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Percent Error - the absolute value of the difference divided by the expected value, with the result multiplied by 100: percent error = ( measured value - expected value/ expected value ) x 100.

When the expected value is very small, perhaps approaching zero, the percent error gets very large because it involves dividing by a very small number. It is undefined when the expected value is zero. Percent error may not be a useful quantity in these cases.

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Percent Difference - comparison of values, the absolute value of the difference divided by the mean, with the result multiplied by 100. Percent difference = ( value 1 - value 2/ 1/2 (value 1 + value 2) ) x 100.

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Comparing Results: Percent Difference and Percent Error - Two different ways to compare results are percent difference and percent error.

EX: if 5 groups did the same lab, you would compare results, and all might have gotten different; and the target was 68.3 as the answer. We can assume that there is going to be some error. for example they might have not used the same ruler, or maybe one group didn't calibrate their tools. Each group will calibrate their errors and the 5 groups would compare and find the percent error and then their percent accuracy (how far they were from the target).

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Propagation of Error - different ways to make errors, you are adding up all your errors so you can propagate a number to give someone, the propagation we use to add up all our errors

EX: every time you make more than one measurement, the more chances for error.

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Confidence Intervals - range of values within which the true value has a probability of being. something that depends on other variables. If you measure a single quantity, such as the mass of a certain isotope, multiple times, you would expect a small standard deviation compared to the mean, so the confidence intervals would be narrow. A wide confidence interval in this case would indicate the possibility of random errors in your measurements.

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Standard Error - a measure of the data's uncertainty, but it reduces the standard deviation if a large number of data values are included. SE = s/n square rooted.

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Standard Deviation - measure of how spread out data values are. If your measurements have similar values, then the standard deviation is small. Each value is close to the mean. If your measurements have a wide range of values, then the standard deviation is high. It is a measure of uncertainty, so you only use one significant digit.

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Mean - the sum of all the measurement values divided by the number of measurements.

EX: if your data is a sample of a population, then the mean you calculate is an estimate of the mean of the population.

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Analyzing Data - involves calculations, m/v=d, subtracting the mass of the container to find the mass of the substance, using significant digits rules during these calculations, when adding or subtracting the result should have the same number of decimal places as the least number of decimal places in the numbers, multiplying and dividing should have the same number of significant digits as the least number of significant digits.

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Significant Digits - leading zeros never counts, trailing zeros only count if there is a decimal, sandwiched zeros always count, when adding decimal or subtracting round your answer to the least number of decimal places from the original numbers.

EX: answer is 3020.465 and you round it to 3020.47 because the two numbers from the picture you're adding have three decimal places and two decimal places, and you take the least number of decimal places; which is two.

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Experimental Error - errors that happen during and experiment such as systematic and random error, they are out of our control and we have to figure out how it would effect our results, would we have to scrap it.

EX: someone not knowing how to use the equipment, not measuring the right amount.

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Random Error - something happens during your lab or procedure that wasn't supposed to happen, not your fault.

EX: You are working with chemicals and figuring out the temps and the AC kicks on messing up your lab.

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Systematic Error - doing the same thing over and over again and getting the same answer but it's wrong, you don't know what you're doing wrong, error in the system.

EX: measuring on a ruler and starting measuring before the zero or at one making you get the same answer every time you do it but it wouldn't be correct.

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Precision - hitting the same spot every time but not on the target.

EX: shooting free throws and missing but hitting the same place every single time. precision.

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Accuracy - A+, means you got it right, hit the target.

EX: Hitting the target every time and making it. accuracy.

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