Page 130 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 6: Measures of Central Tendency

6.8 Summary Notes

Summarization of the data is a necessary function of any statistical analysis.
Average is a value which is typical or representative of a set of data.

Arithmetic Mean is defined as the sum of observations divided by the number of
observations.
In order that the mean wage gives a realistic picture of the distribution, the wages of
managers should be given less importance in its computation. The mean calculated in this
manner is called weighted arithmetic mean.
If a constant B is added (subtracted) from every observation, the mean of these observations
also gets added (subtracted) by it.
If every observation is multiplied (divided) by a constant b, the mean of these observations
also gets multiplied (divided) by it.
If some observations of a series are replaced by some other observations, then the mean of
original observations will change by the average change in magnitude of the changed
observations.
Arithmetic mean is rigidly defined by an algebraic formula.

Median of distribution is that value of the variate which divides it into two equal parts.
Median conveys the idea of a typical observation
The values of a variable that divide a distribution into four equal parts are called quartiles
Deciles divide a distribution into 10 equal parts and there are, in all, 9 deciles denoted as
D , D , ...... D respectively.
1 2 9
Percentiles divide a distribution into 100 equal parts and there are, in all, 99 percentiles
denoted as P , P , ...... P , ...... P , ...... P , ...... P respectively.
1 2 25 40 60 99
Mode is that value of the variate which occurs maximum number of times in a distribution
and around which other items are densely distributed.

For a moderately skewed distribution, the difference between mean and mode is
approximately three times the difference between mean and median, i.e.,
The geometric mean of a series of n positive observations is defined as the nth root of their
product.
The harmonic mean of n observations, none of which is zero, is defined as the reciprocal
of the arithmetic mean of their reciprocals.

6.9 Keywords

Average: An average is a single value within the range of the data that is used to represent all the
values in the series.
Arithmetic Mean: Arithmetic Mean is defined as the sum of observations divided by the number
of observations.
Deciles: Deciles divide a distribution into 10 equal parts and there are, in all, 9 deciles denoted as
D , D , ...... D respectively.
1 2 9

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