Predicting the Future
Resources for this lesson:
Key Terms
Population mean
Sample mean
> Glossary 
> Calculator Resources
> Teacher Resources: Instructional Notes
Year |
Snowfall Amount |
|---|---|
1990 |
17.3 |
1991 |
9.4 |
1992 |
4.1 |
1993 |
24.4 |
1994 |
17.3 |
1995 |
8.2 |
1996 |
62.5 |
1997 |
15.3 |
1998 |
3.2 |
1999 |
15.2 |
2000 |
26.1 |
2001 |
8.7 |
2002 |
2.3 |
2003 |
58.1 |
2004 |
18.3 |
2005 |
18.0 |
2006 |
19.6 |
2007 |
11.0 |
2008 |
8.5 |
2009 |
9.1 |
2010 |
77.0 |
2011 |
14.4 |
2012 |
1.8 |
Source: http://www.nws.noaa.gov/climate/local_data.php?wfo=lwx
Check Your Understanding
Marissa: That is not much lower than the population mean, is it?
Allyson: No. I guess we were wrong. The average annual snowfall in Maryland is approximately 20.6 inches.
You may be wondering why the girls arrive at a mean of 19.557, when it has been reported that the mean snowfall amount for Maryland is 20.6 inches. The 20.6 inches is the population mean, whereas the 19.557 is the sample mean. The population mean is formed from all of the reported snowfall amounts for all of the reporting years. The sample mean was only the twenty-three data points listed above.
Using this experiment, Allyson can make the following prediction:
Allyson: I predict that next year’s snowfall will be approximately 20.6 inches for the season. The amount of snowfall we have had in Maryland over the last three years has been 77.0 inches, 14.4 inches and 1.8 inches. If we were to average just these three amounts we could claim that the average snowfall for Maryland is 31.07 inches but that might be misleading. In this three-year period, we had one year with an unusually high amount of snowfall of 77 inches and one year with a very low snowfall amount of 1.8 inches. I predict that this year the snow fall amount in Maryland is going to turn to normal, and we will have about 20.6 inches of snow which is the population mean for the snowfall data. I can’t wait!
