Organization and display of data

When an experiment is done then all the data related to that experiment that is used for future prediction and for comparison between the data of different time of that experiment then there will be need of Organization and display of data. It will help in making the efficient and effective plan that is based on the organized data and also helps in making strategies for future that are totally base on the previously stored data .Before storing the data it should be keep in mind that how data is organized and also from where data is collected . (know more about cbse text books, here)
Data should organize correctly and it will be presented in the manner that everyone can easily understand it means and also presentation of the data must be in timely manner that means when data is needed by the user it will be available to him / her on that particular time not after so much delay and also keep in mind when data is needed by someone it can be easily retrieved by them and after collection of the data it should be organized according to some keys.
After all the organization of data there will be next very important concept of display the data. It is the only way that helps the user to understand the previously recorded data and also helps in making of some decision that based on that particular recorded data. Organization and display of data in probability is also helpful to make the future strategies and also helps in comparison of the data.
Data representation has many ways like image processing, Global positioning system. Display of data is used to understand the data and deriving the meaning for conclusion .The representation of data can be done in many ways like Statistical tables, rank order, frequency order.

In the next session we will discuss about variance. 

Precalculus

Hello students, in this blog you will learn about the precalculus. Precalculus is the basic introduction about the mathematics analysis. This is the foundation of mathematics stream. First we will know about what is precalculus, precalculus is necessary to read especially when you are going to deal with the claculus. It is the first step to know more about the calculus.
Precalculus covers many topics, such as sets, real numbers, complex numbers, composite and polynomial functions, trigonometry, limits, vectors, metrics, binomial theorem, mathematical induction, sequence, series, conic section, logarithm function, basic graphs and many more. Let's discuss some of them here.
Set: - It is a collection of objects in a well defined manner. The basic operations of sets are union, intersection, complements and cardinality product.
Real number: - These types of numbers include all number that may be rational and irrational numbers.
Function: - Function describes the property between the input and the respective outputs.
Conic sections: - It is special type of curve and it involves three types of sonic section that are hyperbola, parabola and ellipse, sometimes we take circle as the forth type of conic section because it is special type of ellipse. (know more about cbse sample papers, here)
Limits: - They are the initial part of the calculus and limits are useful when we define the continuity, deviates and integrals.
Mathematical induction: - The Mathematical inductions are used for mathematical proof so that we can determine the given statements is true or false for the given natural numbers.
Trigonometry: - In this we study about the triangles and about their relations.
In the next session we will discuss about Organization and display of data. 

Types of events

In mathematics, the study of probability theory can be considered as a part of mathematics. In the probability theory we generally perform the calculation of finding the likelihood occurrence that is related to any particular event. It means to say that when an event occurring so many times; at that time we are not able to predict what will be the outcome at each and every time. So at that we use the concept of probability to find out the probability for outcome of any event.  In the simple we can say that probability is the most important concept of mathematics that deals with the calculation of likelihood of a given event’s occurrence. In probability theory, an event which is related to the probability can be expressed in the form of number range from one to zero.
 In the probability theory, anything that happens is named as events. It means to say that event is a term which is used to show the outcome on the occurrence of something. In the probability theory events can be categorized in different types of events. The Types of events are (a) independent event (b) dependent event.
Independent event: independent events are those events which has the no effect by any other type events. It means to say that the outcome of any event must not be dependent on another event. These events are considered as independent event. Suppose you toss a coin two times , in first it comes ‘tail’ then at that time you are not able to predict what will be the second outcome form the second toss. This thing is known as independent event.
Dependent event: Dependent events are those events whose outcome depends on outcome of another event. Suppose: there we select a card form a pack of card. The card is of heart of king. Now if we want to pick the next card then it will sure that the next card will not be king of heart. This event is known as dependent event.
In the next session we are going to discuss conditional probability, Grade IX.

Permutations and combinations

Hello students, in this blog we are going to discuss the topic of permutations and combinations. These two topics are extensively used in mathematics.
Permutations: - The different arrangement of a given number of things by taking some or all at a time, are called the permutations. Let’s take a close look on the permutations.
All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking two at a time are (ab, ba, ac, ca, bc, cb).
 All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking all at a time are (abc, acb, bac, bca, cab, cba).
Combinations: As name suggest of the combination that it is concept in which every number of separate groups are made by the when we include few or all number of an object, then it is known as the combination.
Suppose we want to select two out of three boys A, B, C. Then possible selections are AB, BC and CA.
Note that AB and BA represent the same selections.
Formula for permutation and combination are:
For permutation: “P r = n (n - 1) (n - 2)……(n –r + 1) = n! / (n - r) !,
Example for this: 1. 6 p2 =(6 * 5) = 30.                  2. 7 P 3 = (7 * 6 * 5) = 210.
 For combination: “C r = n ! / (r !) (n - r) ! = (n - 1) (n - 2)……to r factors / r !,
Example. ¹¹ C ₄ = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330, (know more about icse board papers, here)
So applying both the formulas we can solve any permutation and combination problems.
In the next session we will discuss about Types of events. 

