Statistical Inference: A Short Course

2.2 Tabular and Graphical Techniques: Ungrouped Data

Suppose we have a sample of n observations on some variable X. This can be written as

Our first construct is what is called an absolute frequency distribution—it shows the absolute frequencies with which the “different” values of a variable X occur in a set of data, where absolute frequency (f_j) is the number of times a particular value of X is recorded.

Example 2.1

Let the n = 15 values of a variable X appear as

Table 2.1 describes the absolute frequency distribution for this data set. Note that while there are 15 individual values for X (we have X: X_i, i = 1, . . . , 15), there are only six “different” values of X since most of the X values occur more than once. Hence, the j subscript indexes the different X's (there are only six of them so j = 1, . . . , 6). So given this absolute frequency distribution, what sort of pattern emerges? Is there a “most frequent” value or a “least frequent” value?

Table 2.1 Absolute Frequency Distribution for X

X	Absolute Frequency (fj)
1	3
2	2
3	4
4	3
5	1
6	2
15 = Σfj = n

Our next descriptive tool is the relative frequency distribution—it expresses each absolute frequency (f_j) as a fraction of the total number of observations n. Hence, a relative frequency is calculated as ...