BUSINESS STATISTICS: How to compute Mean, Standard deviation and Coefficient of Variation

Business Statistics

Statistics:

Croxton and Cowden says – “Statistics may be defined as the science of collection, presentation, analysis and interpretation of numerical data”.

Boddington says – “Statistics is a Science of estimation and probability”.

“Statics may be called the Science of Counting” – A. L. Bowley.

Encyclopedia of Britannica, - “As is commonly understood now-a-days, statistics is mathematical discipline connected with the study of masses of quantitative data of any kind”.

Statistics is a science of making decisions with respect to the characteristics of a group of persons or objects on the basis of numerical information obtained from a randomly selected sample of the group.

Nature of Statistics:

1 Statistics are aggregates of facts: 

   Statistics are affected considerably by multiplicity of courses:

3.      Statistics are numerically expressed:

4.      Statistics should be based on actual counting or estimation:

5.      Statistics is always with reasonable standard of accuracy:

6.      Statistics is collected in a systematic way:

7.      Statistics is placed in relation to each other:

Importance of Statistics:

1.      The raw data may be converted into more meaningful information:

Statistics enables conversion of raw data collected into meaningful information by applying statistical methods and procedure. The data relating to population will be of no use if the data is classified meaningfully like the number of males, females, children etc.

2.      Facilitates easy calculation of averages:

Statistics provides for easy calculation of averages for a huge data so that the data can be reduced to one single number to derive conclusion and facilitate comparison of the same for different periods and different variables.

3.      Determination of variability of measurements:

Using statistical methods, techniques and principles it is also easy to find the variation of data from various averages.

4.      Facilitates to find the relationship between two variables:

Statistics helps to establish relationship between two variables and also helps to know the kind of relationship. It helps in knowing whether sales and advertisement expenses are related and the kind of relationship.

5.      Facilitates in framing policies and programmes:

Statistical enables policy makers in all the sectors to frame policies and programmes for development. The forecasts that can be made using statistical tools are helpful to policymakers in fixing targets for achievement and appraise performances.

6.      Helps in testing assumptions:

The assumptions relating to a particular field of study can be tested statistically by applying various tests like t-test, F-test, Z-test etc. depending upon the samples chosen for the study and the objectives of the study.

7.      Expands thinking horizon of individuals:

By learning statistics and applying statistical methods the thinking horizon of an individual gets expanded.

8.      It is indispensable to research work:

Statistics is indispensable for any kind of research. Statistical tools are used in humanities, science, commerce and management research.

9.      Easy to understand by common man:

The results of a statistical survey can be presented through graphs, tables and figures. This helps even the common man to understand the subject matter easily.

Limitations of Statistics:

1.      Statistics deals with only quantitative data:

Statistics deals only with those facts which can be expressed in numerical terms. Statistics ignores qualitative data that are not convertible into numerical terms.

2.      Statistics ignore individual items:

Due to fact that statistics deals with only group items or aggregate data, solutions arrived also apply only to aggregate items and not to individual items.

3.      Statistics does not ensure mathematical accuracy for a phenomenon:

Statistics enables approximation and the results obtained are near accuracy and not exactly accurate.

4.      Statistics does not deal with the problem in its entirely:

Statistics does not reveal the entire story of a problem investigated. It addresses only the issues that are predetermined.

5.      Statistical laws hold good only for the averages:

It does not hold good for an individual item. For example, the average age of students studying in I B.com students are 19 years. But there may be students in I B.com who are above or below 19 years. So, statistics is for the averages of a grouped data and not for an individual item.

6.      Statistics is liable to be misused:

It is of great help only if it is utilized by people who have the expertise. Inadequate and wrong methods of data collection might lead to arriving at wrong results which leads the individual to draw only wrong conclusions.

LAWS OF STATISTICS:

There are two fundamental laws of statistics.

1.      The Law of Statistical Regularity.

This law states that, “A moderately large number of items, chosen at random from a large group, are almost sure on an average to possess the characteristics of the large group”.

2.      The Law of Inertia of Large numbers.

This law states, “Other things being equal, as the sample size increases the result tends to be more reliable and accurate”.

KEY TERMS USED IN STATITISTICS

POPULATION AND SAMPLE:

The aggregate of all the units relating to a study is called “Population” or the ‘Universe’. That is, population is the target group under study on which an investigator makes inferences and draws conclusion.

Sample means a representative unit of the population under study. It is a member of the population or the universe. It is the unit of study. In short, a part of population is called sample.

PARAMETER AND STATISTIC:

A ‘parameter’ explains the features of a population. It is a descriptive measure of some characteristic of the population. That is, if an average is obtained from the set of all observations of a population, the average is a parameter. A population mean is denoted by ‘µ’ (read as ‘mue’).

On the other on hand, a descriptive measure that is obtained from the observations of a sample is called a ‘statistic’ or sample average or sample mean. There can be more than one measure of statistic or the parameter for a given study. They may be Mean, standard deviation etc.

Methods and Sources of Data Collection

Data are facts and other relevant information, past and present, serving as bases for the study and analysis. Data are of two types, (i) Quantitative Data (Which can express numerically), (ii) Qualitative Data (Which cannot express numerically).

Methods of collection of Data:

1.      Census Method

2.      Sample Method

Census method:

In this method, Data is collected from each and every item or from every item or from every individual in the study. Therefore, collecting the data from all and drawing the conclusion about all is called as censes method.

Advantages:

1.      Correct information may be obtained.

2.      Decision taken from this information is always reliable.

3.      This method is most suitable in the case of industries.

Disadvantages:

1.      Very expensive

2.      More time consuming

3.      More risk

4.      Results may be different.

5.      Sometimes there is no relation between result and the existing conditions.

Sample method:

In this method only a few items or individuals representing the population are selected for drawing the conclusion. This method of studying a few persons and drawing the conclusions about all is called sample method.

Advantages:

1.      Less time consuming.

2.      Less labour involved.

3.      Less capital required

4.      Where census method is not possible sample method is used.

5.      Where detailed information is not required, sample method can be used.

Disadvantages:

1.      Correct information may not be provided by the samples.

2.      Sample chosen may not represent the population under study.

3.      Different conclusions may be obtained for different samples chosen.

4.      The conclusions drawn are not universally applicable.

Sources of Data Collection

The data required for a study may be collected from various sources.

I.             Primary Sources

      II.            Secondary sources.

Primary sources:

These are the first-hand information collected by the investigator.

Methods

1.      Observation

2.      Mail survey method

3.      Interviewing

4.      Schedules sent through enumerators.

Secondary sources: Secondary source are those sources containing data which have been collected and complied for another purpose.

Tabulation

When classified data is arranged in a tabular form it is called ‘Tabulation’. The data is arranged systematically in rows and columns.

Presentation of classified data in a tabular form is called tabulation.

Parts of a table: Table number, Title of the table, head note, Column Headings, Row Headings, Body of the Table, Total, Grand Total, Foot note, Source.

Types: General purpose table, Special Purpose tables, Simple Tables, Complex tables.

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