1. 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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2. How Science works:
Taking
measurements
N w Phy s ic s fo r Yo u, page 362
e
3. Learning Objectives
You should learn :
• About taking measurements,
• The meaning of ‘variation’, ‘range’ and ‘mean
(average)’,
• The meaning of ‘accuracy’ and ‘precision’.
4. Taking measurements
When you take measurements
there may be some variation
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.
6. 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 to 10.3
7. 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?
8. 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 = 10.1 s
=
5
9. 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.
11. Definitions Accuracy and
Precision …sound
the same thing…
…is there a
difference??
12. 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
(with a better resolution). It will respond to
smaller changes in temperature.
13. Definitions : Precision
As well as accuracy,
precision is also important.
Precision is connected to
the smallest scale division
on the measuring instrument
that you are using.
For example:
14. Definitions : Precision
For example, using a ruler:
A ruler with a millimetre scale
will give greater precision than
a ruler with a centimetre scale.
15. Definitions : Precision
A precise instrument also
gives a consistent reading
when it is used repeatedly
for the same measurements.
For example:
16. Definitions : Precision
For example, 2 balances: 3 times:
A beaker is weighed on A,
The readings are: 73 g, 77 g, 71 g A
So the Range is = 71 g – 77 g = 6 g
It is then weighed on B, 3 times:
B
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.
17. Accuracy compared with Precision
Suppose you are measuring the length
of a wooden bar:
0
true
value
The length has a true value
And we can take measurements
of the length, like this:
Let’s look at 3 cases…
18. Accuracy compared with Precision
0 Precise
(grouped)
but not
true accurate.
value
0 Accurate
(the mean)
but not
precise.
0 Accurate
and
Precise.
19. Learning Outcomes
You should now understand:
• 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’.
20. For more details, see:
New Physics for You, page 362
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