Probability and Statistics

In the mathematical field, there are lots of concepts and lots of theories are defined to solve the problem, which are related to math’s subject. In the real, there are lots of problem related to performing calculation, these calculations are based on several aspect of the mathematics. During the study of mathematics, we can divide the mathematics into several categories that are: arithmetic, geometry, discrete mathematics and statistics. All have the different work area to apply the concept of this mathematics. Here we give you a brief introduction to probability and statistics. Probability and statistics are two different academic topics to study. Statistics is the way to perform the process of analyzing the fact and figures and generate the output. Statistical analysis includes the topic of probability distribution. In the probability and statistic we generally include the experimental part of the statistic subject. This subject asks to perform the repeated calculation of same thing again. The concept of probability and statistics helps the students of Grade IX to understand the basic of this topic. So to remove the problem of repeated calculation statistic subject provide lots of formulas to perform the calculation in the simpler manner and this repeated type of calculation generally known as probability.
In below we show you the perfect example that helps in understanding the concept of probability and statistics. Suppose we toss a coin, now the possibility of getting head is 50% and the possibility of getting tail is also 50%. The formula for performing the probability is: (know more about cbse sample papers 2013, here)
In the mathematics, the numbers of ways to get ‘H’ heads or ‘T’ tails in ‘n’ no of toss is spoken as number of combination of n things taken ‘H’ or ‘T’ at a time. This can be written as:
                                                   (H or T / n)
So, to calculate the probability ‘P’ of given values of ‘H’ and ‘T’ can be performed by:
           Probability =(‘H’ or ‘T’ / n) = (no of ways for an event/ total number of possible outcome)
The probabilities can be described in between the value of 0 to 1. In the next session we will discuss about Mean. 

Triangle inequality theorem

As we all are very well aware that geometry provides lots of shapes and figures to solve out the problems that are related to mathematics. In mathematics, triangle is a shape that provides the various concepts to solve the problem. Triangle inequality is one of them, which states that the sum of lengths of any two sides of the triangle must be greater than or equal to the length of third side. Euclidean geometry says that triangle inequality is a theorem about the distance. In simple definition of the triangle inequality theorem we can say that the total of any two sides of triangle must be greater than the third side of the triangle. If in case the above theorem is not applied at the time of triangle creation then that figure is not considered as a Triangle. This theorem helps the student of Grade IX to understand the concept.
Suppose a triangle has three sides which named as A, B and C. Now we check that the given triangle is a complete triangle or not by applying the inequality theorem. The Triangle Inequality theorem says that:
B + C > A,
A + B > C,
C + A > B,
If in the given triangle, available values satisfy the above combination or pairs of inequality then the triangle can be considered as complete triangle. In study of Triangle of geometry, we generally study three types of triangle which are equilateral triangle, isosceles triangle and right angle. In all types of triangle we can easily see the operation of triangle inequality theorem. (know more about icse syllabus 2013 , here)
Example: Can a triangle have the side lengths of side 1 = 4cm, side 2 = 8 cm and side 3 = 2cm?
Solution: Now we need to apply the triangle inequality theorem. By applying the Triangle inequality theorem we create three combinations that are given below:
Side 1 + side 3 > side 2,
  4 + 2 > 8,
The first equation get false then we can say that the above given sides are not able to form the triangle.
In the next session we will discuss about Basic constructions.