After reading this article you will learn about:- 1. Definition of Statistics 2. Characteristics of Statistics 3. Classes 4. Statistical Error.
Definition of Statistics:
According to Horace Secrist:
‘By Statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a pre-determined purpose and placed in relation to each other.’
Characteristics of Statistics:
Statistics should contain the following characteristics:
i. Numerical data should be aggregates of facts.
ii. Data should be affected to a marked extent by multiplicity of causes.
iii. Data should be numerically expressed.
iv. Data should be enumerated or estimated according to reasonable standards of accuracy.
v. Data should be collected in a systematic manner.
vi. Data should be collected for a predetermined purpose.
vii. Data should be placed in relation to each other.
Classes of Statistics:
Webster defined statistics in the same sense:
‘Statistics are the classified facts respecting the conditions of the people in a state … specially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement.’
According to Seligman:
‘Statistics is the science which deals with the methods of collecting, classifying, presenting, comparing and interpreting numerical data collected to throw some light on any sphere of enquiry.’
King defined statistics as ‘the science of statistics is the method of judging collective, natural or social phenomenon from the ‘results obtained from the analysis or enumeration or collection of estimates.’
A. L. Bowley suggested statistics variously as:
i. Science of counting,
ii. Science of averages,
iii. Science of measurement of the social organism regarded as a whole in all its manifestations.
Boddington defined statistics as the science of ‘estimates and probabilities’, while, Lovitt* defined it as collection, classification and tabulation of numerical facts as the basis for explanation, description and comparison of phenomena.
Thus, statistics may be defined as:
i. Collection,
ii. Presentation,
iii. Mathematical analysis,
iv. Logical analysis of the numerical date.
Statistics has 2 main classes:
Statistical methods are devices, rules of procedure and general principles which are applicable to all kinds or groups of data. Thus, they include all the general principles and techniques which are commonly used in the collection, analysis and interpretation of data relating to any sphere of enquiry.
Applied statistics deals with the application of statistical methods to specific problems or concrete forms.
When the tools (principles) of statistics are applied to study living organisms or in other words it can be said that numerical data obtained from biological organisms it is called Biostatistics or Biometry.
Variables:
Data can be of 2 types, such as:
Qualitative, e.g., flower colour, leaf shape, pupil colour of eye, etc., these are non-numerical characters.
Quantitative, e.g., plant height, number of branches per plant, seeds per capsule, fish yield, etc. The item representing the quantitative characters is known as variable, that is, a character differing in value from one organism to another, from one sample to another.
Again variable may be discrete or continuous.
Discrete the units are obtained by counting and such variables are always represented as integers, e.g.,
Continuous variable which can take into account any value within a certain range, e.g.,
Population and Sample:
If one had to count the number of Rhododendron plants in the hills of Darjeeling then it is practically impossible to do it. In such case, smaller pockets are taken which bears characteristics of the Darjeeling hills and subsequently survey can be made. Thus, Darjeeling hills is the population and smaller pockets taken are the samples. So, samples are true representative of the population.
Random Sampling:
Collection of data unbiasedly. Selection is done purely on chance occurrence only. Size of the sample is very essential for accuracy. Bigger size sample gives more accuracy; however, unmanageable size is often unnecessary.
Statistical Error:
It is difference between the true value and the estimated value.
Errors may arise due to instability of the collected data. Such errors are called errors of origin. Errors may also arise on account of manipulation in counting, measurement, description or approximation. Such errors are known as errors of manipulation. However, errors arising due to inadequate size of the sample are known as errors of inadequacy.
Errors may be biased or unbiased and can be measured either absolutely (difference between true value and estimated value) or relatively (ratio of the absolute error to the estimate).