Lecture 4/ Measures of Central Tendency/2018 - 2019 /

Measures of center
[Agresti & Finlay (1997), Johnson & Bhattacharyya (1992), Weiss
(1999) and Anderson & Sclove (1974)]
Descriptive measures that indicate where the center or the most typical value
of the variable lies in collected set of measurements are called measures of
center. Measures of center are often referred to as averages.
The median and the mean apply only to quantitative data, whereas the mode
can be used with either quantitative or qualitative data.
4.1 The Mode
The sample mode of a qualitative or a discrete quantitative variable is that
value of the variable which occurs with the greatest frequency in a data set.
A more exact de?nition of the mode is given below.
Definition 4.1 (Mode). Obtain the frequency of each observed value of the
variable in a data and note the greatest frequency.
1. If the greatest frequency is 1 (i.e. no value occurs more than once),
then the variable has no mode.
2. If the greatest frequency is 2 or greater, then any value that occurs with
that greatest frequency is called a sample mode of the variable.
To obtain the mode(s) of a variable, we ?rst construct a frequency distribu-
tion for the data using classes based on single value. The mode(s) can then
be determined easily from the frequency distribution.
Example 4.1. Let us consider the frequency table for blood types of 40
persons.
We can see from frequency table that the mode of blood types is A.