Standard deviation is a statistic that tells you how closely a group of numbers (for example, temperatures) are clustered around a mean value (average temperature). When the standard deviation is small, the numbers are fall close to the mean. When the standard deviation is large, the individual values are spread out far from the mean.
When expressing the mean of a set of temperature values, it is helpful to give the standard deviation as well. If the mean temperature value has a large standard deviation associated with it, it probably means there were large fluctuations in the data. If, on the other hand, the standard deviation is small, the temperatures measured were probably fairly uniform.
To calculate standard deviation, subtract the average value from each number in your set, and then square each of the differences. Sum up all of the squares and divide by the number of values in the set. Then take the square root.
Problem:
Do current weather conditions fall outside of the historical norm?
Materials:
- Calculator (Microsoft Excel may alternately be used if it is available to the student.)
Procedure:
- Based on your personal observations of the weather patterns, formulate a hypothesis that predicts whether local weather conditions are outside historical norms.
- Decide on a location whose weather patterns you wish to monitor.
- Check the United States Historical Climatology Network web site to see whether it includes historical weather data for the location you have chosen to study. If it doesn’t, select a nearby location. The website has temperature precipitation data going back over 100 years for many locations in the U.S.
- Calculate the average temperature and precipitation values for each month going back at least 30 years.
- Tabulate and plot your results.
- Compare temperature and precipitation data for the current month with the historical values.
- Determine whether the average measured temperature falls within one, two or three standard deviations of the mean.
- Evaluate your hypothesis. If necessary, revise it and perform additional calculations.
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