Problem solving strategies

To become a better problem solver you need to analyze the problem in deep first and it require a systematic approach. Problem solving strategies requires practice, the more you practice, the better you get.
 Strategies of problem solving are:
1.      Look for the clues: In problem solving strategies, first read the problem carefully and underline the clue words. Look for the facts given and what do you need to find out.

2.      Make a plan: In strategies of problem solving, firstly set a plan. Or if you have done any problem like this before then do what you did.  You can use formulae, sketches, tables or any pattern.

3.      Now solve: In problem solving strategies, whatever plan you have thought of, just solve the problem according to it.

4.      Checking your answer: In strategies of problem solving, look over the solution. Check if it is the probable answer and also check for the units to be used in the answer.

In problem solving strategies, the first thing you do is looking for a clue, for which you need to a skills in solving problems and practice is most important here.
For example: In strategies of problem solving, if we are looking for clues in addition.
Then clues can be total, sum, in all, perimeter and so on.
Now in problem solving strategies, if you are looking for the subtraction clues, then they can be difference, exceed or how much more.
Similarly, in strategies of problem solving, if we are looking for the clues of multiplication, then you should look for the words: total, area, times, product, etc.
And in problem solving strategies, if you are looking for the clues related to division, then you should look for the words: distribute, quotient, average, share, divide,etc.


In strategies of problem solving, after all of the above points , one point which you need to remember is practice as much as you can to become a good problem solver.
In The Next Session We Are Going To Discuss Grade VI, Tools To Solve Problems.

Make generalizations

Hello students,Previously we have discussed about verifying trigonometric identities and In this blog I am going to tell you about the generalizations which comes under 12th state board syllabus tamilnadu. We can understand the generalization as the means of conclusions. Here a important point is that all generalization can be conclusions but it is not necessary that all conclusions may be generalizations. In generalization we extend the concept pf concept in more precise form.
Generalization may be faulty and valid generalization. The simple definition of the generalization is that, it is that type of broad statement that comes from the various valid resources like from observations, experiences and by doing surveys of the entire group of people    A valid generalization follows some properties: -
(I) There should be some facts to support the particular generalize statements.
(II) There should be various types of examples to support that generalize statements
(III) There should be some past facts, surveys and experience.
(IV) There should be valid logic and reasoning.
If any statements do not the follow the above properties then it is said to be faulty generalization.
Below are some examples to make generalizations.
Simple type of information - Government schools, Colleges, courts, offices are closed on the second of October.
In generalize form – Most of the government buildings are closed on national holiday.
Simple type of information – My brother sneezes every time of second when Diwali comes.
In generalize form – My brother is allergic to crackers.
Some predefined generalizations are: - Asians are bad drivers? And white men can’t jump?
Generalization means either the word all or every. Below are the some generalization’s clue words, they are: -
All                    None
Most                Many
Always             Some
Usually            Seldom
Never               Sometimes
Few                 Generally and last Overall.
The above mention words support instruction for the generalization.
In the next session we will discuss about online tutor and You can visit our website if you need help with algebra.

Mathematics in daily life

In our daily routine life mathematics play an important role to fulfill our most of the task that can’t be possible without the help of mathematics. Mathematics provides lots of concept, rules, methods and properties to accomplish the task which is related to the maths. People have been using the mathematical principal and tool form thousands of years, across several countries and continents. In our daily routine life, mathematics work as a body part to solve the problem by providing solving equations with fractions and other problems. Mathematics is a universal concept, which did not invent. Mathematics in daily life is discovered by the human being across the world and is an important part of tamilnadu education board.
There are several applications of mathematics in daily life that belongs to our daily routine activities. Suppose a man went to the market to buy something. He had $ 50 in his pocket. He bought many things for his house. Now the question arises that how he calculate, “how much money he spends?” and “how much he saves?” the solution of these problem are provided by the mathematics. In mathematics various types of operation are defined to solve the calculative problem in terms of money or more things, like addition, subtraction, multiplication division and so on. The importance of mathematics is not limited to the calculative part, they are widely used in various filed like several field of science, in the field of space research or many more fields that are related to the human being.
Suppose a man wants to paint their house. The cost of paint the house will be $ 3 per m². At that time there are various formula provided by the mathematics to calculate the geographical surface of the earth. These formulas are very helpful in estimating the cost of painting the house or any type of maintenance work.  According to my view the importance of Mathematics in daily life can’t be explain in words because it is concept which are used by everybody in each and every moment of life.
In the next session we are going to discuss about how to Make generalizations
and You can visit our website for getting information about math word problem solver.

