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Using A Statistics Formula To Establish Confidence Intervals of a Poll

In many if not most statistical studies, a conclusion is made as to whether a particular set of data is significantly different from a control set of data. In order to make that conclusion, one must know the variability of the data.  The measure of variability used is nearly always the standard deviation. The standard deviation is approximately equal to the average deviation from the mean and is one of the first formulas a student of introductory statistics will learn.  The standard deviation formula is fairly straightforward, but its formula may appear confusing at first glance.

The Standard Deviation Formula

In this formula, x is the value of the mean, N is the sample size, and xi represents each data value from i=1 to i=N..  The ∑ symbol indicates that you must add up the sum
 (x1 - x)2 + (x2 - x)2 + (x3 - x)2 + (x4 - x)2 + (x5 - x)2. . . +  (xN - x)2.
The ∑ symbol represents the "summation function" in mathematics.  A student with little or no algebra background would perhaps find this formula confusing.  A student completing several years of algebra would probably not have difficulty working with this formula however.  For sure a student completing calculus would have no problem following this formula since the ∑ symbol  is used in many calculus concepts.

This example shows why the average first year introductory statistics course in college requires a minimum of 1 or 2 years of algebra.  And, statistics is required for most degrees, even non-science and non-math degrees.


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