Page 53 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 4: Central Tendency: Mean, Median and Mode and their Properties

• If there is an even number of items, then the median is half-way between the two middle ones Notes
and it is found by taking the average of these two items. For example, if the marks secured by
10 students in an examination are 75, 48, 63, 89, 100, 55, 35, 28, 93 and 79 and we wish to know the
median mark, the marks must be arranged either in ascending or descending order of magnitude
and then the average of the value of the 5 item and the 6 item will be the median mark.
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• The term ‘mode’ has come from French in which it means ‘to be in fashion’. As a statistical
language, mode is the value that occurs most frequently in a statistical distribution. Thus ‘Mode’
is the most representative average and is a position of greatest concentration of values. It has
great value conceptually. It is what the doctor means when he describes that a desease of cold
and fever usually takes a week to get cured. Similarly, average size of shirt/shoes sold, average
family income etc. also cannot be most frequently occurring value.
• In continuous unimodal distributions the median lies, as a rule of thumb, between the mean
and the mode, about one third of the way going from mean to mode. In a formula, median ≈ (2
× mean + mode)/3. This rule, due to Karl Pearson, often applies to slightly non-symmetric
distributions that resemble a normal distribution, but it is not always true and in general the
three statistics can appear in any order.
4.4 Key-Words

1. Central tendency : In statistics, the term central tendency relates to the way in which quantitative
data tend to cluster around some value.[1] A measure of central tendency is
any of a number of ways of specifying this "central value". In practical
statistical analysis, the terms are often used before one has chosen even a
preliminary form of analysis: thus an initial objective might be to "choose an
appropriate measure of central tendency".
2. Harmonic mean : The reciprocal of the arithmetic mean of the reciprocals of a specified set of
numbers
4.5 Review Questions

1. What is meant by measures of central tendency? What are the characteristics of good measure of
central tendency?
2. Explain the relative importance of arithmetic mean, median and mode as measures of central
tendency in statistical analysis.
3. Define mean, median and mode. Mention its merits and demerits.
4. What are the properties of mean, median and mode?
5. Define Harmonic mean and give a situation in which it is used.
Answers: Self-Assessment
1. (i) cumulative frequency (ii) open-end
(iii) mean (iv) geometric mean
(v) harmonic mean
4.6 Further Readings

1. Elementary Statistical Methods; SP. Gupta, Sultan Chand & Sons,
New Delhi - 110002.

2. Statistical Methods — An Introductory Text; Jyoti Prasad Medhi, New Age
International Publishers, New Delhi - 110002.
3. Statistics; E. Narayanan Nadar, PHI Learning Private Limied, New Delhi - 110012.

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