Page 16 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 1: Quantitative Techniques for Managers

Self Assessment Notes

Fill in the blanks:
6. ………………….are those in which each component exhibits a linear behaviour.
7. A …………….is the experimentation on a mathematical structure of real-life system.

1.5 Various Statistical Techniques

A brief comment on certain standard techniques of statistics which can be helpful to a decision-
maker in solving problems is given below. However, each one of these techniques requires
detailed studies and in our context we are merely listing these to arouse your interest.
(i) Measures of Central Tendency: Obviously for proper understanding of quantitative data,
they should be classified and converted into a frequency distribution (number of times or
frequency with which a particular data occurs in the given mass of data). This type of
condensation of data reduces their bulk and gives a clear picture of their structure. If you
want to know any specific characteristics of the given data or if frequency distribution of

one set of data to be compared with another, then it is necessary that the frequency
distribution itself must be summarized and condensed in such a manner that it must help
us to make useful inferences about the data and also provide yardstick for comparing
different sets of data. Measures of average or central tendency provide one such yardstick.
Different methods of measuring central tendency provide us with different kinds of
averages. The main three types of averages commonly used are:
(a) Mean: The mean is the common arithmetic average. It is computed by dividing the
sum of the values of the observations by the number of item:: observed.
(b) Median: The median is that item which lies exactly half-way between the lowest and
highest value when the data is arranged in an ascending or descending order. It is
not affected by the value of the observation but by the number of observations.
Suppose you have the data on monthly income of households in a particular area.
The median value would give you that monthly income which divides the number
of households into two equal parts. Fifty per cent of all the households have a
monthly income above the median value and fifty per cent of households have a
monthly income below the median income.
(c) Mode: The mode is the central value (or item) that occurs most frequently. When the
data organised as a frequency distribution the mode is that category which has the
maximum number of observations.

Example: A shopkeeper ordering fresh stock of shoes for the season would make use of
the mode to determine the size which is most frequently sold.
The advantages of mode are that (a) it is easy to compute, (b) is not affected by extreme values in
the frequency distribution, and (c) is representative if the observations are clustered at one
particular value or class.
(ii) Measures of Dispersion: The measures of central tendency measure the most typical value
around which most values in the distribution tend to converge. However, there are always
extreme values in each distribution. These extreme values indicate the spread or the
dispersion of the distribution. The measures of this spread are called ‘measures of dispersion’
or ‘variation’ or ‘spread’. Measures of dispersion would tell you the number of values
which are substantially different from the mean, median or mode. The commonly used
measures of dispersion are range, mean deviation and standard deviation.
The data may spread around the central tendency in a symmetrical or an asymmetrical
pattern.

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