Question

what is the significance and difference between % error and % accuracy
in scientific measurement, the degree of precision required varies. usually very precise measurements are necessary but it is still helpful to be able to make estimates. the degree of accuracy in estimating varies considerably with the individual and the extent of their experience. the first time a person attempts to make an estimate, their accuracy is probably much less than it would be the tenth time. how accurate will you be in estimating different kinds of measurements? in this investigation you will find out by making several estimates, comparing them to the precise measurements and then calculating your percent accuracy. in the process you will also gain experience in using some of the equipment and measuring tools that we will be using throughout the year in this class.
step #1: calculate the difference between observed measurement and actual measurement/theoretical measurement
step #2: convert any negative result to a positive number by taking its absolute value
step #3: divide the result from step #2 by the actual/accepted/theoretical value
step #4: multiply the result by 100 (this will convert your answer to a percentile).
practicing how to calculate % error and % accuracy
we do: stephanie measured her index finger at 7.5 cm. the average length of a female index finger is 6.5 - 7.0 cm. what is the % error in her observed measurement?
step #1
step #2
step #3
step #4
you do: joseph measures the volume of a liquid using a graduated cylinder and finds it to be 40.5 ml. the actual volume of the liquid in the container is 42.6 ml. what is his % error?
show your work!!!

Explanation:

Step1: Calculate difference for Stephanie

The average length range is 6.5 - 7.0 cm. We'll take the mid - point of the range as the actual value, so the actual value $a=\frac{6.5 + 7.0}{2}=6.75$ cm. The observed value $o = 7.5$ cm. The difference $d=o - a=7.5-6.75 = 0.75$ cm.

Step2: Ensure positive value (already positive)

The value 0.75 cm is already positive, so we keep it as is.

Step3: Divide by actual value

The $\%$ error formula is $\%E=\frac{|o - a|}{a}\times100$. Substituting the values, we have $\%E=\frac{0.75}{6.75}\times100$.

Step4: Multiply by 100

$\%E=\frac{0.75}{6.75}\times100=\frac{75}{6.75}\approx11.11\%$

For Joseph:

Step1: Calculate difference

The observed value $o = 40.5$ mL and the actual value $a = 42.6$ mL. The difference $d=o - a=40.5-42.6=- 2.1$ mL.

Step2: Take absolute value

$|d| = 2.1$ mL.

Step3: Divide by actual value

$\%E=\frac{|d|}{a}\times100=\frac{2.1}{42.6}\times100$.

Step4: Multiply by 100

$\%E=\frac{2.1}{42.6}\times100=\frac{210}{42.6}\approx4.93\%$

Answer:

Stephanie's % Error is approximately $11.11\%$ and Joseph's % Error is approximately $4.93\%$