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CHAPTER 2
Measures of Central Tendency And Dispersion

2.1 Introduction

In this chapter we will study various types of data, methods of data collection , data representation and measures of central tendency.

First question is ‘What is data’? Data is a set of something that we want to know about the object or objects under study. For example if we want to study performance of students in an examination, set of marks obtained by students will be our data.

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Confidence Interval.
A confidence interval is percentage of observations that are supposed to lie in that interval. e.g. 95% confidence interval is supposed to contain 95% of observations according to the specified criteria.

Confidence Level
Confidence level is the confidence interval in which we expect to lie the given parameter of the hypothesis.

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Hypothesis:
An Assumption of outcome of statistical testing is called as hypothesis. e.g.: Sample is as per required norms according to the given parameter.

Parameter
Parameter is criterion on which sample is accepted or rejected. Parameter could be mean, standard deviation etc.

Estimator.
Estimator is a parameter which is used to estimate the value of the population parameter. An example of an estimator is the sample mean, which is an estimator of the population mean.

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Mutually Exclusive Events
Two or more events which cannot happen at the same point of time are called as mutually exclusive events.

Exhaustive Events
If two or more events cover the entire sample space i.e. if two or more events cover all possible outcomes of an experiment, then such events are called as exhaustive events.

Certain event
If probability of an happening of an event is 1, the event is a certain event.

Impossible event

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Event and Happening of an event.

Event is a set of one or more outcomes of an experiment. An event is said to have happened if the outcome is the result of the experiment. e.g. In the experiment of tossing of an coin there are two outcomes head and tail. Two events A and B can be defined as follows:
Event A: Head shows up in the experiment of tossing of a coin.
Event B: Tail shows up in the experiment of tossing of a coin.

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Probability
It is theory of chance when taken as science.
It is chance of happening an event when considered in connection with the event. Probability of any event is between 0 and 1, both included.

Mathematical or Objective Probability
Probability theory, which is based on statistical data and probability axioms, is called as mathematical probability.

Axioms of Probability.

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Sample Size:
The number of elements in a sample is called as sample size.

Sample Survey:
A survey based on the responses of a sample of individuals, rather than the entire population.

Cluster Sample.
In a cluster sample, the entire population is divided into heterogeneous group and some of such groups are selected as sample which is chosen on geographical basis is example of cluster sampling. If the blocks are chosen separately from different strata, so the overall design is a stratified cluster sample.

Convenience Sample.