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How To Calculate Precision Physics

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How To Calculate Precision

Accuracy and Precision

Precision is how close a measurement comes to another measurement. If using a particular tool or method achieves similar results every time it is used, it has high precision, such as stepping on a scale several times in a row and getting the same weight every time. You can calculate precision using different methods, including range of values and average deviation.


Precision is not the same as accuracy. Precision is how close measured values are to each other, and accuracy is how close experimental values come to the true value. Data may be accurate but not precise, or precise but not accurate.

Estimating Uncertainty From A Single Measurement

In many circumstances, a single measurement of a quantity is often sufficient for the purposes of the measurement being taken. But if you only take one measurement, how can you estimate the uncertainty in that measurement? Estimating the uncertainty in a single measurement requires judgement on the part of the experimenter. The uncertainty of a single measurement is limited by the precision and accuracy of the measuring instrument, along with any other factors that might affect the ability of the experimenter to make the measurement and it is up to the experimenter to estimate the uncertainty .

Calculating Margin Of Error

To calculate the margin of error is a complex process, even if you are using Excel. To simplify matters, there are many online margin of error calculators you can use for free. There are three numbers you need to know:

  • The size of your sample.
  • The size of the entire population.
  • The confidence level for your sample .
  • The confidence level essentially means that if you took all the possible samples from your entire population, the confidence level is the number of times your average would work out to the same number. Fortunately, in the world of marketing, this is not something you normally need to calculate: The industry standard is 95 percent.

    With the margin of error involved, you get a better description of your data and estimates. For example, with a confidence level of 95% and margin of error of 6%, you can expect your statistics to be within a 6% range of your sample statistic in 95% of samples.

    Example of Margin of Error

    Suppose you have 5,000 customers who bought a product from you in the past year and you want to get their opinion on a new logo you have designed. You send them all an email and after one hour, 12 respond saying they prefer it, while eight respond saying they like your old logo better. This means that 60% like the new logo better.

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    Example : Calculating Percent Uncertainty: A Bag Of Apples

    A grocery store sells } bags of apples. You purchase four bags over the course of a month and weigh the apples each time. You obtain the following measurements:

    • Week 1 weight: }
    • Week 2 weight: }
    • Week 3 weight: }
    • Week 4 weight: }

    You determine that the weight of the } bag has an uncertainty of } What is the percent uncertainty of the bags weight?


    First, observe that the expected value of the bags weight, \textbf , is 5 lb. The uncertainty in this value, \textbf , is 0.4 lb. We can use the following equation to determine the percent uncertainty of the weight:


    Plug the known values into the equation:


    We can conclude that the weight of the apple bag is \pm8\%} . Consider how this percent uncertainty would change if the bag of apples were half as heavy, but the uncertainty in the weight remained the same. Hint for future calculations: when calculating percent uncertainty, always remember that you must multiply the fraction by 100%. If you do not do this, you will have a decimal quantity, not a percent value.

    Check Your Understanding 3

    Accuracy, Precision of Instruments and Errors in Measurements

    1: Perform the following calculations and express your answer using the correct number of significant digits.

    A woman has two bags weighing 13.5 pounds and one bag with a weight of 10.2 pounds. What is the total weight of the bags?

    The force\boldsymbolon an object is equal to its mass\boldsymbolmultiplied by its acceleration\boldsymbol.If a wagon with mass 55 kg accelerates at a rate of\boldsymbol^2}, what is the force on the wagon?

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    Solved Question For You

    Question 1: Briefly differentiate between accuracy and precision?

    Answer: Precision refers to the amount of information whose conveyance takes place by a number in terms of its digits. It reflects the closeness between two or more measurements. In contrast, Accuracy refers to the closeness of the measurements that are related to a specific value and it is the description of the systematic error.

    Precision Of Measuring Tools And Significant Figures

    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 0.01 millimeter. 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.

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    Key Takeaways: Accuracy Versus Precision

    • Accuracy is how close a value is to its true value. An example is how close an arrow gets to the bull’s-eye center.
    • Precision is how repeatable a measurement is. An example is how close a second arrow is to the first one .
    • Percent error is used to assess whether a measurement is sufficiently accurate and precise.

