Teacher’s Notes

This sequence of slides is designed to introduce, and explain the taking of measurements, including the meaning of variation, range, mean (average) and the difference between accuracy & precision, as explained on page 362 in New Physics for You, 2006 & 2011 editions.

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How Science works:

Ne w Phys ic s fo r Yo u, page 362

TakingTakingmeasurementsmeasurements

• About taking measurements,

• The meaning of ‘variation’, ‘range’ and ‘mean (average)’,

• The meaning of ‘accuracy’ and ‘precision’.

Learning Objectives

You should learn :

Taking measurements

When you take measurements there may be some variation in the readings.

If you time the fall of a paper parachute over a fixed distance, the times may vary slightly.

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s

Let’s look at these results more closely.

For example:

Taking measurements

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s

What is the Range of these results?

Taking measurements : Range

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s

and the maximum value

Range = from min to max = 9.9 to 10.3

Find the minimum value

Taking measurements : Mean

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s

What is the mean (or average) of these results?

Taking measurements : Mean

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s

Add up the 5 numbers:

10.1+10.2+9.9+10.0+10.3 = 50.5

There are 5 items, so divide by 5:

Mean (or average) == 50.5

5

= 10.1 s

Taking measurements : Mean

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s

Why is it a good idea to calculate the mean of your results?

Because it improves the reliability of your results.

Your results will be more reliable.

Accuracy

Precision

and

Definitions Accuracy and Precision …sound the same thing…

…is there a difference??

Definitions : AccuracyIn your experiments, you need to consider the accuracy of your measuring instrument.For example:An expensive thermometer is likely to be more accurate than a cheap one.It will give a result nearer to the true value.It is also likely to be more sensitive (with a better resolution). It will respond to smaller changes in temperature.

As well as accuracy, precision is also important.

For example:

Precision is connected to the smallest scale division on the measuring instrument that you are using.

Definitions : Precision

For example, using a ruler:

Definitions : Precision

A ruler with a millimetre scale

will give greater precision than a ruler with a centimetre scale.

For example:

A precise instrument also gives a consistent reading when it is used repeatedly for the same measurements.

Definitions : Precision

For example, 2 balances:A

B

A beaker is weighed on A, 3 times:The readings are: 73 g, 77 g, 71 g

It is then weighed on B, 3 times:The readings are: 75 g, 73 g, 74 gSo the Range is = 73 g – 75 g = 2 g

Balance B has better precision.Its readings are grouped closer together.

Definitions : Precision

So the Range is = 71 g – 77 g = 6 g

Accuracy compared with Precision

Suppose you are measuring the length of a wooden bar:

0

The length has a true value

truevalue

Let’s look at 3 cases…

And we can take measurements of the length, like this:

Accuracy compared with Precision

0

truevalue

0

0

Precise (grouped) but not accurate.

Accurate (the mean) but not precise.

Accurate and Precise.

• The meaning of ‘variation’ and ‘range’,

• How to calculate the mean (or average),and why this improves the reliability of your results,

• The difference between ‘accuracy’ and ‘precision’.

Learning Outcomes

You should now understand:

For more details, see:

New Physics for You, page 362

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