conditional probability

In mathematics, probability can be considered as a branch of mathematics. The concept of probability deals with the calculation of the likelihood occurrence of any given event. The term probability describes their value in the range between 0 and 1. In the concept of probability the value one refers to the certainty of the occurrence of any particular event. In the same aspect the value zero refers to the impossibility of occurrence of any event. The basic behind using the concept of probability in mathematics is that when the lots of situations happens and we are not able to predict the outcome of the particular event then the concept of probability is used in this case to analyze the different possibilities and how likely each of them is. (know more about cbse board papers, here)
   There are various concepts are defined that helps in understanding the probability more clearly. Form that concepts conditional probability is one of them. In the probability theory, the conditional probability is a concept which defines the conditional relationship between two occurring events. It means to say that the conditional probability of ‘X’ given ‘Y’ is the probability of X if Y is known to occur. In the mathematical notation we can represent the conditional probability as P (X / Y).  It means to say that the conditional probability of occurrence an event Y is only when the occurrences of the event ‘X’ is already done.  In probability theory the definition of conditional probability can be represented by using formula for conditional probability:
       P (X / Y) = P (X and Y) / P (Y),
In the above definition of probability we need to remember one thing that the value of the P (Y) must be greater than zero. In most of the cases the P (X / Y) can be visualized as probability of event ‘X’ when the sample space of the event ‘Y’ is restricted. In the next session we will discuss about Permutations and combinations. 

Data representation methods

In statistics we have several methods of data representation that are used for represent the data in a specified manner that means once data is collected by the person or group of persons that is related with the specific experiment is then it will be presented in the way that user of data can understand it very easily and it is not used only for present scenario but also it will be used in future for making some decisions or for comparing the results of different years , so there are some well defined methods of data representation in statistics that helps the user of data to make efficient and effective decision very efficiently in very short span of time .These Data representation methods are as follows :
Data will be represented in the tabular form that will support to understand the data with its entire attributes.
For representing the data there one more technique that is known as graphs or pie charts that will help in understanding the way how data is changed in the particular environment or for specific experiment .
We can also draw some charts for representation of data.
The graphs are also categorized in some types that are line graph or histogram or bar graph or pyramids etc.
So for presenting the data there should some step that must be follow by the user for making the graphs or charts as: (know more about cbse sample papers for class 10, here)
First of all a suitable scale will be selected by the user.
After selection of scale follow all the design as index, directions and titles etc.
After it user select the appropriate way for representing the data that data will represent in two dimensional ways or in three dimensional ways.
In the next session we will discuss about conditional probability. 

Tools of data analysis

Hello students, in this blog we are going to discuss about the tools of data analysis but before discussing the tools of data analysis statistics. We should be familiar with the data analysis term. Data analysis is the process of summarizing the information by using the following steps,
-Inspecting the data.
-Cleaning the data.
-Transforming the data.
-And last modeling the data.
There are various tools that analyze the data more clearly and more precisely. Some of them are: -
1. Histogram: - This is the most common technique for data analyzing. This is the graphic technique that shows the frequency distribution.
2. Survey: - Usually the surveys are organized by the various NGOs to collect the data. This is done publicly so that we can know the behavior, opinions and knowledge of the public.
3. Scatter diagram: - In this type of data analysis tool we create the diagram for the numerical data.
4. Series of experiments: - In this type data analysis tool, we predefine the some series of experiments on the particular data or information. Then data passes through the various series of experiments and meaningful data is drawn.
5. Box and whisker Plot: - Various types of data sets are plotted on the single graph.
6. Check sheet: - It is like ms excel sheet that stores the data in tabular format, so that data can easily be understand by everyone. It is a prepared form for data collecting and data analyzing.
7. Control chart: - It is used to control the data process. It compares the data that change from one state to another. (know more about cbse board papers, here)
But mostly used data analysis tool is histogram.
This bog will be helpful for Grade IX students to understand the Tools of data analysis.
In the next session we will discuss about Data representation methods.