Overview
Data in real-world situations doesn’t always fall into neat linear relationships. The actual values may be plotted in a scatterplot. Trend lines approximate the direction and size of the relationship between data points, as do median-fit lines.
Scatterplots
Actual data values can be plotted by ordered pairs on a graph called a scatterplot. The domain or independent value is on the x axis and the range or dependent value is on the y axis. The more data values there are available, the more can be plotted, even if they don’t fall on a line. Scatterplots are useful because they show the range and direction of many different data points.
Correlations
Scatterplots are also useful because they can show the relationships between variables, such as height and weight, average temperature and power usage, or hours of study and test scores. The relationship between two different types of data is called correlation. If the values for both types of variables increase, the correlation is positive. Suppose a seed is planted and the height of the plant is measured every day. There is a positive correlation between the height of the plant and the number of days since it was planted, because the plant grows. If the values along one axis increase while the values along the other axis decrease, the correlation is negative. For example, as it is darker outside, the more light is needed inside. The darkness outside increases, while the light inside increases. Some variables have no relationship, called a zero correlation. For example, there is probably no correlation between the number of sunny days in Seattle, Washington with the number of cars sold in Denver, Colorado. The scatterplot for those two variables will not show a clear relationship.
Trend Lines
Once data points have been plotted on a scatterplot and the direction of a correlation has been observed, a line can be drawn estimating that relationship, called a trend line. It may or may not go through specific data points, and usually has as many points showing above the line as below the line. If data are plotted on a graphing calculator or a computer spreadsheet, the trend line is often calculated automatically.
Median-Fit Lines
Median-fit lines are specific types of trend lines that use the values found in the data set. First, all values in the data set can be plotted on a graph as a scatterplot to see the direction of the correlation. Divide the data into three groups with equal numbers of data points in each group. If there are not three groups of equal size, make sure the first and third groups are equal. Next, find the median value for the x values and y values for each group. Plot the median values on the same graph and draw a line connecting the median points of the first group and the third group. The median-fit line will be parallel to that line.
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