Steps in problem solving

Previously we have discussed about verifying trigonometric identities worksheet and In today's session we are going to discuss about Steps in problem solving which is the most important part of secondary school education andhra pradesh, The problems that looks very complex initially are not solve directly so there are basically some Steps in problem solving that are use in solve math problems as follows:
Step no (1): Problem understanding – In this step first states the problem in your own words then find the main problem or thing you want to solve.
Then find the all unknown variable into the given problem and check the other information you need to find the solution for main problem.
Step no (2): After writing the problem into own understanding way make a plan to solve the problem – There are some steps or strategies that helps in making a plan:
First of all check the pattern of the problem then research for the other problems that are solved before having the same pattern .After getting the all results then make the tables and diagram according to the given problem and at last make the suitable expression for the problem that have the same pattern as before solved problems
Step no (3) : act according to the plan – After making a useful plan implement according to the plan means perform the necessary actions and computations that are helping us in solving problem .when getting the answer check them that these are according to the expected answer or not and if these are not according to them then apply other plan for problem solving .Maintain the record for each and every calculations .
Step no (4) : Back track :Check the Result by putting in the original problem and find another method to cross check the answer and also find the other related problem that are in more general form by solve with the existing technique or method .
In the next session we are going to discuss about Mathematics in daily life and You can visit our website for getting information about online math help.

equally likely events

Hello students,Previously we have discussed about inverse function worksheet and In today's session we are going to discuss about equally likely events which is a part of board of intermediate education andhra pradesh, In the mathematics we deals with the probability and their events such as exhaustive, dependent, independent, mutually exclusive, favorable and many more. Equally likely events are one of them. Let’s talk about the equally likely events definition : - In some experiments we know the results in advance but actually do not know the exact result, this type of results are called the random experiments and the result of random experiments are called equally likely events if the different outcomes have the same chance of occurrence.
For example when a die is thrown, each of the faces bearing one, two, three, four, five or six dots is equally like to appear.
Another example when we toss a coin then we have a chance to get either a Head or Tail.
Means it includes all those experiments in which we know the all results but we do not know the actual or exact results.
Let’s take examples -
Which of the following experiments have equally likely outcomes or events.
I) A driver attempts to start a car. The car start or does not start.
II) A players attempts to shot a basketball. she/he shoots or misses the shot.
III) A trial is made to answer a true false question. The answer is right or wrong.
IV) A baby is born. It is a boy or girl
Solutions : - (I) A driver attempts to start a car. The car starts or does not start, is not equally like events.
(II) A players attempts to shot a basketball. she/he shoots or misses the shot are not equally like events.
(III) A trial is made to answer a true false question. The answer is right or wrong is an equally like to occur.
(IV) A baby is born. It is a boy or girl is an equally like occur event.


In the next session we are going to discuss Grade VI, Steps in problem solving and You can visit our website for getting information about free math tutor.

Mathematical Reasoning

Previously we have discussed about difference between rational and irrational numbers and In today's session we are going to discuss about Mathematical Reasoning which is a part of ap secondary education board, Mathematical reasoning explained by solving the problem without knowing that what is to be done but when you know how to solve the problem then it is not consider as mathematical reasoning .For the question about what is mathematical reasoning the answer is that collection of the problems that are not in routine life and they are not solved by using any normal procedure and these problems are solved by making own strategies and by making own methods , also these are not based on the single strategy but based on the variety of strategies are known as the mathematical
There are some mathematical reasoning examples to understand the way of solving the problems of mathematical reasoning: Example: If Jon have 23 chocolates and he put equal number of chocolates in two bags and after putting seven chocolates are left then how many chocolates he put into each bag? The problems will need only little bit of attention to solve are considered as mathematical reasoning problems.
These types of problems are helping the students to make their mathematical concept strong as well as they helps the student to save their extra time that is spend in problem solving as for example If we want to multiple the number 36 * 18 then it will solved in more easy way as add 4 to 36 that is equal to 40 (36 + 4) and add 2 in 18 to make it 20 as (18 + 2) and multiply them that is much easier then multiply 36 * 18 and answer for multiplication 40 * 20 = 800 and subtract 4 and 2 that is totally 6 from 800 that is 794 that is the actual answer for multiplication of 36 * 18 .
In the next session we are going to discuss Grade VI, equally likely events and You can visit our website for getting information about free online tutor.

