Graphical Summary

Confidence Intervals for Mean, Standard deviation, and Median

  

A confidence interval is an interval used to estimate a population parameter from sample data. The upper and lower bounds of the confidence intervals for m (mu), s (standard deviation), and the median are displayed in the graphical summary. In addition, the confidence intervals for m and the median are displayed graphically.

Confidence intervals are composed of two basic parts:

·    point estimate - a single value computed from the sample data. This value is considered to be an estimate of the parameter of interest, however it is unlikely that the point estimate is equal to the parameter. Therefore, to account for the possibility of estimation error, the error margin is included in the confidence interval to provide a range of possible parameter values.

·    error margin - determines the width of the confidence interval through the use of probability. To construct the confidence interval, you simply add and subtract the error margin from the point estimate.

If a 95% confidence interval is selected, the method used to construct the interval has a probability of 0.95 of producing an interval containing the parameter of interest. In other words, you can be 95% confident that the true value of the parameter is within the interval. Thus, if one hundred 95% confidence intervals were constructed, you would expect around 95 of the intervals to contain the parameter.

Example Output

image\grph_4n.gif

95% Confidence Interval for Mean

2.0388                5.2339

95% Confidence Interval for Median

2.0000                4.0822

95% Confidence Interval for StDev

1.6615                4.1731

 

The confidence intervals are pictured in the lower left corner of the Graphical Summary. The corresponding statistics are located to the right of the graphs.

Interpretation

 

The confidence intervals for the precipitation data indicate that you can be 95% confident that:

·    m (mean) is between 2.0388 and 5.2339.

·    s (standard deviation) is between 1.6615 and 4.1731.

·    the median is between 2.0000 and 4.0822.

 


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