool. In general, a precise measuring tool is one that can measure values in very small increments. For example, a standard ruler can measure length to the nearest millimeter, while a caliper can measure length to the nearest 0.

The caliper is a more precise measuring tool because it can measure extremely small differences in length. The more precise the measuring tool, the more precise and accurate the measurements can be. When we express measured values, we can only list as many digits as we initially measured with our measuring tool.

For example, if you use a standard ruler to measure the length of a stick, you may measure it to be You could not express this value as It should be noted that the last digit in a measured value has been estimated in some way by the person performing the measurement. For example, the person measuring the length of a stick with a ruler notices that the stick length seems to be somewhere in between Using the method of significant figures, the rule is that the last digit written down in a measurement is the first digit with some uncertainty.

In order to determine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digit written on the right.

For example, the measured value Significant figures indicate the precision of a measuring tool that was used to measure a value. Special consideration is given to zeros when counting significant figures.

The zeros in 0. There are two significant figures in 0. The zeros in The zeros in may or may not be significant depending on the style of writing numbers. They could mean the number is known to the last digit, or they could be placekeepers.

So could have two, three, or four significant figures. To avoid this ambiguity, write in scientific notation. Zeros are significant except when they serve only as placekeepers. Determine the number of significant figures in the following measurements:. When combining measurements with different degrees of accuracy and precision, the number of significant digits in the final answer can be no greater than the number of significant digits in the least precise measured value.

There are two different rules, one for multiplication and division and the other for addition and subtraction, as discussed below. For multiplication and division: The result should have the same number of significant figures as the quantity having the least significant figures entering into the calculation.

For addition and subtraction: The answer can contain no more decimal places than the least precise measurement. Suppose that you buy 7. Then you drop off 6. Finally, you go home and add How many kilograms of potatoes do you now have, and how many significant figures are appropriate in the answer? The mass is found by simple addition and subtraction:. Next, we identify the least precise measurement: This measurement is expressed to the 0.

Thus, the answer is rounded to the tenths place, giving us In this text, most numbers are assumed to have three significant figures. Furthermore, consistent numbers of significant figures are used in all worked examples. You will note that an answer given to three digits is based on input good to at least three digits, for example. If the input has fewer significant figures, the answer will also have fewer significant figures. Care is also taken that the number of significant figures is reasonable for the situation posed.

In some topics, particularly in optics, more accurate numbers are needed and more than three significant figures will be used. Perform the following calculations and express your answer using the correct number of significant digits. What is the total weight of the bags? Taking multiple measurements also 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 of 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 decreased the uncertainty in the time measurement.

Maria also has a crude estimate of the uncertainty in her data; it is very likely that the "true" time it takes the ball to fall is somewhere between 0. Statistics is required to get a more sophisticated estimate of the uncertainty. When dealing with repeated measurements, there are three important statistical quantities: 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 calculate statistics easily. Once you have the data in Excel, you can use the built-in statistics package to calculate the average and the 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 one. The Upper-Lower Bounds method of uncertainty in calculations is not as formally correct, but will do.

The basic idea of this method is to use the uncertainty ranges of each variable to calculate the maximum and minimum values of the function. 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. Example Try measuring the diameter of a tennis ball using the meter stick. What factors limit your ability to determine the diameter of the ball?

What is a more realistic estimate of the uncertainty in your measurement of the diameter of the ball?