Page 98 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes conducted multiple times. The reported margin of error is typically about twice the standard
deviation—the radius of a 95 percent confidence interval. In science, researchers commonly report
the standard deviation of experimental data, and only effects that fall far outside the range of standard
deviation are considered statistically significant—normal random error or variation in the
measurements is in this way distinguished from causal variation. Standard deviation is also important
in finance, where the standard deviation on the rate of return on an investment is a measure of the
volatility of the investment.
7.1 The Mean Deviation

The average deviation or mean deviation is a measure of dispersion that is based upon all the items
in a distribution. It is the arithmetic mean of the deviations of the data from its central value, may it
be arithmetic mean, median or mode. While, considering the deviations from its central value, only
absolute values are taken into consideration, (i.e., without considering the positive or negative signs).
Mean deviation is denoted by δ (delta).
Mean/Average Deviation (denoted by δ )
d
∑ X
δ X = N (Deviation taken from Arithmetic Mean)
d
∑ M
δ M = N (Deviation taken from Median)
∑ Mo
d
δ Mo = N (Deviation taken from Mode)
Coefficient of Dispersion:
δ
Coeff. of δ X = X X ( X is arithmetic mean)

δ
M
Coeff. of δ M = M (M is Median)
δ
Mo
Coeff. of δ Mo = Mo (Mo is Mode)
Example 1: A batch of 10 students obtained the following marks out of 100. Calculate the mean
deviation and its coefficient.
Marks: 58, 39, 22, 11, 44, 28, 49, 55, 41 and 42.
Solution: The median value for the series is:
⎛ + ⎞ N1 th 11
th
⎜ ⎟ item = = 5.5 item.
⎝ 2 ⎠ 2
The series in ascending order:
11, 22, 28, 39, 41, 42, 44, 49, 55, 58
41 + 42 83
∴ Median = = = 41.5.
2 2
Calculation of Deviation from Median

d
Marks Deviation( M )
11 11 – 41.5 = |30.5|
22 22 – 41.5 = |19.5|
28 28 – 41.5 = |13.5|

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