Page 77 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 5: Application of Mean, Median and Mode

half. The median of a finite list of numbers can be found by arranging all the observations Notes
from lowest value to highest value and picking the middle one. If there is an even
number of observations, then there is no single middle value; the median is then usually
defined to be the mean of the two middle values. A median is only defined on one-
dimensional data, and is independent of any distance metric. A geometric median, on
the other hand, is defined in any number of dimensions.
In a sample of data, or a finite population, there may be no member of the sample
whose value is identical to the median (in the case of an even sample size); if there is
such a member, there may be more than one so that the median may not uniquely
identify a sample member. Nonetheless, the value of the median is uniquely determined
with the usual definition. A related concept, in which the outcome is forced to correspond
to a member of the sample, is the medoid…
3. Mode : The mode is the value that appears most often in a set of data.
Like the statistical mean and median, the mode is a way of expressing, in a single
number, important information about a random variable or a population. The numerical
value of the mode is the same as that of the mean and median in a normal distribution,
and it may be very different in highly skewed distributions. The mode is not necessarily
unique, since the same maximum frequency may be attained at different values. The
most extreme case occurs in uniform distributions, where all values occur equally
frequently. The mode of a discrete probability distribution is the value x at which its
probability mass function takes its maximum value. In other words, it is the value that
is most likely to be sampled.
The mode of a continuous probability distribution is the value x at which its probability
density function has its maximum value, so, informally speaking, the mode is at the
peak.
5.6 Review Questions

1. Give two examples where arithmetic mean and median would be most appropriate average.
2. Can the value of mean, mode and median be the same in a symmetrical distribution ? If yes, state
the situation.
3. Discuss the application mean and median.
4. How do you determine median and mode graphically ?
5. 'The arithmetic mean is the best among all the averages.' Give reasons.
Answers: Self-Assessment

1. (i) Positional (ii) mean, median, 1/3, mean, mode
(iii) 24.67 (iv) concentration, frequencies
(v) is equal to, is equal to
5.7 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.
4. Quantitative Methods—Theory and Applications; J.K. Sharma, Macmillan
Publishers India Ltd., New Delhi - 110002.

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