Page 111 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes The formula for the computation of Q can be written by making suitable changes in the formula
1
of median.
After locating the first quartile class, the formula for Q can be written as follows:
1
n
– C
4
Q = L h
1 Q1 f Q 1
Here, L is lower limit of the first quartile class, h is its width, f is its frequency and C is
Q 1 Q 1
cumulative frequency of classes preceding the first quartile class.
By definition, the second quartile is median of the distribution. The third quartile (Q ) of a
3
distribution can also be defined in a similar manner.
For a discrete distribution, Q is that value of the variate such that at least 75% of the observations
3
are less than or equal to it and at least 25% of the observations are greater than or equal to it.
For a grouped frequency distribution, Q is that value of the variate such that area under the
3
histogram to the left of the ordinate at Q is 75% and the area to its right is 25%. The formula for
3
3N
C
4
computation of Q can be written as Q 3 L Q , h where the symbols have their usual
3 3 f
Q
3
meaning.
6.4.2 Deciles

Deciles divide a distribution into 10 equal parts and there are, in all, 9 deciles denoted as D , D ,
1 2
...... D respectively.
9
For a discrete distribution, the i th decile D is that value of the variate such that at least (10i)% of
i
the observation are less than or equal to it and at least (100 - 10i)% of the observations are greater
than or equal to it (i = 1, 2, ...... 9).
For a continuous or grouped frequency distribution, D is that value of the variate such that the
i
area under the histogram to the left of the ordinate at D is (10i)% and the area to its right is
i
(100 - 10i)%. The formula for the i th decile can be written as
iN
C
10
D L h (i = 1, 2, ...... 9)
i i D f
i D
6.4.3 Percentiles

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
For a discrete distribution, the kth percentile P is that value of the variate such that at least k%
k
of the observations are less than or equal to it and at least (100 – k)% of the observations are
greater than or equal to it.

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