14 s4 i scatter plot final
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A scatter plot is a graphical representation that shows the relationship between two related variables, allowing for visualization of correlations, such as between age and height or temperature and ice-cream sales. The document explains how to create a scatter plot using data, with steps including data collection, axis construction, and plotting points. It also emphasizes the distinction between correlation and causation and provides tips on interpreting the results, highlighting positive, negative, and no correlation scenarios.
14 s4 i scatter plot final
- 1. © ABCi 2019 What is a Scatter Plot? A scatter plot is a mathematical diagram that plots variables that somehow “belong” together, against each other, (e.g. age and height of a person under 18, outdoor temperature and ice-cream sales on a given day, etc.). What are the benefits of using this tool? The human eye is fantastic at detecting patterns. Scatter plots enable you to visualise if there is a relationship between variables and if so, the type of relationship e.g. linear or non-linear. The examples given in this guide are linear in nature. When would you use this tool? Scatter plots help you determine if there is a relationship between two variables by plotting them against each other on a graph, e.g. plotting age against height of a person under 18 years or temperature against ice-cream sales. How do you do it? Let’s look at a specific example to create a scatter plot. Hunch - there is a relationship between outdoor temperature and ice-cream sales Step 1: Collect data for the two variables (outdoor temperature and ice-cream sales each day, one pair of observations per day) – see table above right. Step 2: Using Microsoft Excel or a piece of paper construct two axis. One variable will be plotted along the horizontal axis (temperature) and the other variable along the vertical axis (ice-cream sales). What resources do I need? • You will need multiple sets of paired observations (measurements), meaning that each dot in the scatter plot is made up of one observation for the first variable (e.g. age or ice-cream sales) plotted against one observation for the second variable (e.g. height or outdoor temperature) in a given circumstance (e.g. person under 18 or on a given day). • Microsoft Excel, or if in doubt you can use graph paper and a pencil. Average Daily Temperature (C) Daily Ice-cream sales (£) 14.3 £214 16.5 £326 11.8 £184 15.1 £331 18.6 £407 22.2 £523 19.5 £411 25.0 £613 23.3 £543 18.2 £422 22.6 £446 17.3 £407 Scatter PlotABC improvement iSkills for
- 2. © ABCi 2019 How do you interpret a Scatter Plot? The closer the dots are to making a line, the higher the correlation between the two variables (the stronger the relationship), this may be positive or negative. The examples below demonstrate linear (straight line) correlation. In our example (above) there is a strong positive correlation between outside temperature and ice- cream sales, as the temperature rises, so do the ice- cream sales. Positive correlation – data points make an upwards facing straight line However if there is little or no correlation between the two variables, there will not be a visible line and the plots will be spread out across the whole chart area – see left. Hints & Tips It is important to understand that correlation does not mean causation. Just because there is a correlation between two variables, it does not mean that one variable has directly caused or affected the other. In our example (above) there is a strong negative correlation between waiting time in clinic and patient satisfaction score, as the waiting time increases, the satisfaction score decreases. Negative correlation – data points make a downwards facing straight line Hunch - there is a relationship between outdoor temperature and ice-cream sales Step 3: Plot each dot on your scatter plot by placing the dot where the two variables meet. The first row in the table has been plotted – see scatter plot right. Step 4: Interpret the correlation of the two variables by looking at the pattern of the dots on the graph.