Page 167 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes Distance measures: The measures which express the spread of observations in terms of distance
between the values of selected observations. These are also termed as distance measures, e.g.,
range, interquartile range, interpercentile range, etc.
Interquartile Range: Interquartile Range is an absolute measure of dispersion given by the
difference between third quartile (Q ) and first quartile (Q )
3 1
Symbolically, Interquartile range = Q – Q .
3 1
Measure of central tendency: A measure of central tendency summarizes the distribution of a
variable into a single figure which can be regarded as its representative.

Measure of variation: The measure of the scatteredness of the mass of figures in a series about an
average is called the measure of variation.
Quartile deviation or semi-interquartile range: Half of the interquartile range is called the
quartile deviation or semi-interquartile range.
Range: The range of a distribution is the difference between its two extreme observations, i.e.,
the difference between the largest and smallest observations. Symbolically, R = L – S where R
denotes range, L and S denote largest and smallest observations.
Standard deviation or root-mean square deviation: The squares of the deviations from arithmetic
mean are taken and the positive square root of the arithmetic mean of sum of squares of these
deviations is taken as a measure of dispersion. This measure of dispersion is known as standard
deviation or root-mean square deviation
Variance: Square of standard deviation is known as variance.

7.11 Review Questions

1. “Frequency distribution may either differ in numerical size of their averages though not
necessarily in their formation or they may have the same values of their averages yet
differ in their respective formation”. Explain and illustrate how the measures of dispersion
afford a supplement to the information about frequency distribution furnished by averages.
2. “Indeed the averages and measures of variation together cover most of the need of practical
statistician but their interpretation and use in combination require a good knowledge of
statistical theory”. — Tippet
Discuss this statement with the help of arithmetic mean and standard deviation.

3. “ Measures of dispersion and central tendency are complementary to each other in
highlighting the characteristics of a frequency distribution”. Explain this statement with
suitable examples.
4. Explain briefly the meaning of (i) Range (ii) Quartile Deviation.
5. Distinguish between an absolute measure and relative measure of dispersion. What are
the advantages of using the latter?
6. Explain how the standard deviation is a better measure as compared to other measures of
dispersion? Mention its defects, if any.
7. What do you understand by mean deviation? Explain its merits and demerits.
8. Explain mean deviation, quartile deviation and standard deviation. Discuss the
circumstances in which they may be used.

162 LOVELY PROFESSIONAL UNIVERSITY