    You can think of accuracy and precision in terms of hitting a bull’s-eye. Accurately hitting the target means you are close to the center of the target, even if all the marks are on different sides of the center. Precisely hitting a target means all the hits are closely spaced, even if they are very far from the center of the target. Measurements that are both precise and accurate are repeatable and very near true values.

    Increasing Precision With Multiple Measurements

    Calculating Reliability, Accuracy & Precision | Chemical Calculations | Chemistry | FuseSchool

    One way to increase your confidence in experimental data is to repeat the same measurement many times. 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 , the better your estimate will be.

    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 and the number 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:

    0.32 s, 0.54 s, 0.44 s, 0.29 s, 0.48 s

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    How Do You Do Precision In Physics

    One way to analyze the precision of the measurements would be to determine the range, or difference, between the lowest and the highest measured values. In that case, the lowest value was 10.9 in. and the highest value was 11.2 in. Thus, the measured values deviated from each other by at most 0.3 in.

    Significant Figures In This Text

    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. Finally, if a number is exact, such as the two in the formula for the circumference of a circle, \textbf} , it does not affect the number of significant figures in a calculation.

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    Difference Between Accuracy And Precision

    We have often statements like a spot on and bullseye. These statements usually come when one guesses the right answer to a question. Similar to this quiz, the accuracy of data shows how close a measurement is to the true value.

    Lets consider the bullseye for example. If one hits the target that one was throwing darts at, and the very center of the target is hit, one would be considered very accurate because that is the true value.

    However, in case one hits outside the center of the target each time, one would be considered inaccurate because it is not near the true value. So, the farther one is from the center, the lesser will be the accuracy.

    Accuracy is very important when it comes to data collection. For example, one may wish to measure a certain chemicals volume in the experiment.

    If the actual volume was 60 ml but the measurement was 75 ml, it would not be a very accurate value due to the fact that it is not close to the true value of 60 ml. However, if the measurement is of 59 ml, one may consider this as an accurate value because of its immense closeness to the true volume.

    Now let us go back to the target. This time, when throwing off the darts takes place, the hit is nowhere near the centre. However, one hits the same spot every time.

    In this case, the person was not accurate but rather precise. This is because precision refers to the agreement of repeated measures.

    The Uncertainty Of Measurements

    Projectile Motion Lab

    measurementsuncertainty analysiserror analysistrue valuepreciseaccurateaccuracyprecisionAccuracyerrorPrecisionuncertaintyNote:erroruncertaintyaccuracyaccuracyaccuracyacceptedstandardprimary mass standardaccuraterelativefractional uncertaintym

    75.5 80.0


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    An Introduction To Measurements

    Our day-to-day activities would be incomplete without Measurements. Measurements need the use of both conventional and unconventional equipment, and different people may get different results from the same instrument. As a result, value measurements can be precise or accurate. Any measured value’s accuracy is determined by how close it is to the true value. Precision relates to the degree to which the various measured quantities are connected.

    For students who are searching for a deeper understanding of the concept of Precision in mathematics, Vedantu’s experts have discussed and elaborated on it below. Vedantu offers the best education options for students who are studying for examinations and want to improve their marks in their respective subjects.

    Precision And Accuracy: Other Factors To Consider

    While all of the above techniques will help you to measure the precision of your data, it is always important to remember that this will not necessarily mean your data is accurate. There are innumerable factors that could influence the accuracy of your data.

    The age of your data can be a cause for inaccuracy. If there was a drastic change in the economy last month, for example, any data you have from last year on consumer buying habits may now be highly inaccurate. How you word questions in a survey, where you approach people and what time you approach them can also affect the accuracy of your data. Imagine doing a survey on consumer confidence the day before a stock market crash.

    As another example, suppose you decided to send a survey to your clients asking them about their opinion on your new organic food products. In appreciation for their time, you offer them a $10 coupon to the local farmers market. While this may be a kind gesture, you need to realize that you have immediately skewed your result to favor people who would go to the farmers market. Those who may not want to spend more for organic foods may not bother answering your survey, making it biased and inaccurate.

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    Sample Data And Precision

    Whenever you use samples to gather data, there are two areas that can vary in their precision. Because data from any individual can fall over a range of different values, a sample is best described by using an average value. This average can vary depending on circumstances and concepts applied.

