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## Accuracy vs. Precision

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**Accuracy vs. Precision**What’s the Diff?**Accuracy**• Accuracy: How closely a measurement matches true or actual values • To be accurate only requires the true value (the bulls eye) and one measurement (one arrow to hit the target).**Precision**• Precision refers to the reproducibilityof a measurement. • Requires several measurements • (notice multiple arrow holes) • Has nothing to do with the true value • (none of the values are close to the target but all the holes are close together).**Does this picture represent accuracy or precision?**• Accuracy • Precision • Both**Does this picture represent accuracy or precision?**• Accuracy • Precision • Both**Accurate and Precise**• In order to be accurate and precise, one must pay close attention to detail to receive the same results every time as well as “hit the target”.**A sample is known to weigh 3.182g. Jane weighed the sample**five different times with the resulting data: 3.200g, 3.180g, 3.152g, 3.126g, & 3.189g. Which measurement was the most accurate? • 3.200g • 3.180g • 3.152g • 3.126g • 3.189g**Problem #1 Answer**• Answer: The most accurate measurement would be 3.180 g, because it is closest to the actual weight of the sample.**Consider the data (in cm) obtained for the length of an**object as measured by three students. The length is known to be 14.5 cm. Which student had the most precise work? • Student A • Student B • Student C**Consider the data (in cm) obtained for the length of an**object as measured by three students. The length is known to be 14.5 cm. Which student had the most accurate work? • Student A • Student B • Student C**Problem #2 Answer**• Answer: Student A had the most precise work since there is only 0.1 cm between the highest and lowest values, and Student C had the most accurate work since two of the measurements were exactly at the true value and the other three measurements were within 0.1 cm of the actual value.**Good accuracy**Good precision Poor accuracy Good precision Good accuracy Poor precision In order to win the archery tournament, the archer must hit the target the most times. The winner must be accurate and precise. The first archer is just precise. He or she hit the same area of the target every time The second archer was accurate because he hit the target once. However, the third archer was accurate and precise because he or she hit the target every time. Therefore, he or she wins!**K H Da base D C M**345 m = ____ km • 345,000 • 34,500 • 0.345 • 0.000345**K H Da base D C M**7.5 cg = _____ g • 0.75 • 0.075 • 750 • 7,500**K H Da base D C M 83.74 km = ______ cm**• 0.0008374 • 0.8374 • 837,400 • 8,374,000**Limits of Measurement (Fig 20, p. 25)**Accuracy: A description of how close a measurement is to the true value of the quantity measured What is meant by this statement? “You can only be as accurate as your instrument.”**How precise can you be?**• Can we all agree that it is at least 8 cm? • Will we all have the same number next? 8.3 cm??? • We can only estimate one place beyond what we are sure of…so we will say we are precise to +/- 0.1 cm • In other words…I am confident that you will all measure this within .1 cm of 8.3 cm. szdfasdadfadfasdf szdfasdadfadfasdf**How precise can you be now?**• I can now be confident that we will all say this is 8.2. • Now what would you estimate to? • Can I confidently say that we will all measure this as 8.22 +/- .01 cm. • Is there another way I could write that? • Yes! 8.22 +/- .1 mm**Limits of Measurement (Fig 20, p. 25)**Precision of a calculated answer is limited by the least precise measurement used in the calculation (*determined by significant figures) Example: A ruler with millimeters would give you a more precise measurement than a ruler with just centimeters. When reading an instrument…You may only estimate ONE place beyond the smallest unit actually measured!**So how do we keep track of how precise a measurement is?**Significant Figures**Determining Significant Figures**• If a decimal point is absent, count significant figures starting with the first non-zero digit on the right (atlantic side of the US) Atlantic Ocean**Determining Sig Figs cont…**• If a decimal point is present, count significant figures starting with the first non-zero digit on the left (pacific side of the US) Pacific Ocean**How many significant digits are in 12.005 cm?**• 1 • 2 • 3 • 4 • 5 • 6**How many significant digits are in 12,500?**• 1 • 2 • 3 • 4 • 5 • 6**Did you remember the rule?**• If a decimal point is absent, count significant figures starting with the first non-zero digit on the right (atlantic side of the US) Atlantic Ocean**How many significant digits are in 0.01250 cm?**• 1 • 2 • 3 • 4 • 5 • 6**Did you remember the rule?**• If a decimal point is present, count significant figures starting with the first non-zero digit on the left (pacific side of the US) Pacific Ocean**Significant Digits**Notes on Significant Figures in Calculations**Adding/Subtracting with Sig Figs!**• When quantities are added or subtracted, the number of decimal places in the answer is equal to the number of decimal places in the quantity with the smallest number of decimal places • In other words… your answer cannot have more decimal places than the numbers you added together/ subtracted.**Example:**• Example : 1.5 + 3.098 = _____________cm • 1.5 + 3.098 = 4.598 cm • BUT… your answer cannot have more decimal places than the numbers you added together • So how many decimal places must we round to? • 0.1 (tenths place) • Therefore the answer is… 4.6 cm**Add the following including the correct number of**significant figures in your answer. 5.424s + 12.04s+ 62.345s + 0.0025s= ? sec • 79.8115 sec • 79.812 sec • 79.81 sec • 79.9 sec • 80. sec • 80 sec**Multiplication with Sig Figs!**• When quantities are multiplied or divided, the number of significant figures in the answer is equal to the number of significant figures in the quantity with the smallest number of significant figures. • In other words…you answer can’t have more SIGNIFICANT FIGURES than your data**Multiply the following including the correct number of**significant figures in your answer. 10.34 cm x 0.0234 cm x 2.54 cm = ? cm • 0.6145682 cm3 • 0.614cm3 • 0.61 cm3 • 0.6146 cm3 • 0.614568cm3**How many significant digits are in 1.250 x 10-3 cm?**• 1 • 2 • 3 • 4 • 5 • 6