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Statistics study consist on topics like F distribution, multiplication theorems, probability, random variable, T distribution, geometric probability distribution, marginal probability, sampling, skewness, symmetrical distribution and transformation, estimates. This solved assignment includes: Constructing, Graph, Variable, Scale, Sampled, Population, Target, Inferential, Descriptive, Statistics, Random, Error
Typology: Exercises
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Question: What are the points which should be kept in view while constructing a graph? Answer: The following points should be remembered while constructing the graph. Use clear titles and indicate when and how the data were collected (i.e. the theme of the graphs and the source of data). Ensure that the scales are clear, understandable and represent the data accurately. When possible, use symbols for extra data. Always keep in mind the reason why a graph is being used (i.e. to highlight some information or data in a striking and unambiguous way) and anything that facilitates this objective is desirable. Question: What is variable? Explain its types. Answer: Variable: A characteristic that can vary or differ is called a variable, such as age, location, or education level. It is a term used in statistics to describe the factors that are to be studied. A variable can be classified in to qualitative and quantitative according to the form of char acteristics of interest. Qualitative variable: A variable is called a quantitative variable when a characteristic can be expressed numerically such as age, weight, income or number of children. Quantitative variable: A variable is called a quantitative variable when a characteristic can not be expressed numerically such as education, sex, eye- color, quality, intelligence, poverty, satisfaction, etc A quantitative variable can be classified in to two categories, discrete va riable and continuous variable. Discrete variable: A discrete variable can assume v alues by counting process, such as the number of persons in a family, the number of rooms in a house, the number of deaths in an accident, the income of an individual, etc. It can take on only a discrete set of integers or whole numbers. Continuous variabl e: A continuous variable can assume values by measuring process such as such as the age of a person, the height of a plant, the weight of a c ommodity, the temperature at a place, etc. It can take on any value-fractional or integral––within a given interval. Question: Explain Sampled population and Target population. Answer: Sampled population - The population from which the sample is taken. Target population - The population about which inferences are made. I explain u with the help of the following example Suppose we want to know the opinions of college students in the province of Punjab with regard to the present examinati on system. Then our Population will consist of the total number of students in all the colleges of Punjab. Suppose we conduct a sur vey only on five colleges through out the province due to shortage of resources. In such a case, the target population consists of the students of all the colleges in Punjab while on the other hand, the sampled populations consists of students of five coll eges. The students of these five colleges are the representative of the students of all the colleges; the result would be applicable to all the colleges. Question: Differentiate between inferential and descriptive statistics. Answer: Descriptive Statistics: It is that branch of statistics which deals with concepts and methods concerned with summarization & description of th e important numerical data. Inferential Statistics: It deals with procedures for making inferences about the characteristics of the larger group of data or the whole called the population, from the knowledge derived from only the part of data. Question: define infrentional statistics. Answer: Inferential Statistics uses sample data to make estimates, decisions, predictions, or ot her generalizations about a larger set of data (population). It is further divided in two main areas: 1 Estimation 2 Testing of Hypothesis Question: What is observation give details? Answer: OBSERVATION: In statistics, an observation often means any so rt of numerical recording of information, whether it is a physical measurement such as height or weight; a classification such as heads or tails, or an answer to a question such as yes or no. Question: What is random error?
Answer: RANDOM ERROR: An error is said to be unbiased or random error when the deviations, i.e. the excesses and defects, from the true value tend to oc cur equally often. Unbiased errors and revealed when measurements are repeated and they tend to cancel out in the long run. These e rrors are therefore compensating and are also known as accidental errors. Question: What is the relation between Probability and Statistics? Answer: Probability and statistics are fundamentally interrelated. Probability is often called the vehicle of statistics. The area of inferential statistics in which we are mainly concerned with drawing inferences from experiments or situations involving an element of uncertainty, leans heavily upon probability theory. Question: What is Random sampling and its is usefullness. Answer: Random sampling : A process for obtaining a sample from a population that requires that every individual in the population ha s the same chance of being selected for the sample.It is widely used in various areas such as industry, business etc. Question: Explain the frames or sample frames and what are the uses of them in Statistics? Answer: sampling frame or simply frame is a complete list or a map that contains all the sampling units of population, for example, a complete lis t of the names of all the students in the Virtual University. A list of all households in a city, a map of a village showing all fields, etc. The r equirements of a good frame are 1 It does not contain inaccurate sampling units. 2 It is complete 3 It is free of errors 4 It is as up-to- date as possible at the time of use. It helps us to select a good sample from the population. Question: What is error of measurement and give detail with real life examples? Answer: ERRORS OF MEASUREMENT: Experience has sho wn that a continuous variable can neverbe measured with perfect fineness because of certain habits and practices, methods of easurements, instruments used, etc. the measurements are thus always recorded correct to the nearest units and hence are of limited accuracy. The actual or true values are, however, assumed to exist. Example: If a student’s weight is recorded as 60 kg (corr ect to the nearest kilogram), his true weight in fact lies between 59.5 kg and 60.5 kg, whereas a weight recorded as 60.00 kg mean s the true weight is known to lie between 59.995 and 60. kg. Thus there is a difference, however small it may be between the measured value and the true value. Question: What are the advantages of sampling in daily life? Answer: Sampling is procedure of taking sample from population. It is not a place or an area which can be empty or full. We are all familiar with the id ea of sampling in our everyday life. A cook takes a bit of the cooked food to see whether it has been properly cooked. Customers, b y observation, sample the quality of fruits and vegetables they intend to buy. A food inspector takes a sample of the food items like milk, oil, flour, etc.to find out wheth er they are pure our not. Medical doctors receive samples of various medicines to try them on a sample of patients to determine their effectiveness in curing the disease Question: What is Quantitative Analysis? Answer: Quantitative Analysis: It means the analysis of those variables which can be expressed numerically such as age, income or number of children. Question: what are population parameters and sample statistic? Answer: Population Parameters or simply Parameters are numerical values that describe the characteristics of a whole population. Comm only represented by Greek letters. Sample Statistic or simple Statistic are numerical values describing the characteristics of a sample. Commonly repres ented by Roman letters. Note that the term statistic refers to a sample quantity and the term parameter refers to a population quantity.