ACCURACY vs. PRECISION

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The facts...

Most of the numbers you deal with in science are measurements. They are taken from some device…meter stick, stopwatch, ruler, balance etc.

Every measuring device has a certain degree of precision. For instance, a centimeter ruler is precise to the nearest mm. This means that all measurements taken with a centimeter ruler should be the same to the tenths place. The hundredths place can be estimated.

The precision of any measurement can be effected by human error.

When measuring length the error occurs anytime you must make a decision, such as estimating the last place, or setting the first tick mark on the ruler at the correct location. BE CAREFUL! Try to make each measurement the same way.

Click here to see an example of making a length measurement using a centimeter ruler. Note that the last place is estimated (this is where the human error is) and will be either a zero or a five.

Precision has all to do with how repeatable your measurements are. 

Precision in measurements has to do with how close a series of measurements come to each other.

More Facts:

 Accuracy depends on how close your

measurement comes to the accepted value…

More facts

You do not know if a measurement is accurate unless you have an accepted value to compare it to.

EXAMPLE 1:

•Your teacher tells you the acceleration due to gravity is 9.80m/s2.

•You do an experiment and determine the acceleration due to gravity is 9.41m/s2.

•Your accuracy is expressed as a percent.  •Here your measured value differs from the accepted value by -4%.

EXAMPLE 1:

• The negative sign tells You that you were under the accepted value by 4%. 

•If the teacher never told you what the accepted value is, you would not if you were accurate or not! 

•Also note that accuracy is a continuum...from very accurate to poor accuracy...depending on the %. 

Example 2:

You and a lab partner each use a stopwatch to measure the time it takes for a ball to roll down a ramp. Here are your respective measurements:

Your DataYour Partner's Data

2.10s 2.80s

2.05s 2.77s

1.85s 2.77s

2.35s 2.78s

2.22s 2.77s

2.11s 2.78sAVERAGE:

Your Data

Your Partner's Data

2.10s 2.80s

2.05s 2.77s

1.85s 2.77s

2.35s 2..78s

2.22s 2.77s

In the data collected, you can see that the data you collected was not as precise as the data your partner collected.

This is because the measurements you took were not very consistent. Your partner's times were all very close to each other.

Your Data

Your Partner's Data

2.10s 2.80s

2.05s 2.77s

1.85s 2.77s

2.35s 2..78s

2.22s 2.77s

Even though your measurements are less precise than your partners, they may actually be more accurate than your partners. You don’t know this because you were never given an accepted value!

AVERAGE: 2.11s 2.78s

Your Data

Your Partner's Data

2.10s 2.80s

2.05s 2.77s

1.85s 2.77s

2.35s 2..78s

2.22s 2.77s

If the actual value from some reference…like your teacher, is 2.10s, then you are more accurate…though less precise.

AVERAGE: 2.11s 2.78s

Look at these diagrams. It shows 6 shots fired at four targets. 

•If you consider the bullet holes to represent measurements, then this target represents good precision and poor accuracy.

•Good precision because the shots (or measurements) are close to each other.

•This is poor accuracy because the shots (or measurements) fell far from the bulls eye or actual value.

This target represents poor accuracy and poor precision.

The bullets fell far from the bulls eye (poor accuracy) and poor precision because they were not close to each other.

In this target, the bulls eye represents the accepted value, as 9.80m/s2 did in the acceleration due to gravity data in Example 1.

Target "C" is what we all hope for, accurate, precise, measurements. 

Here the measurements are close together AND they are equal to the accepted value.

Target "D" is a more common result, especially in a high school where we don't usually have measuring devices with a high degree of precision.

This target does not show very good precision, but the AVERAGE accuracy is good. The AVERAGE position of the bullet holes is the bulls eye.

In an experiment we run many trials and then average the results. We average the data and hope that the averaging process gives us a closer approximation of the actual value…whatever that might be.

This is the same reason we use a best fit line on a graph.

The best fit line shows the average position of the data points on the graph and hopefully, a better approximation of the actual value.

This is especially important in experiments where we do not know the actual value.

Acceleration vs. Mass

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