Question

what is arthmatic mean ?Descrive its marits and demarits ?​

Answer 1

Merits of Mean :

1) Arithmetic mean rigidly defined by Algebraic Formula.

2) It is easy to calculate and simple to understand.

3) It is based on all observations of the given data.

4) It is capable of being treated mathematically hence it is widely used in statistical analysis.

5) Arithmetic mean can be computed even if the derailed distribution is not known but some of the observation and number of the observation are known.

6) It is least affected by the fluctuation of sampling.

7) For every kind of data mean can be calculated.

Demerits of Arithmetic mean :

1) It can neither be determined by inspection or by graphical location.

2) Arithmetic mean can not be computed for qualitative data like data on intelligence honesty and smoking habit etc.

3) It is too much affected by extreme observations and hence it is not adequately represent data consisting of some extreme point.

4) Arithmetic mean can not be computed when class intervals have open ends.

5) If any one of the data is missing then mean can not be calculated.

Uses :

1) Mean is used in fields such as business, engineering and computer science.

2) It is used in report card or in our population.

3)In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent. For example, per capita GDP gives an approximation of the arithmetic average income of a nation's population.

4)While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influenced by outliers.

5) It’s used to compute the variance and SD (Standard Deviation). It’s good for inferential statistics.

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Answer 2

Hi mate

Here is ur answer ⤵⤵

$\huge\mathfrak{\underline{\underline{\red{Answer}}}}</p><p>$

$\large\bold{\blue{Arithmetic \: mean}}$

In mathematics and statistics, the arithmetic mean, or simply the mean or the average, is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey.

$\large\bold{\blue{properties \: of \: Arithmetic \: mean}}$

Some important properties of the arithmetic mean are as follows:

• The sum of deviations of the items from their arithmetic mean is always zero, i.e. ∑(x – X) = 0.
• The sum of the squared deviations of the items from Arithmetic Mean (A.M) is minimum, which is less than the sum of the squared deviations of the items from any other values.
• If each item in the arithmetic series is substituted by the mean, then the sum of these replacements will be equal to the sum of the specific items.

$\large\bold{\blue{Merits \: of \: Arithmetic \: mean}}$

• The arithmetic mean is simple to understand and easy to calculate.
• It is influenced by the value of every item in the series.
• A.M is rigidly defined.
• It has the capability of further algebraic treatment.
• It is a measured value and not based on the position in the series.

$\large\bold{\blue{Demerits \: of \: Arithmetic \: mean}}$

• It is changed by extreme items such as very small and very large items.
• It can rarely be identified by inspection.
• In some cases, A.M. does not represent the original item. For example, average patients admitted to a hospital are 10.7 per day.
• The arithmetic mean is not suitable in extremely asymmetrical distributions.