Height and Weight for Growing Children
Background: Doctors use charts to assess children's growth. They compare the height and weight of the child against other children of the same age. You have been given a copy of the chart they use to keep track of a child's growth. In order to computerize this information, we need to translate the charts into functions.
Choose a gender, age group, and either height or weight.
Understanding the data for one year: Choose one age. Construct a table of values for all the percentiles given on the curve for that age. Use this data to sketch a normal distribution curve. Approximate the standard deviation for the data. Justify your approximation. Label your normal distribution curve with the values for the intervals from x (bar) - 3s to x (bar) + 3s. How big would a child this age and gender be if he/she was at the 84 percentile? Find a child that matches your chosen age and measure him/her. Estimate his/her percentile. Justify your responses.
Comparing models for a child's growth: Choose a percentile curve. Construct a table of values for your percentile for each age on your curve. Use your calculator to determine the regression equations for your data. Find three different models: linear, logarithmic and exponential. Construct a graph comparing each model to the actual data. Write a description of how well each model fits the given data. Be specific about where it fits well and where it doesn't.
Constructing the best model: Break the data into sections and choose which type of model is best for each section. Find new regression equations for only the part of the data for that model. Construct a new chart that uses the different equations for the different areas of the curve. Describe how well your new model fits the data. Discuss the decisions you made on where and how to break up the data. Describe alternate solutions you tried.
Interpolate and Extrapolate: Choose a half-year data point and compare the values given by the different models. Choose a data point either before or after the values on your curve and compare the values given by the different models.
Rate of Change: Describe how the rate of change of the growth of a child changes over the years. Describe how this is reflected in each of your models.
End Behavior of Models: Describe what is happening to the growth of the child at the end of your curve. Compare this to the behavior of each of your models if the curve continued.
Summarize: Which function would you recommend be used to model your percentile curve? Justify why this is the best model for the data.
Well Child Graphs
