Page 121 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Methodology of Research and Statistical Techniques

Notes 8.1 Individual and Group Measurements

Measurement is the means of providing quantitative description where numbers are assigned
to objects or events according to some rules. These objects or events may sometimes relate to
the individuals or groups of individuals depending upon the purpose of measuring an attribute.
The rules adopted become the criteria and help in providing systematic and objective mode
for deriving accurate judgements about individuals or groups of individuals leading to solutions
to various educational problems. The nature of rules may vary from simple to complex and
we come across the lowest to highest forms of measurements. From lower to higher levels we
have nominal, ordinal, interval and ratio measurement scales. The higher level scales require
more restrictive rules and the obtained measurement may require one to undertake more
operations.
Concept of Measures of Central Tendency
You as a teacher might be coming across a variety of data pertaining to student's achievement
or other characteristics, both of individuals or groups of individuals. We may often be interested
in having a concise description of the performance of the group as a whole. In case there are
more than one group one may like to compare the groups in terms of their typical performance.
Such descriptions of group performances are known as measures of central tendency. Let us
assume that we have got the scores of students of three sections of class IX with 40 students
each in these sections. We may compute an index of the sets of scores of 40 students in each
section which would represent the average performance of the three sections in a given subject.
Such an index would be a measure of central tendency. It can very well be used to understand
the nature of scores in each section and for making inter-group comparisons. The most commonly
used measures of central tendency are Mode, Median and Mean.

Scales of Measurement and Measures of Central Tendency
If we have data on some characteristics of students and we wish to describe the group we
would be trying to look for an appropriate measure of central tendency. It would be pertinent
to note that selection of appropriate measure of central tendency would largely depend upon
the nature of data, more specifically the scale of measurement used for representing it. Several
kind of averages may be worked out. Here we will discuss the mode, median and mean for
data collected on nominal, ordinal and interval scales respectively.

8.2 Data on Nominal Scale and Measure of Central Tendency

8.2.1 The Mode

Data obtained on the nominal scale is of classificatory type and mostly qualitative. We can
count the number of cases in each category and obtain the frequencies. We may then be
intested in noting down the class which is most populous or popular. We frequently deal with
‘scores’ in measurement in education. The score obtained by the largest number of individuals
is the mode of that group of scores. For example, if in a section of 40 students of class IX the
number of students obtaining the score of 55 is the highest, 55 would be called the mode of
the scores for that section. Generally such values are seen to be centrally located, with other
values in either direction having relatively lower frequencies. Thus the mode presents a rough
estimate of the most typical or the average score in a group of values. It is not essential to have
precise scores of all the individuals of the group for finding out mode.

116 LOVELY PROFESSIONAL UNIVERSITY