General Education and Assignments

Modeling Real Data

A Math 1010 project

 

Data from the United States Census Bureau about children living with both parents has been decreasing steadily in the United States.  The following table shows the percent of children (under 18) living with both parents since 1980.  In this project, you will have the opportunity to use the data in the table to find a linear function  that represents the data, reflecting the change in living arrangements of children.

 

 

PERCENT OF U.S. CHILDREN LIVING WITH BOTH PARENTS

Year	1980	1983	1988	1992	1997	2000	2005	2008
X	0	3	8	12	17	20	25	28
Percent    Y	77	75	73	71	68	69	67	67

 

 

1.         Plot the data given in the table as ordered pairs.

 

2.         Use a straight-edge to draw on your graph what appears to be the line that  “best    fits” the data you plotted.  Hint:  Use two points that are already on the graph.

 

3.         Estimate the coordinates of two points that fall on your  “best fits” line.  Use these    points to find the slope of the linear function .

 

                       (0,77) (20,69)

 

            The slope of the function is  .   M= -2/5

 

4.         Interpret the meaning of the slope.  Be specific.  Does it make sense in the context of this situation?

 

-The slope is negative meaning that every two years there are about five percent more children living without both parents.

 

 

5.         What is the y-intercept of your line of “best fit”?  What does it mean?

            Write the function of the  “best fit” line.

 

-The Y intercept = 77 This means we started the graph and data at 77% of kids living with both parents. The meaning of “Best Fit” is an educated guess that helps plot a line of what will most likely happen if the same trend of data keeps up.

 

 

6.         Compare your graph with another person or group. Are           the linear functions the        same?  Are they different?  If so, explain why.

 

-No, their line of best fit was steeper than mine. This would change the slope and changes all other data.

 

 

7.         Find the value of ?  Is this what you expected by looking at the data from the table above?

 

f(x) = -2/5 x + 77

f(10) = -2/5 (10) + 77

f(10)= 73 – Yes, it falls on the line of best fit, and is decreasing since 1980

 

8.         In what year would you expect to have 61 percent of children in the United States   living with both parents?

 

61 = -2/5 x +77

-16 = -2/5 x

-16/(-2/5) = x

X = 40 … The year 40 = 61%

 

9.         Use your function to predict the percent of children living with both parents in         2030, 2080 and 2230.   Do these predictions make sense?  Why or why not?

 

f(50) = -2/5 (50) +77 = 57% - this makes sense it could happen.

f(100) = -2/5 (100) +77 = 37% - this could be possible if the rate stays the same.

f(250) = -2/5 (250) +77 = -23% - this is not possible. It isn’t realistic. You can’t have negative kids living with both parents.

 

10.       Reflection:  Write a paragraph or two discussing what you have learned by doing    this project.  Include something about “real world data” and the accuracy of long- range predictions?

 

I noticed how this graph only works for the short time. Especially because there will come a point where people will still stay together and kids will still have both parents. If you try guessing far into the future using the “line of best fit” it might give you an idea of what will happen, but it will not be accurate. Also if you chose a “line of best fit” that is too steep or to shallow of a slope, then your statistics and data could be very far off real data.