predictions

Hello students, in this blog we are going to learn about the predictions mean guessing for something. The simple definition of the Predictions is that, it is statement that is made about the future or act of predicting (as by reasoning about the future). The act of foretelling and that which is foretold is predictions. In other words when we predict anything that means that those things will be happen in the future and generally all forecasting is based on the experience or knowledge.
A very suitable synonym for the predictions is the Forecast. But between the prediction and the forecast, there is a overlap and why it is? Let’s see....
In prediction we expect some output while forecast contains the possible outcomes.
Predictions is made for the future means we planned for future that what will be happen when several types of conditions will arises. It is not necessary that every prediction will be right some may be wrong. It can also be defined in the terms of uncertainty.
The most important example about the predictions is that some astrologers said before few years that the world will be no more after the 12 December 2012, and everyone heard this statement, but nobody knows the truth, because it is also a prediction that is based on the some knowledge and books.
Predictions can be done in every field like in science, finance, fiction, politics and in many more.
And it can be done by collecting the past and current data of that particular field that which we want to predict and for collecting data there is several methods.


I hope this information that I gave above will be truly useful for the Grade VI students.

In the next session we are going to discuss Measures of central tendency and dispersion

Measures of central tendency/dispersion

Measures of central tendency are define in the statistics in the form of Mean ,median and mode .Measures of central tendency defines the single value for the group of values .Sometimes these are known as the average of the bunch of values .When we talk about the Measures of central tendency it defines that which is the value repeated mostly or which value have the greater frequency .If we take some examples as in a class what is the average height of the students or in a group what is the average age of peoples so these type of questions are solved with the help of Measures of central tendency that are describe as mean , median or mode as gives the single value that define the whole group of values .
Measures of central dispersion is denoted as the gap of the values from the center means it is define the
spreadness of the values .It is defined in terms of Range or variance or standard deviation .If we take some examples to understand the Measures of central dispersion as if the age of students in the class is 9 or 15 then there is lot of variation in the group of values so these are calculated through the Measures of central dispersion .This is helps the students of grade VI for understand how we can measure the central tendency of bunch of data or central tendency of dispersion. (know more about cbse syllabus for class 10 , here)
There are some examples as if in a group there are 5 students and their age is 8 , 7 , 6 , 9 , 7 then the central tendency is define as the value having the maximum frequency that is 7 then the answer is 7 or sometimes we talk about the mean that is define also as the average value then it is calculated as
( 8 + 7 + 6 + 9 + 7) / 5 = 37 / 5 = 7 .4 years that is about the 7 in round figures.
In the next session we will discuss about predictions. 

Collect/organize/graph data

Hello students, in this session we are going to discuss the collecting data, organize it and graphing data. Let’s take a look step by step. To organize and graph data, firstly it should be properly collected. And there are various methods to collect the data according to our requirements.
Data collections mean store the data at a particular place and also describing that how it was collected. And in data collection we get the information from many source such as from persons. By the data collections we store the information at a particular place so that we can use this information for further use. Before data collection you should know about the types of data. Data may be primary and secondary, after finding the types of data we apply the collection methods, and they are also two types grouped and Un grouped.
Methods for primary data collection are: - Data collection through investigation, Data collection through telephones and Personal investigation methods.
Methods for secondary data collection are: - Official methods include the data collection from the ministry of finance and industry by using some tools. (know more about icse board , here)
Semi official methods include the data collection from the banks, board of railway.
After collecting data we need to organize the data. To organize the data generally we use tables. Because the retrieval and insertion of data and information in table is easy than any other.
Let talk about the graph of data, to do this we use several types of graphing methods such as : - pie chart, line plot, box plot, pictograph, map chart, bar graph, line graph, stem and leaf plot, frequency polygon and histogram that are mainly used.

I hope this information that i gave above will be truly useful for the Grade VI students.
In the next session we will discuss about Measures of central tendency/dispersion. 

Independent

In probability, two events are said to be independent when the occurrence of one event does not make any effect on the other event. It means that any two related events that have no effect on each other. Here an event refers to any type of activity that is performed manually. In mathematical definition two events are independent if the outcome of one event does not make any influence in the outcome of second event. In the process of finding the probability of two independent events requires to multiply the probabilities of the two events. After obtaining the outcome, if needed then simplifies the final result.
Suppose the event of getting a Red heart in first attempt and the event of getting a black heart in second event are independent event. So, we can say that any two random variables are independent if the conditional probability distribution of either given the observed value of the other is the same as if the second event’s value had not been observed. The concept of independent event is most widely used in probability to give knowledge to the students of Grade VI. (know more about syllabus of cbse board, here)
In the form of standard definition independent events can be defined as:
Suppose we have two independent events x and y then they can be represented as
 P (x ∩ y) = P (x) . P (y),
In the above notation ‘x ∩ y’ can be defined as intersection of ‘x’ and ‘y’. It means that it is an event where both events ‘x’ and ‘y’ occur. In probability of independent events we can apply the multiplication rule that is given below:
Rule for probability of independent event:
If two events ‘x’ and ‘y’ is independent then probability of occurrence is:
   P (x and y) = P (x) . P (y),
In the next session we will discuss about Collect/organize/graph data. 

