How Science works: Taking measurements

Learning Objectives You should learn : About taking measurements, The meaning of ‘variation’, ‘range’ and ‘mean (average)’, The meaning of ‘accuracy’ and ‘precision’.

Taking measurements - When you take measurements there may be some variation (or differences) in the readings. For example: 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.

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 Find the minimum value and the maximum value Range = from min to max = 9.9 s to 10.3 s

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?

= 50.5 5 Taking measurements : Mean The results were: 10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s Add up all of the 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 Mean (or average) = sum of values total # of values

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 and Precision

Accuracy and Precision …sound the same thing… 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: 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 and will respond to smaller changes in temperature.

Definitions : Precision As well as accuracy, precision is important. Precision is how close the measured values are to each other. It may be connected to the smallest scale division on your measuring instrument.

Definitions : Precision For example, using a ruler: A ruler with a millimeter scale will give greater precision than a ruler with a centimeter scale. Your measurement is more precise.

Definitions : Precision A precise instrument also gives a consistent reading when it is used repeatedly for the same measurements. For example:

Definitions : Precision For example, 2 balances: A pencil is weighed on A, 3 times: The readings are: 7.3 g, 7.7 g, 7.1 g A So the Range is = 7.1 g – 7.7 g = 0.6 g It is then weighed on B, 3 times: The readings are: 7.5 g, 7.3 g, 7.4 g So the Range is B = 7.3 g – 7.5 g = 0.2 g Balance B has better precision. Its readings are grouped closer together.

Accuracy compared with Precision Suppose you are measuring the length of a wooden bar: true value The length has a true value And we can take measurements of the length, like this: Let’s look at 3 cases…

Accuracy compared with Precision Precise (grouped) but not accurate. true value Accurate (the mean) but not precise. Accurate and Precise.