📈 Statistics

Application, Biometry, Vital statistics, Frequency Distribution Table

  • Statistics is a branch of science, which deals with collection of data, presentation of data, analysis of data, and interpretation of data.
  • Statistics can be used either as plural or singular.
  • When it is used as plural, it is a systematic presentation of facts and figures. It is in this context that majority of people use the word statistics. They only meant mere facts and figures. These figures may be with regard to production of food grains in different years, area under cereal crops in different years, per capita income in a particular state at different times etc., and these are generally published in trade journals, economics and statistics bulletins, newspapers, etc.
  • When statistics is used as singular, it is a science which deals with collection, classification, tabulation, analysis and interpretation of data.

Collection → Classification → Tabulation → Analysis → Interpretation

  • The first step of summarizing the data is classification.

Application of Statistics

  • Statistics plays an important role in our daily life, it is useful in almost all sciences – social as well as physical – such as biology, psychology, education, economics, business management, agricultural sciences etc. The statistical methods can be and are being followed by both educated and uneducated people. In many instances we use sample data to make inferences about the entire population.
  • Planning is indispensable for better use of nation’s resources. Statistics are indispensable in planning and in taking decisions regarding export, import, and production etc., Statistics serves as foundation of the super structure of planning.
  • Statistics helps the business man in the formulation of polices with regard to business. Statistical methods are applied in market and production research, quality control of manufactured products.
  • Statistics is indispensable in economics. Any branch of economics that require comparison, correlation requires statistical data for solving problems
  • Statistics is helpful in administration in fact statistics are regarded as eyes of administration. In collecting the information about population, military strength etc., Administration is largely depending on facts and figures thus it needs statistics.
  • Bankers, stock exchange brokers, insurance companies all make extensive use of statistical data. Insurance companies make use of statistics of mortality and life premium rates etc., for bankers, statistics help in deciding the amount required to meet day to day demands.
  • Problems relating to poverty, unemployment, food storage, deaths due to diseases, due to shortage of food etc., cannot be fully weighted without the statistical balance. Thus, statistics is helpful in promoting human welfare
  • Statistics are a very important part of political campaigns as they lead up to elections. Every time a scientific poll is taken, statistics are used to calculate and illustrate the results in percentages and to calculate the margin for error.
  • In agricultural research, Statistical tools have played a significant role in the analysis and interpretation of data.
    • In making data about dry and wet lands, lands under tanks, lands under irrigation projects, rainfed areas etc.,
    • In determining and estimating the irrigation required by a crop per day, per base period.
    • In determining the required doses of fertilizer for a particular crop and crop land.
    • In soil chemistry also statistics helps classifying the soils basing on their analysis results, which are analyzed with statistical methods.
    • In estimating the losses incurred by particular pest and the yield losses due to insect, bird, or rodent pests’ statistics is used in entomology.
    • Agricultural economists use forecasting procedures to determine the future demand and supply of food and also use regression analysis in the empirical estimation of function relationship between quantitative variables.
    • Animal scientists use statistical procedures to aid in analyzing data for decision purposes.
    • Agricultural engineers use statistical procedures in several areas, such as for irrigation research, modes of cultivation and design of harvesting and cultivating machinery and equipment.

Biometry

  • The application of Statistical concepts and procedures to study of biological problems.

Vital statistics

  • Are conventionally numerical records of marriage births, sickness, and death by which the health and growth of community may be studied. Or
  • It is a branch of biometry deals with data and law of human mortality, morbidity, & demography.
  • Father of vital statistics was Caption John Grant.

Limitations of Statistics

  • Statistics does not study qualitative phenomenon.
  • Statistics does not study individuals.
  • Statistics laws are not exact laws they are average.
  • Statistics does not reveal the entire information.
  • Statistics is liable to be misused.
  • Statistical conclusions are valid only on average base.

Types of data

  • Primary Data: It is the data collected by the primary source of information i.e. by the investigator himself.
  • Secondary Data: It is the data collected from secondary sources of information, like newspapers, trade journals and statistical bulletins, etc.,

Variable

  • Variability is a common characteristic in biological sciences. A quantitative or qualitative characteristic that varies from observation to observation in the same group is called a variable.
  • A single observation or measurement is called variate.
  • In case of quantitative variables, observations are made using interval scales whereas in case of qualitative variables, nominal scales are used.

Interval Scale

Nominal Scale

  • Conventionally, the quantitative variables are termed as variables and qualitative variables are termed as attributes.
  • Thus, yield of a crop, available nitrogen in soil, daily temperature, number of leaves per plant and number of eggs laid by insects are all variables.
  • The crop varieties, soil types, shape of seeds, seasons and sex of insects are attributes.

Continuous and Discrete Variables

  • The variable itself can be classified as continuous variable and discrete variable.
  • The variables for which fractional measurements are possible, at least conceptually, are called continuous variables.
  • For example, in the range of 7 kg to 10 yield of a crop, yield might be 7.15 or 7.024kg. Hence, yield is a continuous variable.
  • The variables for which such factional measurements are not possible are called discrete or discontinuous variables.
  • For example, the number of grains per panicle of paddy can be counted in full numbers like 79, 80, 81 etc. Thus, number of grains per panicle is a discrete variable.
  • The variables, discrete or continuous are denoted by capital letters like X and Y.

Construction of Frequency Distribution Table

  • In statistics, a frequency distribution is a tabulation of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way the table summarizes the distribution of values in the sample.
  • The following steps are used for construction of frequency table:
  • Step-1: The number of classes are to be decided
    • The appropriate number of classes may be decided by Yule’s formula, which is as follows:

    Number of classes = 2.5 x n1/4

    • Where ‘n’ is the total number of observations
  • Step-2: The class interval is to be determined. It is obtained by using the relationship.
  • Step-3: The frequencies are counted by using Tally marks
  • Step-4: The frequency table can be made by two methods
    • Exclusive method
    • Inclusive method

a) Exclusive method

  • In this method, the upper limit of any class interval is kept the same as the lower limit of the just higher class or there is no gap between upper limit of one class and lower limit of another class.
  • It is continuous distribution.
  • Ex.

b) Inclusive method

  • There will be a gap between the upper limit of any class and the lower limit of the just higher class.
  • It is discontinuous distribution.
  • Ex.
  • To convert discontinuous distribution to continuous distribution by subtracting 0.5 from lower limit and by adding 0.5 to upper limit.
  • Note: The arrangement of data into groups such that each group will have some numbers. These groups are called class and number of observations against these groups are called frequencies.
  • Each class interval has two limits:
    • Lower limit
    • Upper limit
  • The difference between upper limit and lower limit is called length of class interval.
  • Length of class interval should be same for all the classes.
  • The average of these two limits is called mid value of the class.

👀 Example: Construct a frequency distribution table for the following data 25, 32, 45, 8, 24, 42, 22, 12, 9, 15, 26, 35, 23, 41, 47, 18, 44, 37, 27, 46, 38, 24, 43, 46, 10, 21, 36, 45, 22, 18.

🤔 Solution:

  • Number of observations (n) = 30
  • Number of classes = 2.5 x n1/4
  • = 2.5 x 301/4 = 2.5 x 2.3 = 5.8 ≈ 6
  • C.I. = (Maximum value in the given data – Minimum value in the given data)/(Number of classes)
  • = (46 – 8)/6 = 6.3 ≈ 6

Exclusive method

Inclusive method

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