11.3.6 Using the Graph
Since you would expect the woman’s weight to change steadily between hospital visits, it is possible to use the graph to estimate her weight at other times during the six weeks. [ It may be helpful to print this page, so that you may draw lines on the graphs to identify values. You may also use an object with a straight edge, such as a ruler or piece of paper, and hold it up to your monitor to help visualize where certain points appear in relation to the axis. ]
For example, to estimate her weight at 35 weeks, first find 35 on the horizontal axis. Then from this point, draw a line parallel to the vertical axis, until the line meets the curve at point P. From P, draw a line horizontally, to meet the vertical axis. Read off this value: here, it is about 168.4 lb.
So, an estimate of the woman’s weight at 35 weeks is between 168 and 169 lb. Determining values between the plotted points is known as interpolation.
Activity: Reading a Value from a Graph
Use the graph above to answer the following.
(a) How would you estimate the woman’s weight at 37 weeks?
(a) Find 37 on the horizontal axis and draw a line vertically up to the curve. Then draw a line horizontally from this point to intersect the vertical axis. This value is approximately 171.2 lb. The woman’s weight at 37 weeks is estimated to be about 171 lb.
(b) When do you think the woman’s weight was 167 lb?
(b) Find 167 lb on the vertical axis. Draw a horizontal line to meet the curve. Then draw a line vertically down to meet the horizontal axis. Read off the value: it is just over 34 weeks. So the woman’s weight is estimated to have been 167 lb after about 34 weeks.
(c) From the graph, can you predict the weight of the woman at times later than 40 weeks?
(c) Sometimes it is possible to extend a graph past the plotted points and use the graph to read off values outside the data set. For example, if the baby had still not been born after 41 weeks, then you might estimate that the mother would weigh about 173.4 lb.
However, a woman’s pregnancy usually lasts about 40 weeks and when the baby is born, her weight will fall substantially. If the baby is born before 41 weeks , the woman’s weight at 41 weeks would not be 173.4 lb. As there is no information given on when the baby was born, it is not possible to use the graph to estimate the woman’s weight after 40 weeks.
Trying to estimate the coordinates of points on the graph that lie outside the plotted points is known as extrapolation. It can sometimes be used to find values that are close to the plotted data set, if you are confident that the graph continues in a similar manner. However, you do need to be cautious: we cannot be certain that trends shown in graphs will continue.
The graph can also be used to determine the overall trend in the data—how one value is changing with the other. In this case, the graph emphasizes the change in the woman’s weight during the last few weeks of pregnancy. It shows that she gained weight quite rapidly between weeks 34 and 36, but from week 36 to week 40 she gained less.