Using A Statistics Formula To Establish Confidence Intervals of a
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
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.