The covariance is a single statistical figure that represents how one data set relates to another. In the example mentioned in the introduction, height and weight are being measured. You would expect that as individuals grow taller, their weight would also increase, leading to a positive covariance figure. As another example, suppose data is collected representing the number of hours someone practices golf and the score he or she may earn. In this case, you would expect a negative covariance, which means that as the number of practice hours increases, the golf score will decrease. (In golf, a lower score is better.)Consider the sample data set that was calculated above. The resulting covariance is -8.07. The negative sign here means that as the x-values increase, the y-values will tend to decrease. In fact, you can see that this is true by looking at a few of the values. For example, the x-values of 1 and 2 correspond to y-values of 7, 8 and 9. The x-values of 8 and 12 are paired respectively with y-values of 3 and 2. 


, If the number of the covariance score is large, either a large positive number or a large negative number, then you can interpret this as meaning that the two data elements are very strongly connected, either in a positive or negative way.For the sample data set, the covariance of -8.07 is fairly large. Notice that the data values range from 1 through 12, so 8 is a pretty high number. This indicates a strong connection between the x and y data sets.
 If you wind up with a covariance equal to or very near 0, you can conclude that the data points are relatively unrelated. That is, an increase in one value may or may not lead to an increase in the other. The two terms are almost randomly connected.For example, suppose you are comparing shoes sizes against SAT scores. Because there are so many factors that affect a student’s SAT scores, we would expect a covariance score of near 0. This would indicate almost no connection between the two values.
 To understand covariance visually, you can plot your data points on the x-y coordinate plane. When you do that, you should see fairly easily that the points, although not in an exactly straight line, tend to form a cluster that approximates a diagonal line from the upper left to the lower right. This is the description of a negative covariance. Also, notice that the covariance value is -8.07. This is a fairly large number compared to the data points. The high number suggests that the covariance is fairly strong, which you can see by the linear appearance of the data points.

To review plotting points on the coordinate plane, see Graph Points on the Coordinate Plane.
Look for a positive or negative relationship.
Interpret the magnitude of the covariance.
Understand a lack of relationship.
View the relationship graphically.
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