Concepts of Ogive or S shaped curve

Introduction:
             The scientific methods of collection of data, its classification and application to commerce and everyday life is called statistics.
Graphical Representation:
     There are various methods of graphical representation of statistical data. In our study, we learn only two types. (i) Histogram (ii) Ogive or Cumulative Frequency Curve.
Ogive (Cumulative Frequency Curve):
     A plot of the cumulative frequency against the upper class boundary with the points joined by line segments. Any continuous cumulative frequency curve, including a cumulative frequency polygon, is called an ogive. There are two ways of constructing an ogive or cumulative frequency curve. (Ogive is pronounced as O-jive). The curve is usually of 'S' shape.
Summary:
     1. Two types of graphical representation of data are the histogram and the ogive.
     2. A histogram is a diagram which represents the class interval and frequency in the form of a rectangle.
     3. An ogive or a cumulative frequency curve is a 's' shaped curve. Points on the ogive have abscissae as the actual upper / lower limits for 'less than' / more than curve and ordinates as the cumulative frequencies.

Hope you liked the above explanation. Please leave your comments, if you have any doubts.

Event and its Types

Introduction on Eevent:

        

        In Probability, an event is the outcome or a combination of outcomes of an experiment. In other words, an event is a subset of the sample space. The event in the math represents the probability event for the math. 

Eg:

• {a head} in the experiment of tossing a coin is an event.

• {a sum equal to 6} in the experiment of throwing a pair of dice is an event.

Types of Events:

Lets go through the different types of events below with simple explanation:

S= {1,2,3,4,5,6}]
If the event is set of elements less than 2, then E = {1} is a simple event

1) Simple Event: If an event has one element of the sample space then it is called a simple or elementary event.

2) Compound Event: If an event has more than one sample points, the event is called a compound event .

3) Null Event (f): As null set is a subset of S, it is also an event called the null event or impossible event.
4) Sure event or certain event: The sample space S= {1, 2, 3, 4, 5, 6} in the above experiment is a subset of S. The event represented by S occurs whenever the experiment is performed. Therefore, the event represented by S is called a sure event or certain event.

5) Complement of an Event: The complement of an event E with respect to S is the set of all the elements of S which are not in E. The complement of E is denoted by E' or E^C.
        Hope you liked the above explanation on Event. Please leave your comments, if you have any doubts.