    As an example, suppose you asked 10 people to rate a product’s quality using a scale of one to 10. Five people gave it a one and five people gave it a 10. The average score would be 5.5 and, if it was not given with any additional explanation, the average score would suggest customers felt the product quality was average, which is not the case at all. To gauge the precision of the average compared to individual responses, you should calculate the standard deviation.

    Similarly, a sample of 10 people is quite small if you have thousands of customers who did not complete the survey. Calculating the precision of the sample compared to the population as a whole is called the standard error. In statistics, 25 is the generally-accepted minimum amount for a sample to be reflective of the population, as long as the sample population is selected in an unbiased fashion.

    How To Calculate Precision Of Data

    Accuracy and Precision (Part 2)

    Today, more than at any other time in history, small businesses and large businesses alike have access to staggering amounts of data. Using website analytics software, you can get hard data on customer buying behaviors, where they go on your website, what they like and what they do not like. Using client relationship management software, you can look even deeper at customer data to determine what products or services they may be interested in next year based on their behavior today.

    However, with this vast amount of data and the potential to use it for making business decisions, it is more important than ever to understand how precise and accurate your data is. Without understanding standard deviations or margins of error, you could find yourself making decisions on the wrong data.

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    How Precise Is This Estimate

    OK, you have decided that the length of the pendulum is mostlikely about 25.43cm – but how precise is this measurement?

    You could plot these values on a number line to determine therange of likely values like this:Lookingat this graph, you can easily determine that all of the measurementsfall within 0.07 cm of the mean value. Therefore, if you were “onautomatic pilot”, you might conclude that the best estimate of thelength is 25.43 cm with an uncertainty of 0.07 cm, or:

    Actually, I wouldn’t do that. Here is a general principle:

    It is illogical to be extremely precise about uncertainty.

    Look at the data table again. Notice that the actual uncertaintyin the length is in the tenth’s place – it varies from 3 to 5. Ithink that it makes more sense to express the length as .The 0.1 cm specifies the “uncertainty interval” for thismeasurement.

    Precision Of A Measurement: Accuracy Measurement

    Senior Content Specialist| Updated On -Apr 5, 2022

    Precision of a measurement depends on the size of the smallest measuring value because smaller the measured unit of the instrument the greater will be accuracy in a measured value. Science is all about collecting the data and researching, analysing and illustrating it, sometimes data shows error regardless of whether those measurements are accurate and precise or not.

    Table of Content

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    Which Measurement Is The Right One

    Which of the five measurements above do I use to represent thelength of my pendulum? Clearly, the best thing to do is calculate theaverage value of the data values and use this average torepresent the best estimate of the length of the pendulum. Simply addup the data values and divide by the number of data values.Fortunately, this calculation is easily and conveniently handled byjust about any calculator or spreadsheet. In the table above, themean value has been calculated as 25.43 cm.

    Accuracy And Precision With Example And Differences

    Percent Error Formula Chemistry : Accuracy And Precision Percent Error ...

    We often hear the two words accuracy and precision during the measurement of a physical quantity in an experiment. Most of the students feel that these two terms have the same meaning. But these are much different to each other. In this article, we are going to discuss the concepts and differencebetween accuracy and precision with example of an experimental data. Errors are the causes of inaccuracy in a measurement.

    Contents in this article:

  • What is accuracy of a measurement?
  • What is precision measurement?
  • Explanation of accuracy and precision with example of experimental data
  • Difference between accuracy and precision in a measurement
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    Accuracy Precision And Calibration

    Do you think it’s better to use an instrument that records accurate measurements or one that records precise measurements? If you weigh yourself on a scale three times and each time the number is different, yet it’s close to your true weight, the scale is accurate. Yet it might be better to use a scale that is precise, even if it is not accurate. In this case, all the measurements would be very close to each other and “off” from the true value by about the same amount. This is a common issue with scales, which often have a “tare” button to zero them.

    While scales and balances might allow you to tare or make an adjustment to make measurements both accurate and precise, many instruments require calibration. A good example is a thermometer. Thermometers often read more reliably within a certain range and give increasingly inaccurate values outside that range. To calibrate an instrument, record how far off its measurements are from known or true values. Keep a record of the calibration to ensure proper readings. Many pieces of equipment require periodic calibration to ensure accurate and precise readings.

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