vdoc

218 Part IV: Quality Assurance
Part IV.A.4
Let X 1 , . . . , X n be a set of quantitative data. We would like to construct a
frequency distribution table for this data set. In order to prepare such a table we
need to go through the following steps.
Notes:
Step 1. Find the range of the data that is defined as
Range (R) = largest data point – smallest data point (18.13)
Step 2. Divide the data set into an appropriate number of classes/categories.
The appropriate number of classes/categories is commonly defined
by using Sturgis’s formula as follows:
m = 1 + 3.3 log n (18.14)
Where n is the total number of data points in a given data set.
Step 3. Determine the width of classes as follows:
Class width = R/m (18.15)
Step 4. Finally, prepare the frequency distribution table by assigning each
data point to an appropriate class or category. While assigning
these data points to a class, we must be particularly careful to
ensure that each data point be assigned to one, and only one,
class and that the whole set must be included in the table. Another
important point is that the class on the lowest end of the scale must
be started with a number that is less than or equal to the smallest
data point and that the class on the highest end of the scale must
end with a number that is greater than or equal to the largest data
point in the data set.
1. Quite often when we determine the class width, the number obtained
by dividing R with m is not an easy number to work with. In such cases
we should always round this number up, preferably to a whole number.
Never round it down.
2. When we use Sturgis’s formula to find the number of classes, the value
of m is usually not a whole number. In that case one must round it
up or down to a whole number since the number of classes can only
be a whole number.
EXAMPLE 18.17
The following data define the lengths (in millimeters) of 40 randomly selected rods
manufactured by a company:
145 140 120 110 135 150 130 132 137 115
142 115 130 124 139 133 118 127 144 143
Continued