Presenting Data in Tables How Science Works Presenting Data in Tables © SSER Ltd.

Knowing Your Units It is important that you always include the units alongside any numerical data you collect. Figures on their own are meaningless. Drag and drop the units into the table below, so it correctly displays the main SI units you will use.

Knowing Your Units It is important that you always include the units alongside any numerical data you collect. Figures on their own are meaningless. Drag and drop the units into the table below, so it correctly displays the main SI units you will use.

Repeating Readings Readings should be repeated to improve the reliability of the mean. Here are two readings: 13 5 What is wrong with these readings? Repeating readings twice is not sufficient. With these two readings, you do not really know which of them is closer to the true value, or whether one of them is an anomaly.

Repeating Readings When taking a reading, it is good practice to obtain three values... Which of these readings appears anomalous? 5 13 6 13 appears anomalous, and needs to be repeated and possibly replaced before calculating the mean. More than three readings would provide greater accuracy for the mean, but may be considered too time consuming.

Presenting Data Data collected from an investigation must be presented in the most appropriate form. The two most common forms are: Tables Graphs Displaying data in tables... Stores the data in an organised way Helps you to spot patterns and anomalies Prepares the data for drawing graphs and calculating statistics

Raw Data Raw data is collected while carrying out an experiment. Before raw data can be used, it needs to be organised into a final table.

Organising Raw Data A sample of 40 people were asked to name their favourite colour. The variable ‘favourite colour’ is categoric. The raw data would look something like this:

Organising Raw Data In order to make sense of the raw data, it needs to be organised into a frequency table (or ‘tally chart’)... 14 Blue 5 Black 2 Green 12 Yellow Orange Red Frequency Tally Colour This allows you to see at a glance the colour preferences of your sample of 40 people. The frequency column can be totalled to check that it is equal to the sample size of 40. It is easy to see that ‘Blue’ is the mode.

Showing Units When using tables, there are some key points to remember: Figures without units are meaningless. Always put the units in the column headers, so that you do not write the units next to each piece of data, which is wasteful and looks cluttered. 100ºC 8 min 7 min 93ºC 6 min 86ºC 5 min 80ºC 4 min 69ºC 3 min 55ºC 2 min 36ºC 1 min 16ºC 0 min Temperature Time 100 8 7 93 6 86 5 80 4 69 3 55 2 36 1 16 Temperature (°C) Time (min)

Grouping Numerical Data Numerical raw data may be sorted into groups (class intervals) for the following reasons: The Raw Data from Measuring the Heights of 40 People There is a lot of data There are many distinct values of the variable The spread of the data is large

Grouping Numerical Data A group of data (class interval) is a range of values of the variable, i.e. a group of values between two end-points (boundaries). Grouping reduces the number of values which need to be indicated on a graph. Grouping is usually done by tallying and entering the data into a table... 2 160 - 169 6 150 - 159 10 140 - 149 15 130 - 139 7 120 - 129 Frequency Tally Height (cm)

Using Units Consistently Before writing data into a results table, you need to give careful consideration to how many decimal places or significant figures you need to use. What is wrong with the way this data is presented? 2.5 2.6 2 1.8 Volume of Oxygen Produced (mm3) 2.4 1 2.2 1.7 5 4 3 Experiment Number Some of the figures have been expressed as whole numbers and some to one decimal place You must make sure that you measure and display your results to a consistent number of significant figures or decimal places.

Using Units Consistently Before writing data into a results table, you need to give careful consideration to how many decimal places or significant figures you need to use. What is wrong with the way this data is presented? 2.5 2.6 2.0 1.8 0.0 Volume of Oxygen Produced (mm3) 2.4 1.0 2.2 1.7 5 4 3 2 1 Experiment Number Some of the figures have been expressed as whole numbers and some to one decimal place You must make sure that you measure and display your results to a consistent number of significant figures or decimal places.

Simplifying Tables When presenting the mean in your final results table, you may want to modify your column headings. The following table appears rather cluttered... 2.4 2.2 1.7 0.0 Volume of Oxygen Produced (mm3) 2.5 2.6 2.0 1.8 1.0 1.5 Average Volume of Oxygen Produced (mm3) 5 4 3 2 1 Experiment Number How could you simplify this table of data?

Volume of Oxygen Produced (mm3) Simplifying Tables This table contains the same data, but is less cluttered... Average Reading 3 Reading 2 Reading 1 2.4 2.2 1.7 0.0 2.5 1.5 2.6 2.0 1.8 Volume of Oxygen Produced (mm3) 1.0 5 4 3 2 1 Experiment Number

Using Separate Tables There may also be occasions when you want to keep your raw data completely separate from the final calculated data. 2.4 2.2 1.7 0.0 Volume of Oxygen Produced (mm3) 2.5 2.6 2.0 1.8 1.0 5 4 3 2 1 Experiment Number Table 1 2.5 2.2 1.5 0.0 Average Volume of Oxygen Produced (mm3) 5 4 3 2 1 Experiment Number Table 2 Table 1 shows the raw data and Table 2 shows only the final calculated means that will be used to draw a graph.

The Effect of Repeated Readings

Using Repeated Readings

Calculating Means Calculate the two missing values in the table below, then type in your answers...

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