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WHY GRAPH? In Chemistry, we make frequent use of graphs to provide a visual representation of data. This will often make the data easier to interpret. We can easily see trends or relationships. We can predict unknown values. Line graphs for continuous data. Bar graphs for non-continuous data. Fig1. Favourite Subject WHAT IS A GRAPH? A graph is a visual representation of numerical systems and relationships. For example, a straight line can be represented by the equation to the right where: y = the value on the vertical axis x = the value on the horizontal axis m = the slope of the line (Δy/Δx) b = the y intercept What is the slope of this line and what would the slope represent? COMPONENTS OF A LINE GRAPH Title Error Bars (not shown here) Reasonable scale Key (if needed) Labels (units) Smooth lines Big enough: (takes up more than ½ the graph For detailed rules on constructing a graph click HERE PLOTTING A LINE GRAPH there are two axes - horizontal (called the x-axis) and vertical (called the y-axis), a point on the graph is denoted by an ordered pair (or coordinates (e.g., (3,8)) where: the first number refers to horizontal position on the x-axis, the second number refers to vertical position on the y-axis, sometimes the ordered pairs are listed in tabular format with headings that correspond to the labels on the axis the two axes intersect at point called the origin with coordinates (0,0), the reason that we plot data is so that we can more easily observe trends or behaviour of the data (modified from Anderson and Swanson, 2005) TYPES OF LINEAR LINE GRAPHS Fig. 1 Directly proportional Fig. 2 Inversely proportional Directly proportional graphs show variables that are directly related to one another while inversely proportional graphs show an inverse relationship (e.g. P = 1/V as in Boyle’s Law.) NON-LINEAR LINE GRAPHS These non-linear graphs show exponential relationships – growth (right) and decay (left) LINE OF BEST FIT When presenting data, it is most likely that the point-to-point connection of the data points will not result in a smooth curve or straight line. Often you will need to draw a “best fit line” to show the overall relationship that is present. This will allow you to make predictions about other data points or to measure gradients. Look at the graph below. How would you draw a best fit line? • The line should represent the general trend as close as possible • There should be as many points above as there are below the line • Excel and Logger Pro will draw best fit lines for you. BAR/COLUMN GRAPHS Bar graphs can also be used in scientific reporting. We choose to use a bar graph when we have non-continuous data. That is, there is no reason to show data between two points on the graph. Notice that it would make no sense to draw a line between testosterone and prolactin as there is no data between them (i.e. non-continuous) If there is only one set of data, we use a bar graph (i.e. no x and y data) You must still fully label your bar graph. WHAT’S WRONG WITH THESE GRAPHS? A B C D