Properties Of Mean
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Properties Of Mean
Statistics of Class 10
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Sum of deviations from mean is zero. i.e.
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If a constant real number ‘a’ is added to each of the observation than new mean will be
+ a
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If a constant real number ‘a’ is subtracted from each of the observation then new mean will be
- a
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If constant real number ‘a’ is multiplied with each of the observation then new mean will be a
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If each of the observation is divided by a constant no ‘a’, then new mean will be
/a
MERITS OF ARITHMETIC MEAN:
(i) It is rigidly defined, simple, easy to understand and easy to calculate.
(ii) It is based upon all the observations.
(iii) Its value being unique, we can use it to compare different sets of data.
(iv) It is least affected by sampling fluctuations.
(v) Mathematical analysis of mean is possible. So, It is relatively reliable.
DEMERITS OF ARITHMETIC MEAN:
(i) It cannot be determined by inspection nor it can be located graphically.
(ii) Arithmetic mean cannot be used for qualities characteristics such as intelligence, honesty, beauty etc.
(iii) It cannot be obtained if a single observation is missing.
(iv) It is affected very much by extreme values. In case of extreme items, A.M. gives a distorted picture of the distribution and no longer remains representative of the distribution.
(v) It may lead to wrong conclusions if the details of the data from which it is computed are not given.
(vi) It cannot be calculated if the extreme class is open, e.g. below 10 or above 90.
(vii) It cannot be used in the study of rations, rates etc.
USES OF ARITHMETIC MEAN:
(i) It is used for calculating average marks obtained by a student.
(ii) It is extensively used in practical statistics and to obtain estimates.
(iii) It is used by businessman to find out profit per unit article, output per machine, average monthly income and expenditure etc.
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