Statistical
Analysis
Statistics concerns scientific methods
for collecting, organizing, summarizing, presenting, and analyzing data as well
as drawing valid conclusions and making reasonable decisions on the basis of
such analysis. The following statistical
quantities should be computed for your experimental data:
Mean:
The arithmetic mean is defined as the sum of a set of numbers divided by
the number of elements in the set.
Standard
Deviation: The standard deviation is defined as:
s = 
Xis an element of the set
N is the
total number of elements in the set
The
summation is performed over all elements of the set
Optional
quantities include:
Median:
The median of a set of numbers arranged in order of magnitude is either
the middle value or the arithmetic mean of the two middle values.
Mode: The
mode of a set of numbers is that value which occurs with the greatest
frequency; that is, it is the most common value. The mode may not exist, and even if it does exist
it may not be unique.
Histograms: The
steps in constructing a histogram are:
1. Find the range of the data. The range of the data is the difference
between the largest and smallest number.
2. Divide the range into a convenient number of class
intervals having the same size. 10 is
usually convenient.
3. Determine the number of data points belonging
to each data class. This is called the
class frequency.
A histogram consists of a set of
rectangles having equal sized bases on the x axis. The center of each rectangle should
correspond to the middle of each class.
Width of the rectangles is equal to the class interval size. Height of the rectangles, on the y axis, is equal to the class frequency.
Size
of Sample: Experts often claim that “40 is
enough”. The rest of us
wonder. Test this out in a hardness test
by plotting the average value of your readings
versus the number of readings taken.
This moving average will fluctuate initially, but then will settle down
as you include more sample data points in the analysis. Try it out!
