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# descriptive stats - CHAPTER-6 Lecture 27 28 DESCRIPTIVE...

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CHAPTER-6 Lecture # 27 & 28 ------------------------------------------------ DESCRIPTIVE STATISTICS

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Statistics In Statistics, we want to study properties of a (large) group of objects, generally termed as population . Methods of statistics study small subsets of population. This is called sample . The science developed for this purpose is called descriptive statistics. Study of samples is used to infer the properties of the entire population. The science developed for this purpose is called statistical inference.
Characteristics of a statistical Problem: 1. Associated with the problem is a large group of objects about which inferences are to be made. This group of objects is called the population . 2. There is at least one random variable whose behavior is to be studied relative to the population. RANDOM SAMPLING --------------------------------------

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3. The population is too large to study in its entirety, or techniques used in the study are destructive in nature. In either case we must draw conclusions about the population based on observing only a portion or “sample” of objects drawn from the population.
Population of interest : values of a random variable. Its properties of interest : parameters of its distribution.

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Example If the population has normal distribution, the location and shape are described by μ and σ. For a binomial distribution consisting of n trials, the shape is determined by p .
Often the values of parameters that specify the exact form of a distribution are unknown. You must rely on the sample to make inference about these parameters.

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Need of sampling(illustrations): Need of sampling(illustrations): An agronomist believes that the yield per acre of a variety of wheat is approximately normally distributed, but the mean μ and the standard deviation σ of the yields are unknown.
To estimate the proportion of tires manufactured by Dunlop tires which are sturdy, the quality control dept of the company needs to apply a certain amount of stress on tires and see if they survive it. Rather than applying stress to each and every tire, it is practical to do it on an appropriate sample and use it to infer for the whole set of tires.

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If you want the sample to provide reliable information about the population, you must select your sample in a certain way!
Populations Many a times populations are described by the distribution of the observations. We refer to population in terms of the corresponding probability distribution f(x) of the random variable X .

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Definition : A set of observations X 1 , …, X n constitutes a random sample of size n from the infinite population f(x) if 1. Each X i is a random variable whose distribution is given by f(x), 2. These n random variables are independent.
Remarks : (1) Here the sample can be thought as ordered and with repetition allowed, i.e., an n-tuple (x 1 , …, x n ) represents a sample.

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descriptive stats - CHAPTER-6 Lecture 27 28 DESCRIPTIVE...

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