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 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: = 50.5 There are 5 items, so divide by 5: Mean (or average) = = = 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 : Accuracy In your experiments, you need to consider the accuracy of your measuring instrument. For example: It is also likely to be more sensitive. So it will respond to smaller changes in temperature. An expensive thermometer is likely to be more accurate than a cheap one. It will give a result nearer to the true value.

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 g So 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 true value Let’s look at 3 cases… And we can take measurements of the length, like this:

Accuracy compared with Precision 0 true value 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: