Page 129 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes
Did u know? If all the observations of a variable are same, all the three measures of central
tendency coincide, i.e., AM = GM = HM. Otherwise, we have AM > GM > HM.

Quadratic Mean
Notes
Quadratic mean is the square root of the arithmetic mean of squares of observations.
If X , X ...... X are n observations, their quadratic mean is given by
1 2 n

X 2 X 2  X 2 X i 2
QM 1 2 n
n n
Similarly, the QM of observations X , X ...... X with their respective frequencies as f , f
1 2 n 1 2
2
f X i
i
...... f is given by QM , where N = f i .
n
N
Moving Average
This is a special type of average used to eliminate periodic fluctuations from the time
series data.
Progressive Average
A progressive average is a cumulative average which is computed by taking all the available
figures in each succeeding years. The average for different periods are obtained as shown
below:
X X X X X
X 1 , 1 2 , 1 2 3 , etc.
2 3
This average is often used in the early years of a business.
Composite Average
A composite average is an average of various other averages. If for example,
, , are the arithmetic means of k series, their composite average
1 2

1 2
.

Self Assessment

Fill in the blanks:
27. The harmonic mean of n observations, none of which is............................. , is defined as the
reciprocal of the arithmetic mean of their reciprocals.

28. If all the observations of a variable are same, all the three measures of central tendency
coincide, i.e., AM = GM = HM. Otherwise, we have .................................

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