Chapter 3, Problem 3.1EAA

To determine

The number of first-year, full-time enrollments expected in 2010 if the administrator used the data from 1975 to 1980 and to calculate the percentage error.

Answer to Problem 3.1EAA

The number of first-year full time enrollments expected in 2010 if the administrator used the data from 1975 to 1980 as 375000 students and the percentage error is 226%.

Explanation of Solution

Given information:

As per the given data, to find the error percentage upon usage of the data from 1975 to 1980 to predict the number of first-year full time enrollments expected in 2010.

According to the data in the Engineering for your future book, the following table illustrates the actual data for the years 1975 to 2010 and the predicted data for the year 2010 using only the estimates from 1975 to 1980.

Year	Actual enrollments	Predicted enrollments
1975	45000	45000
1980	118000	118000
1985	115000	143000
1990	90000	200000
1995	80000	237000
2000	82000	287000
2005	110000	328000
2010	115000	375000

The following is a graphical illustration of the same data in the table:

The above graph shows huge differences in the predicted data since it has taken the data belonging to the years 1975 to 1980 and prorated the same to the rest of the years until 2010. By doing this, the administrator has missed few important factors like the number of births every year; number of high school graduates every year, and other economic factors. These factors tend to change year after year and by taking only the data from 1975 to 1980, the number of enrollments for several years cannot be predicted accurately.

The percentage of error can be calculated as:

Percentage error $=\frac{estimate-actual}{actual}\times 100$.

$=\frac{375000-115000}{115000}\times 100=226\%$.

This shows that there is a huge percentage error upon the usage of the data from 1975 to 1980 to predict the number of first-year full time enrollments expected in 2010.

Conclusion:

Thus, the number of first year full-time enrollments expected in 2010 if the administrator used the data from 1975 to 1980 and the percentage error is discussed in details.