Purpose and types of graphs Graphs help analyze and communicate data Purpose of graphs: • Convey information quickly and clearly • Visualization of large amounts or complicated data • Help support claims using evidence Bar Charts Data that is counted and has no in-between value is called discrete data. Discrete data is usually collected in a frequency table and then presented as a bar chart. Pet Cat Dog Fish Rabbit Other A bar chart has a horizontal axis and a vertical axis. • A bar chart must always have a title explaining what it shows. • Bars must be carefully drawn to show the data. 16 • There must be a gap between each bar. 12 A number line is marked on the vertical axis. The scale of this number line is chosen based on the data range. The data categories are organised on the horizontal axis. Each axis must have a label explaining what it shows. A Bar Chart to Show How Many Pets Y6 Have 14 Number of Children • Each bar must be the same width. Number of Children 12 14 7 5 8 10 8 6 4 2 0 Cat Dog Fish Type of Pet Rabbit Other Bar graph • Show data when your IV is categorical (qualitative) and your DV is continuous (quantitative) Comparative Bar Charts Discrete data in each category can also be represented in subcategories: Number of Girls Cat 7 5 Dog 6 8 Fish 3 4 Rabbit 1 4 Other 2 6 We can draw a grouped bar chart to show this data. In this bar chart, each category has more than one bar. A key is used to identify the subcategories of the data. A Bar Chart to Show How Many Pets Y6 Have Number of Boys Number of Girls 10 9 Number of Children Pet Number of Boys 8 7 6 5 4 3 2 1 0 Cat Dog Fish Type of Pet Rabbit Other Histogram Line Graphs The data being measured is shown on the vertical axis. The time the data is being measured over is shown on the horizontal axis. Data is plotted on to a line graph in the same way as a coordinate grid. These data plots are then joined with straight lines. We can use the line of the graph to describe general trends in the change of the measurement over time, or to find precise measurements at a given time. A Line Graph to Show the Temperature of the Classroom 40 38 36 Temperature °c Line graphs are used to show changes to a measurement over time. They show continuous data. 34 32 30 28 26 1 3 Time 5 7 Line graph • Lines connect each data point • IV is usually quantitative • DV is quantitative Pie Charts Pie charts show discrete data as proportional sectors of a circle. Every sector of a pie chart is a proportion of the whole. You can explain what each sector represents using an angle, fraction or percentage. Being able to convert between fractions, percentages and angles is a key skill for answering questions about data presented in a pie chart. We can use fraction, percentage and angle equivalents to interpret the data in a pie chart. If the whole pie chart represents 120, the value of the orange sector is 60. Types of graphs: Pie Chart • Function: shows data as parts of a whole (% of each category, calculated by dividing # in a category total # in all categories *100% • Must add to 100% Types of graphs: Scatter plot • Function: shows overall trend using a regression or trend line for a data set. • Individual points are not connected • IV and DV are quantitative Super toxic newt (Taricha granulosa) Describing Graphs Optimum • Highest point on a graph indicating the optimal (best) condition What is the optimal pH for pepsin, salivary amylase, and alkaline phosphatase? pH = 6 pH = 1.5 X pH = 9 X X Describing Graphs Trend • general pattern observed in a graph Overall trend Describing trends Increase (go higher, positive slope) Decrease/decline (go lower, negative slope) Exceed (one gets bigger than another) Declining Increasing Exceeding (moose EXCEED wolves) Describing trends • Reach a plateau / stabilizing / reach equilibrium • graph levels out and you get a relatively flat horizontal line Validity • Sometimes a data point has a value that is way off from all the other points, so we question its validity. Sometimes it is the result of natural variation and sometimes it indicates that there was a procedural error and is invalid. Is this point likely valid? Describe the overall trend. What is a possible title?
