Page 46 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes
+
+
+
+ 50 10 10 10 10 90
5 = 5 = 18.
Whereas in reality 4 out of 5 students failed. Therefore, ‘18’ marks cannot be termed as
representative.
(2) When data is vast, the calculations become tedious.
(3) In case of open end classes, mean can only be calculated by making some assumptions.
(4) A.M. is not representative if series is asymmetrical.
Purpose or Objectives of Averaging
Central tendency or average is the value by which the data can be represented. The purpose or
objectives of calculating this representative figure are —
(1) To present the most important features of a mass of complex data.
(2) To facilitate comparing one set of data with others, so that conclusions can be drawn quickly.
(3) To help in understanding the picture of a complete group by means of sample data.
(4) To trace the mathematical relationship between different groups or classes.
(5) To help in the decision-making.
(6) To facilitate the process of experimentation and research.
Weighted Arithmetic Mean
Weighted arithmetic mean is the method of calculating a more representative central value and takes
into consideration the relative importance of the various figures in the series. Whereas in simple
arithmetic mean, equal weight or importance is given to each item. If the central value has to more
representative and the data is such that few items are more important than other, the method of
weighted arithmetic mean is used. This method is generally used in the following situations:
(1) When importance of all the items in the series is not equal.
(2) When the classes of the same group contain widely varying frequencies.
(3) Where there is a change either in the proportion of values or items or in the proportion of
frequencies.
(4) When ratios, percentages or rates are being averaged.
(5) When it is desired to calculate the average of series from the average of its component parts.
The formula for the weighted arithmetic average is:

11 + W X 2 2 + W X ...W X n ∑WX
n
Direct Method : XW = =
1 +W 2 + X ...W n ∑W
∑ Wd
Short-cut Method : XW = A w + ∑ W

where XW represents the weighted arithmetic mean.
X represents the variable values i.e., X , X ... X .
1 2 n
W represents the weights attached to variable values i.e., W , W , ... W , respectively.
1 2 n
∑ Wd Sum of the product of the deviations from the assumed mean (AW) multiplied by
the respective weights.
AW Assumed (weighted) mean.
Harmonic Mean

An average rate like kilometer per hour, per day items manufactured etc. are required to be found,
harmonic mean is calculated. Harmonic mean is a type of average which has limited application only

40 LOVELY PROFESSIONAL UNIVERSITY