Measurement Error

Measurement Error

"To err is human, to forgive is divine"

Open Ended

Using a word or a phrase, what do you think when you hear the word "error" ?

Error in a real-world science example

The Digital Balance

Multiple Choice

Your lab has 3 digital balances and you periodically check them against a 50.00 gram mass standard to monitor their accuracy and precision.

You place the 50.00 g weight on each balance three times and record the masses they read.

Balance #1: 49.67 g ; 50.32 g ; 49.85 g

Balance #2: 47.83 g ; 58.35 g ; 36.87 g

Balance #3: 53.24 g ; 53.25 g ; 53.15 g

Which balance would be described as precise, but not accurate?

• 1

• 2

• 3

Multiple Choice

Your lab has 3 digital balances and you periodically check them against a 50.00 gram mass standard to monitor their accuracy and precision.

You place the 50.00 g weight on each balance three times and record the masses they read.

Balance #1: 49.67 g ; 50.32 g ; 49.85 g

Balance #2: 47.83 g ; 58.35 g ; 36.87 g

Balance #3: 53.24 g ; 53.25 g ; 53.15 g

Which balance would be described as both accurate and precise?

• 1

• 2

• 3

Multiple Choice

Your lab has 3 digital balances and you periodically check them against a 50.00 gram mass standard to monitor their accuracy and precision.

You place the 50.00 g weight on each balance three times and record the masses they read.

Balance #1: 49.67 g ; 50.32 g ; 49.85 g

Balance #2: 47.83 g ; 58.35 g ; 36.87 g

Balance #3: 53.24 g ; 53.25 g ; 53.15 g

Which balance would be described as neither accurate nor precise?

• 1

• 2

• 3

Error

• All measurements have some error

• Error is based on accuracy

• Error is the difference between a measured value and the accepted value

• Error = measured - accepted

• Accepted values are considered exact and true. (sometimes called the theoretical value)

• Examples of accepted values are the densities for elements listed in Table S of your Reference Tables.

Percent Error

• The error of a measured value divided by the accepted value. (then, multiplied by 100).

• This is often more useful than the error value alone.

• The error might seem large, but the percent error might be small.

Found on the back of your Reference Tables (Table T)

Error = measured - accepted

Error = 49.67 g - 50.00 g

Error = -0.33 g

Multiple Choice

What is the correct numerical setup to calculate the percent error for a measurement of 49.67 g if the accepted value is 50.00 g ?

• $49.67\ g\ -\ 50.00\ g$

• $\left(\frac{49.67\ g\ -50.00\ g}{50.00\ g}\right)\$

• $\left(\frac{49.67\ g\ -50.00\ g}{50.00\ g}\right)\ x\ 100$
  

 $\left(\frac{49.67\ g\ -50.00\ g}{50.00\ g}\right)\ x\ 100$  

• Numerator is the error

• Divide by the accepted value

• Multiply by 100

• Report answer as a positive percentage 

• (think of the error portion as an absolute value)

•  $\left|49.67\ g\ -\ 50.00\ g\right|$  

Measured Value of 49.67 g and accepted value of 50.00 g means

• The Error is -0.33 grams

• The Percent Error is 0.66 %

• (that is a very low percent error.)

Where does expairimentle erorr come from?

• Human error (try to minimize)

• Equipment inconsistencies and/or degree of precision

• Changes to conditions such as temperature, pressure, humidity, etc.

• Age of chemicals

• Aliens... j/k

Focus of practice will be calculating Error and Percent Error

Error = Measured - Accepted

 $Percent\ Error\ =\left|\frac{measured\ -\ accepted}{accepted}\right|\ \ x\ 100$  

Multiple Choice

What is the error if the measured value is 2.65 g/cm³ and the accepted value is 2.70 g/cm³ ?

• 0.5 g/cm³

• 0.05 g/cm³

• -0.5 g/cm³

• -0.05 g/cm³

Multiple Choice

What is the percent error if the measured value is 2.65 g/cm³ and the accepted value is 2.70 g/cm³ ?

• 1.85 %

• 5 %

• 1.89 %

• 0.05 %

• 0.0185 %

Poll

What is your comfort level with this topic right now?

• Great!

• Okay

• A bit shakey

• No confidence at all

For more practice and examples, see the videos in the lesson guide and try the Quizlet flashcards.