# Analyse Complex Problems To Determine Appropriate Ways In Which Each Aspect May Be Researched

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11.1 identify data sources to:
a) analyse complex problems to determine appropriate ways in which each aspect may be researched
b) determine the type of data that needs to be collected and explain the qualitative or quantitative analysis that will be required for this data to be useful
The type of data collected can vary. The data may be numerical quantities such as the mass of an object, or it may be observations such as the colour of something or its smell.

Data can be analysed qualitatively or quantitatively. Qualitative analysis refers to analysing it in regards to its qualities. For example you may observe the colour of the emission spectra of an element. You are not performing any numerical calculations, therefore you are qualitatively analysing the data. Quantitative analysis refers to analysing it in regards to numerical calculations. You may do an experiment where you change length and measure time. From this data you collect you may apply some mathematical formula to come to some conclusion. As you have performed calculations on this data, you have quantitatively analysing the data.

Data is just data. On its own it is useless. You must analyse this data in order for the information gathered from this data to be useful.
c) identify the orders of magnitude that will be appropriate and the uncertainty that may be present in the measurement of data
The orders of magnitude of measurements of data can be explained with the concept of significant figures. I’ll assume you all know what decimal places are, you may already know what significant figures are but I will explain them anyway. The number of significant figures you have in a particular quantity is just how many digits you use to make up the quantity, omitting leading zeros. For example the number 52 has two significant figures, that being the ‘5’ and the ‘2’. The quantity 3.00 has three significant figures, that being the ‘3’, the ‘0’ and the ‘0’. These three digits define the accuracy of a quantity. For example the quantity 3.00 specifies that the tenths and hundredths of the quantity are zero. This is different to the quantity 3 which means that we only know that the units are 3, we don’t know the tenths or the hundredths. And so 3.00 has three significant figures and 3 has one, this means that 3.00 is much more accurate.

When we get to very small numbers such as 0.0001, it is best to explain these in terms of scientific notation. 0.0001 is represented as 1 × 10-4 in scientific notation. They are equivalent. However now that the quantity is in scientific notation we can see only one digit is used to define the quantity, hence is has one significant figures.

Now you can see why significant figures are more important than the number of decimal places.

Hence when we are measuring data we should ensure that we collect enough significant figures, not decimal places.

When we measure data, we never know exactly the quantity that we measure. We may measure a length to be 35mm. However the distance may vary from 35mm by ±0.5 and still have this measurement. For example in the diagram below the piece of wood is measured to be 15mm. This is because you can only measure to the lines given, however it is actually a bit greater that 15mm. There is a region of values that are all measured to 15mm, that being from 14.5mm to 15.5mm. Hence the uncertainly of the measurement is ±0.5mm

d) identify and use correct units for data that will be collected
SI Base Units:
These are the fundamental measurements, upon which all other measurements are based. So of the SI base units are shown in the table below. Please note that the first three length, time and mass are the three most important. Quantity | Unit | Symbol | Length | metre | m | Time | second | s | Mass | kilogram | kg | Temperature | degrees Kelvin | °K |

For each of these quantities, a standard has been decided upon. For example the