Representing probability

This unit is for the students of Grade VI; here we are going to learn probability representation. We come across the situations in our daily life when the results are unpredictable, like the toss of a coin, where we are not sure whether we will get a head or the tail. In day to day life we come across the statements like “Probably I may get the job next month”, “USA might win this one day cricket match series”. Such cases involve the elements of uncertainty or chance. A numerical measure of such   uncertainties is provided by a very important branch of statistics called the theory of probability. (know more about icse board syllabus, here)

Today this subject has been developed up to such extent that its use is seen in almost every field of life. This tool of measuring probability is used in social, physical science and in the quantitative analysis of all business and economics related problems. Statistics forms the basics of decision theory which means making decisions under the conditions of uncertainty. Representing probability basically means representation of the chances of probability of any event in forms of figures and numbers. When we want to find the probability of occurrence of any event, we must know the possible outcomes and the total number of outcomes of the experiment. It will be clearer with the following example. If you toss a coin and you need to know the probability of getting a head. It is absolutely uncertain event. When we flip a coin, we do not know if it will be a head or a tail. Now we know that there may be two possible outcomes H, T. So the possibility of getting a HEAD is 1 /2.
So the probability of getting a head is P (H) = ½.
 In the next session we are going to discuss Independent.

Estimating probability

Hello students, in this section we are going to discuss the estimating probability, Probability means predictions. Estimating probability means finding the probability. In this we are using favorable event, it means the cases which ensure the occurrence of an event.
Mathematically we have,
Probability of an event ‘A’ that is P (A) = m / n.
Where m = possible outcomes favorable to the occurrence of ‘A’.
n = total number of possible outcomes.
And n - m = possible outcomes unfavorable to the occurrence of ‘A’.
We also notice that
P (A) + P (A)' = m / n + n – m / n = 1,
That is P (A) + P (not A) = 1.
 Probability sum of events in an experiment is equal to one, means if there is an experiment in which three events are occurring, as x , y , z then the probability p (x) , p (y) and p (z) are denoted as p (x) + p (y) +p (z) = 1.
Let us take an example to estimate the probability.
-Estimate the probability of getting the number less than 6 in throwing a die once.
Solution: - Total number of events are: 1, 2, 3, 4, 5, 6.
n (s) = 6,
Favorable events = a number than less than 6 = A = 1, 2, 3, 4, 5,
n (A) = 5,
Hence P (A) = n (A) / n (s) = 5 / 6.
Like this we can solve any examples for probability of Estimating.
I hope this information will be valuable for the Grade VI students.
 In the next session we are going to discuss Representing probability.

Possible outcomes

Hello students, in this section we are going to discuss the possible outcomes in probability. Probability means predictions. Possible outcomes means when we are performing a task then its results will be there, so the total number of expected results are called as the possible outcomes for an event. Let us take a look to understand the possible outcomes for the various experiments.
i) When we toss a coin, we get either a Head (H) or a Tail (T). Thus, all possible outcomes are H, T.
ii) Suppose two coins are tossed simultaneously. Then, all possible outcomes are HH, HT, TT and TH.
Remarks:- HH means head on first coin and head on second coin.
HT means head on first coin and tail on second coin.
iii) When we toss a three coin simultaneously. Then, all possible outcomes are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. (know more about cbse board, here)

Remarks: - HHH means head on first coin, head on second coin and head in third coin too.
HHT means head on first coin, head on second coin and tail on third coin.
iv) In drawing a card from a well shuffled deck of 52 cards, total number of possible outcomes is 52.
v) On rolling a die, the number on the upper face is the outcome. Thus all possible outcomes are 1, 2, 3, 4, 5, 6.
The collection of all or some of the possible outcomes is called the event.
The all possible outcomes are also known as the sample spaces and we denote the sample spaces as ‘s’ = the total number of possible outcomes
 I hope this information will be valuable for the Grade VI students.
 In the next session we are going to discuss Probability Help.

complement

In Grade VI, while studying about set theory, we come across different types of sets. Here we are going to define complement of a set.
If we say that U is the universal set and A is any set, which is the subset of set  U, then the complement of set A will be all the elements which belong to set  U but  does not belong to set A.  Complement of set A can be written as U – A. We express complement of set A as A’.  Thus we can say that
 A’ = U – A
 Also we can say that the elements of set A and the elements of set A’ ( which is the complement of set A, when U is the universal set ) join together to form the universal set  U. mathematically it can be expressed as follows: A  + A’ = U
It will be more clear by the following example: Let U = 1, 2, 3, 4 , 5, 6, 7, 8 , 9, 10 we say that set U is the universal set which represents the natural numbers from 1 to 10. Also let the  set A = 1, 3, 5, 7, 9 which is the set of all odd numbers from 1 to 10. (know more about free download cbse books, here)
 Now A’ = U – A
= 1, 2, 3, 4 , 5, 6, 7, 8 , 9, 10 -   1, 3, 5, 7, 9  = 2, 4, 6, 8, 10
 SO we observe that it will contain all the elements of the universal set U, which are not in A. Also if we add together set A and set A’ , then the resultant set will be the universal set itself.
Another important thing about  a complement is  that  a complement of any complement is the original set itself. It means: ( A’)’ = A
In the next session we will discuss about Possible outcomes.