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Unit 7: Mean Deviation and Standard Deviation

Notes
2
Correct ΣX = 162601 – (50) + (40) = 162601 –2500 + 1600 = 161701
2
2
Correct X 2 2
Σ
Correct σ = – ( ) Correct X
N
161701 2
(
= –39.9 ) = 1617.01 – 1592.01 = 25 = 5.
100
Self-Assessment
1. Indicate whether the following statements are True or False:
(i) Mean deviation can be calculated from arithmetic mean, median or mode.
(ii) Mean deviation ignores the sings of deviations.
(iii) Standard deviation is an absolute measure of dispersion.
(iv) Standard deviations of more than two component parts cannot be combined in one.
(v) Mean deviation is least when deviations are taken from median.
7.3 Summary

• The average deviation is sometimes called the mean deviation. It is the average difference
between the items in a distribution and the median or mean of that series. Theoretically, there
is an advantage in taking the deviations from median because the sum of the deviations of items
from median is minimum when signs are ignored. However, in practice the arithmetic mean is more
frequently used in calculating the value of average deviation and this is the reason why it is
more commonly called mean deviation. In any case, the average used must be clearly stated in
a given problem so that any possible confusion in meaning is avoided.
• In statistics standard deviation (represented by the symbol sigma, σ ) shows how much variation
or “dispersion” exists from the average (mean, or expected value). A low standard deviation
indicates that the data points tend to be very close to the mean; high standard deviation indicates
that the data points are spread out over a large range of values.
• The standard deviation of a random variable, statistical population, data set, or probability
distribution is the square root of its variance. It is algebraically simpler though practically less
robust than the average absolute deviation. A useful property of standard deviation is that,
unlike variance, it is expressed in the same units as the data.
• 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).
• The outstanding advantage of the average deviation is its relative simplicity. It is simple to
understand and easy to compute. Anyone familiar with the concept of the average can readily
appreciate the meaning of the average deviation. If a situation requires a measure of dispersion
that will be presented to the general public or any group not thoroughly grounded in statistics,
the average deviation is very useful.
• The greatest drawback of this method is that algebraic signs are ignored while taking the
deviations of the items. For example if from twenty, fifty is deducted we write 30 and not – 30.
This is mathematically wrong and makes the method non-algebraic. If the signs of the deviations
are not ignored the net sum of the deviations will be zero if the reference point is the mean or
approximately zero if the reference point is median.
• The serious drawbacks of the average deviation should not blind us to its practical utility.
Because of its simplicity in meaning and computation, it is especially effective in reports

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