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Means and Deviations

ENVS 202 On-line Access

Sample Means and Deviations

In class exercise. Class do the following:

Draw a number from the Sacred Box of Sampling in the front of the Lecture room
Return to your seat with that number and note your seat number
Be prepared to tell the instructor your number if your seat numbers is randomly called
That is all

In the Sacred Box of Sampling there are 170 numbers which define this Intrinsic Distribution .

The point of the in class exercises is to demonstarte that a random sampling process done for an intrinsic distribution which is normally distributed (i.e. a bell curve) will provide a robust estimate of the mean and dispersion after just a small number of samples.. While this can be proved with calculus (and in statistics is known as the Central Limit Theorem), the in class example is the probably the best means of demonstrating this.

For this sample as a whole:

The mean = 175

The dispersion = 23

The point of the demo in the class is to see how close we can come to recovering this population mean and dispersion from the sample mean and dispersion.

In general, we use statistics as a means of characterizing the nature of some sample on the basis of a few key indicators.

The first indicator is known as The Sample Mean:

The mean quantity in some sample represents the average value or the most probable value in the sample.
- A sample mean is calculated by summing up the individual measurements and dividing by the number of measurements, usually denoted as N.
- All samples can be characterized by a mean value regardless of the shape of the distribution
  
  Example:

I open a new store at the Gateway mall that specializes in selling thematic environmental wallpaper. I notice that there are 6 people browsing in the store and I ask them their ages. Their ages are:

23 33 43 25 37 51

Use the Tool

The Mean age of the population in the store is 35 years. Does that tell me much?

The second indicator we use is known as the Sample Variance, also known as the Sample Dispersion. This is usually denoted by the greek letter sigma

In general, the dispersion is a more important quantity than the sample mean. The dispersion represents the range of the data about the mean value. Understanding the role of dispersion is the most critical aspect of understanding and interpreting statistical sampling data.

So let's take a look at how dispersion plays such a critical role.

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