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Syllabus M.Sc I Semester AECC-Principles of Statistics(New) Course Objectives: To train the students intensively in both theoretical and practical aspects of statistics, to bring them in contact with basic concepts and methods in Statistics. To create a problem-solving attitude with the aid of statistical methodology. Course Outcomes: Apply to construct frequency distribution and graphical methods. To calculate and apply measures of location and measures of dispersion. Perform Test of Hypothesis and understand the concept of p-values Unit I: Descriptive statistics Importance and Scope of Statistics, Data Types, Variables, Frequency Distribution, Graphical Representation Methods (Histogram, Bar Charts, Pie Charts), Measures of Center Tendency (Mean, Median, Mode,) and Dispersion (Standard Deviation, Variance) Advantages and Disadvantages. Unit II: Probability Basic Terminology: Trial, Events, Sample Space and Sample Points, Basic Laws of Probability, Types of Probability, Normal probability curve, Standard Normal Distribution, Bayes theorem - simple problems. Unit III: Sampling Methods Concept of Population, Sample, Sampling, Sample Size, Sampling Error, Advantages and Disadvantages of Sampling Method, Types of Random Sampling Methods – SRS, Stratified Random Sampling, Systematic Random Sampling and Cluster Sampling. Unit IV: Testing of Hypotheses
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Statistical Hypotheses-Null and Alternative, Level of Significance, Type I and Type II Error, P Value, Degrees of Freedom, Chi-Square Test, Student’s t Test: One Sample t Test and Paired and unpaired t Test, Analysis of Variance. Correlation-Karl Pearson’s and Spearman’s rank correlation. Regression Analysis. References:
- Fundamentals of Biostatistics. Veer Bala Rastogi. Publisher: ANE Books. 2nd Edition, 2009.
- Fundamentals of Mathematical Statistics, S.C. Gupta and V. K. Kapoor, Publisher: Sultan Chand & Sons (2014).
- Fundamentals of Statistics. S.C. Gupta. Publisher: Himalaya Publishing House Pvt. Ltd.Edition.7th Edition, 2012
- Introductory Statistics for Biology. R. E. Parker. Publisher: Cambridge University Press 2nd Edition, 1991.
- Statistics for behavioral science. Chintamani Kar. Publisher : Dominant Publishers & Distributors (P) Ltd. (2015).
- “ A well wrapped statistics is better than Hitler's biglie, it misleads, yet it cannot be pinned on you” :-Darreell Huff
- Who states that there is three kinds of lies: lies, dammed lies, and Statistics: - Disraeli Applications of Statistics: Statistics is considered to be a distinct branch of study applied to investigations in numerous other branches of sciences. It is applied to particular problems in Biology, Medicine, Agriculture, Commerce, Business, Economics, Industry, Insurance, Sociology, psychology, and so on. Statistical methods are mostly used to study the problems related to biological sciences. It is applied to study the growth of plant, movement of population in the ocean, migration of birds, effects of newly invented medicines, effects of fertilizers on yield, birth and death rate, population growth and so on. It deals with problems regarding to growth of population is demography. Insurance premiums are based on the age composition of the residents and death rates. Statistical analysis of variation of price, demand and production are helpful to business men and economist Expenditure of existing index numbers helps in economic planning and fixation of wages. Analysis of demand, price, manufacture and so on help in decision making in business activities. Organization of limited resources and labour in obtaining highest profit is obtained by statistical analysis of data. In industries, statistical quality control methods help in increasing and controlling the quality of produt at minimum cost. A governament administrative scheme is fully dependent on production statistics, income statistics, ecomomic consist of cost, price, etc, economic plannind is completely dependend on statistical data. Functions of statistics (1) Statistics helps in furnish a better understanding and exact description of data
(2) Statistics helps in the efficient and proper planning of a statistical information in any field of study. (3) Statistics helps in collecting quantitative data. (4) Statistics helps to present data through graphs, charts etc. (5) It helps in studying association between different factors (relation between production and commodities) (6) Statistics helps in drawing valid inferences IMPORTANCE AND SCOPE OF STATISTICS
1. Statistics and planning: Statistics helps in decision making and planning. Every organisation makes strategies for its future targets. Better planning is necessary to analysis the statistical data in the field of interest such as availability of raw material, income, consumption, resources available, income, expenditure, etc. In order to analysis these types of data, we need to depend on the statistical techniques. Thus statistics is fundamental for planning. 2. Statistics and economics: Statistical data and techniques of statistical analysis have to hugely helpful in economic problem. For example wages, price, time series analysis, demand analysis. In order to know the growth of a country, it has become essential to obtain the data related to its economic growth. Again, statistical tools are needed to collect related data (such as related to agricultural, industrial, literacy, etc.) and for its analysis. 3. Statistics and business: Statistics is a reckless tool of production control. Business exclusive are trusting more and more on statistical techniques for studying the much and need of the valued customer and it is also used in estimate value of money, analysis of demand, production cost, price etc. 4. Statistics and medicine : Statistics plays a significant role in the field of medicine. Statistical tools helps to find the drug is effective or not and to find association between smoking and cancer etc. by using statistical tools like collection , presentation and analysis of data related to cause and incident disease. 5. Statistics, psychology and education:
In qualitative data nominal and ordinal scales are used as a measurement of scale. some characteristics like colour, sex, intelligence, marital status, qualification, religion, satisfaction, types of trees, beauty, honesty, etc. are qualitative data Nominal scale data Nominal data is usually a names something and it is not allotted in an order in relation to other numbered objects .Nominal data provides some information about asset of event or group, even if that information is limited to mere counts. An example of nominal data might be a "pass" or "fail" classification for each student's test result Ordinal scale data Ordinal data involves assigning information into an order .and it’s not like nominal data. Ordinal data has some order. Ordinal data stand in relation to each other in a ranked fashion. For example, student satisfaction level towards of teaching 1-very poor 2-poor 3-satisfactory 4-good 5-very good QUANTITATIVE DATA o As the name quantitative suggests that it is related to the quantity and it is numeric which exactly measures the characteristics of the study. In quantitative data interval or ratio scales are used as a measurement of scale. some characteristics like weight, height, ages, length, area, volume, money, temperature, humidity, size, etc. are comes under quantitative data For example, (i)height and weight of the students in a class
1. Discrete data If the numerical data can take only an at most countable number of values or a variable which assumes only some specified values in a given range is called discrete variable. An at most countable number is either finite or countable. An example, 1. The number of girl students in a class. 2. The number of computers in a company. 3. The number of parts damaged during transportation.
