Page 131 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Methodology of Research and Statistical Techniques

Notes zero. In computation of mean all observations are taken into consideration. This is preferred
because of its high reliability and its applicability to inferential statistics.

Notes The Mean indicates the average performance of the members of the group. It is
used to give an idea about how varied are the scores from the central value.

Educational Situations and Use of Mean
Mean is used when :
(i) Scores are nearly symmetrically distributed around a central point i.e., distributions are
not markedly skewed.
(ii) We wish to know the centre of gravity of a sample.
(iii) Central tendency with greatest stability is wanted.
(iv) When other statistics (standard deviation, coefficient of correlation etc.) for inferential
purposes are to be calculated.
(v) Group performances are to be compared with accuracy and precision.
Limitations of Mean
Sometimes Mean of a distribution is highly misleading especially when some of the observations
are too large or too small as compared to the others. If you want to study the average class
size and there are 5 classes with 100 - 150 students, 10 classes having 50 to 100 students and
35 classes having 30 to 50 students each. Then the Mean of 55.5 would not represent the
typical case. Even within a class if 5 students’ scores are 12, 15, 20, 25 and 100, the Mean of
34.4 can be misleading. There are situations where mean may not provide meaningful information.

The Combined Mean
You might have noticed in school situations that we have 3 or 4 sections of unequal size and
we find mean achievement of students In a given section using the methods discussed above.
In case we wish to know the school mean, the need for a method to calculate combined mean
would arise. Similarly if we have the means for various schools and the district mean is
required, it would also call for computing the combined mean.
Mean of Sample 44.6 55.0 58.5
Sample size 20 40 140
Combined Mean = (N1M1 + N2M2 + N3M3)/ (N1 + N2 + N3)
= (20 × 44.6 + 40 × 55.0 + 140 × 58.5)/(20 + 40 + 140)
= (892 + 2200 + 8190)/200
= 11282/200

= 56.41
From the above example you may notice that the combined weighted Mean has been obtained
to be 56.41. If someone erroneously adds up the given means and divides by 3 he/she would
come across an average of 52.7. Obviously it is incorrect. We should obtain the coinbined/
weighted mean using the procedure described above.
Relationship between Mean, Median and Mode
In your dealings with a variety of data you may come across situations where these three
measures of central tendency are very close to each other or at divergence. This largely depends

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