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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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Normal Distribution.

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Distribution.
Distribution gives idea about how individuals are distributed in the population. It can be represented by a generalized frequency curve. The distribution can also be represented by some mathematical relationship known as distribution function.

Trials
Number of times the experiment is repeated is called as number of trials.

Binomial Distribution.

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Dispersion
Dispersion gives idea of spread of data from the central value say mean.

Deviation.
Deviation is the difference between a observation and some reference value. Observation value is usually represented by X bar.
Deviation of x from some value A is X – A.
Deviation from mean is X – X

Absolute deviation
When deviation is always taken as positive irrespective of its sign, it is called as absolute deviation. It is represented as | X – X |

Mean deviation

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Central Tendency
Central Tendency is the tendency of the data to converge at some value.

Measures of Central Tendency
Measures Central Tendency are the numerical values representative of the data. These are mean, mode and median.

Arithmetic Mean
It is given by sum of all observations divide by total number of observations. Consider the observations 10,15,20,30,35.
Arithmetic mean = [10+15+20+30+35] / 5 = 19

Geometric Mean
It is given by nth root of product of all observations where n is total number of observations . Geometric mean of 2,2,2,8

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Ordinal Variable.
A variable whose possible values can be arranged in some order, such as short, medium, long . In contrast, a variable whose possible values are India, China, USA, are not ordinal variables. Arithmetic with the possible values of an ordinal variable does not necessarily make sense, but it does make sense to say that one possible value is larger than another.

Random Variable.
A random variable denotes possible outcomes of a random experiment.

Random Experiment.

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Variable or Variate.
A letter which can take values of all observations. e.g. If variable x represent marks of three students who have scored 40, 50 and 60 marks, then x1 = 40, x2 = 50, x3 = 60.

Categorical Variable.
A variable whose value ranges over categories, such as male, female. Some categorical variables are ordinal.

Continuous Variable.