2. Continuous data A variable which assumes all the values in the Range is called continuous data. Continuous data are just opposite of discrete data whereas continuous data can take any number of values. In continuous data the given information could be meaningfully divided into finer levels.. For example, you can measure height at very precise scales — meters, centimetres, millimetres and etc. The continuous variables can take any value between two numbers. 1. The height of children. 2. The amount of time it takes to sell shoes. 3. The weight of a bus 4. The speed of cars. Interval scale data o Interval scales are numerical scales in which we have both order and exact difference between the values without an absolute zero o Interval scales don’t have a “true zero” for example there is no such thing called zero temperature o Example: net promotor score, Likert scale, semantic differential scale,bilor matrix table etc. are the most used interval scale example Ratio scale data : o When numbers have units that are of equal magnitude as well as rank order on a scale with an absolute zero o Examples include: heart rate, blood pressure, distance. 1.3 FREQUENCY DISTRIBUTION Frequency means how frequently the variable takes place. A systematic presentation of different values taken by the variables together with corresponding frequencies it is called frequency distribution and its represents in tabular form called frequency distribution table. A frequency distribution where class intervals are considered is called continuous frequency distribution
The following are the percentage marks of 16 student’s marks 15,12,36,45,32,7,46,8,72,22,28,34,76,65,52, CI TALLIES FREQUENCY 7-20 |||| 4 20-34 ||| 3 34-48 |||| 4 48-62 | 1 62-76 |||| 4 Variable: A quantitative characteristics which vary from individual to individual is a variable, It may be discrete or continuous. A variable which assumes specific values in a given range is discrete variable, A variable which assumes any values on a given range is continuous variable. Examples: number of persons in a family, number of students in a class, number of staff in college is the example of Discrete variable; whereas Height of a tree, weight of a person etc are the examples of continuous variable. Cumulative Frequency: Frequency is number of times an event occurs within a given scenario. Cumulative frequency is described as the running totals of frequencies. It is the addition of all the preceding frequencies up to the present point. There are two types of Cumulative Frequencies
- Less than Cumulative Frequency distribution
- More than Cumulative Frequency distribution Less than Cumulative Frequency distribution: In this type of distribution the frequencies are added from lowest to highest i.e downward addition of frequencies. More than Cumulative Frequency distribution:
In this type of distribution the frequencies are added from highest to lowest i.e upward addition of frequencies. 1.4 GRAPHICAL PRESENTATION Graphical representation is obtained from frequency distribution. It is another way to analyse the numerical data. If-the frequency distribution are taken on a graph the values of variable are presented on x-axis and frequencies on y –axis. ADVANTAGES
- They are easy to understand and helpful to better understand of the theories.
- Graphs are very attractive generally in newspaper or in advertisement graphs draw the attention of the reader.
- It facilitate comparison of different groups of data
- Impression made by the graphs is long lasting. DISADVANTAGES
- Some graphs can be drawn by experts only common people cannot draw the graphs.
- Graphs are not as exact as tabular data. They give only a rough picture.
- The misrepresentation of graphs leads to mislead the readers. **Important types of graphs are
- Histogram** Here the frequency distribution is represented by vertical bars or rectangle. Histograms are continuous data which are grouped into classes of equal width. Here the variables are taken along x-axis and frequency along y axis, the height of rectangle represented the frequency. The total area of the rectangles in the histogram denotes the total frequency. A histogram is located continuously side by side with no gap between adjacent bars. Construction
- Find the class intervals if the frequency distribution has inclusive class interval convert into exclusive
- Mark the class interval along the X axis
graphi cal illustra tion of data. It is used to give a picture of the shape of the data and to descri be trends. It is freque ntly drawn with the help of a histogr am but can be drawn withou t drawin g a histogr am. Freque ncy polygo n is constr
ucted using a line joinin g the mid values of each class interva l, the height of the point repres ents the freque ncy. Steps for the constr uction of Freque ncy polygo n:
- M a r k t h e c
d m a r k t h e m i d p o i n t s o f e a c h c l a s s i n t e r
v a l
- M a r k t h e f r e q u e n c i e s o f e a c h c l a s s o n
o t t h e f r e q u e n c y o f g i v e n c l a s s i n t e r v a l.
T h e h e i g h t d e s c r i b e s t h e f r e q u e n c y. M a k e
