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# Statistics is the science of collection

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a mixed view of statistics

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### Statistics is the science of collection

1. 1. Statistics is the science of collection, analysis and presentation of numerical data. It is used for decision- making and inferential determination in different situations. It deals with :  Large groups of values, not a single entity or value  Uncertainty determination (probability)  Identifying patterns in values  Aspects of information that can be described numerically Branches of statistics: • Descriptive Statistics deals with concepts and methods concerned with summarization and description of important aspects of numerical data. Its consists of condensation of data, their graphical display and the computation of few numerical quantities that provide information about centre of the data and indicate the spread of the observations. • Inferential Statistics deals with procedure for making inferences about the characteristics that describe the larger group of data or the whole called the population, from the knowledge derived from only a part of the data named as sample. It includes the estimation of population parameters and testing of statistical hypotheses. This part is based on probability theory. Population is the set of all outcomes of an event. It can also be considered as a collection of all the observations regarding any phenomenon or entity. It can be finite or infinite. Parameters are numerical values that describe a population e.g. mean. Sample is a subset of the population. Quantitative variable: numerical data 1. Discrete: integer or whole number 2. Continuous: any value between any given range is possible whether it is a whole number or a decimal number or fraction. Qualitative variable: non-numerical data e.g. eye color, gender Scales: 1. Nominal : numbers define classes but there is no significance in ranking or ordering of numbers 2. Ordinal: numbers define classes and ranking or ordering of numbers is significant. 3. Interval: any scale possessing a constant interval size Collection of data: 1. Personal direct investigation 2. Indirect investigation
2. 2. 3. Questionnaires and surveys 4. Local sources ( no formal investigation ) 5. Enumerators The main aims of classification are  To reduce the large set of data to an easily understood summary  To display the points of similarity and dissimilarity  To reflect the important aspects of the data  To make comparison and inference of data easier Frequency curves come in a variety of shapes. A unimodal curve is one that rises to a single peak and then declines. A bimodal curve has two different peaks. Advantages Disadvantages MEAN  Easy to compute and comprehend  All observations taken into account  Can be determined for any set  Accuracy affected by outliers  Misleading results  Highly skewed distribution, mean is not a good measure of location GEOMETRIC MEAN  Rigorously defined mathematical formula  All observations taken into account  Not effected by sampling variability  Cannot be computed for all sets  It is difficult to comprehend HARMONIC MEAN  Rigorously defined mathematical formula  Difficult to comprehend
3. 3.  Not affected by sampling variability  All observations have bearing on its value  Cannot be computed for all types of sets MEDIAN  Easy to compute and comprehend  Not affected by outliers  In highly skewed distribution, it is a good measure of location  Has no strict definition  It cannot be mathematically treated further than what it already is  Necessitates the arrangement of data, time consuming MODE  Simple calculation  Not affected by outliers  Can be evaluated for both Qualit. and Quanti. data  No further mathematical treatment  No strict definition  Does not take into account all observations An experiment that can result in different outcomes, even though it is repeated in the same manner every time, is called a random experiment. Sample space = population Event= sample When A and B have no outcomes in common, they are said to be mutually exclusive or disjoint events.