Informal and mathematical language

Hello students, in daily to daily life we use language to telling something to anyone not only we use but everyone use the language for the communication. The language may be anyone like English, Hindi, Latin and many more. But have you ever think about the language of Maths.  Here we are going to discuss the language of maths especially for the informal and mathematical language. In mathematics we use so many types of methods, theorems, expressions, symbols, proofs and many things, the all are comes in mathematical language. It is true that mathematics language is not used for the communication but without this we can nothing understand in math. Like algebra which is totally written in symbolic form.
We assumes math as a language and generally mathematical language is used for the better understanding, to represents the mathematical theorems more clearly, give their reason very logically so that everyone can easily understand. Mathematical language have own grammar, syntax, symbols and conventions. Like we use x for expressing theorems. The vocabulary words for the logic are ‘and’, ‘or’, ‘not’, ‘if…then’, ‘for all’, and ‘if and only if’. Symbols for operation are +, -, *, /, ∏, ∟, ∞, √, ∑, and ⌠ many more. Mathematical language is only used by the mathematicians for the communicating mathematical thoughts among themselves. (know more about cbse books for class 11, here)
Mathematical language also gives precise information for English like statements like we write a is equal to b in English language but the same statement in mathematical form will be a = b. The informal language in math is only used for understanding the concepts and proofs. Generally this language is not written; usually it is used for spoken and used according to the situations or conditions. In the next session we will discuss about Mathematical Reasoning. 

dependent

Probability can be considered as a branch of mathematics that deals with the calculation of likelihood of a given event’s occurrence. The occurrence of an event can be described in terms of number between the 1 and o. In the terms of probability, an event with a probability of 1 can be describe as certain or in the same aspect the probability of .5 can be specify as a half odd or half even. In the probability, an event is word which can be defined as a particular work which is performed in continues time period. When an event is performed in a particular time period then to estimate the outcome of that event, we use the concept of probability.
In the simple form we can say that when the number of occurring events is divide by the total number of events plus the number of failure of occurrence are known as probability. In the probability, some of the cases occur which has the two events. It means that in the probability some time two events are performed together at a time. On the basis of probability we can categorized the events in two ways, which are given below:
A)      Dependent event
B)      Independent event
Dependent events = Dependents are those events in which outcome of the one event affects the outcome of another event. It means to say that the output of the one event depends on the output of another event.
Independent events: independents events are those events which are independent to each other. It means that the outcome of one event not affect the outcome of another event. (know more about cbse sample papers for class 10, here)

Example: Suppose there is pack of playing card. If in case we pick card of king of heart. In the next time if we pick the card then it is obvious that card is not same to the king of heart. So, we can say that here both events are dependent to each other because in a Dependent Events Probability of the pack of card, there is only one king of heart exists.  In the next session we will discuss about Informal and mathematical language. 

Tools to solve problems

In mathematics, we know that various types of tools are provided to solve the problem that is related to calculation. Problem solving is the logical process which includes the process of finding the problem and estimate there solution. In the process of solving problem, mathematics provides lots of tools like addition, subtraction, multiplication, division, various types of concept like equation and various types of formulas and theorems. Here we are going to discussing about the most popular Problem Solving Model that are used to solving problem.
Addition: addition is the most basic tool of the mathematics which is used to perform the sum of the different objects like total money in the account, total amount of bill etc.
Example: 4 + 3 = 7
Subtraction: this operation is also a most basic tool to perform the difference between two given objects like how money was left after spending in the market and so on.
Example 15 – 5 = 10
Multiplication and division: these are the most popular that helps in to overcome form the problem of repetitive calculation.
The above are the most basic tools that are used in our daily routine life without applying any concept or rule. But in mathematics, sometime we need to solve to solve those types of problem, where we need to find the value of the unknown variable. On the basis of unknown variable the solution of the problem depends. To solve that kind of problem we required the concept of mathematics that is known as algebra. Algebra is the mathematical concept, which is used to change the problem into equation then by finding the value of variable to solve the problem. (know more about cbse sample paper for class x, here)
Example: a + 5 = 9
In the above we can say that there is an example of equation, where we need to fill the value of a by the appropriate number which satisfy the given equation true. In the various field of science mathematical Tools To Solve Problems, are most widely. In the next session we will discuss about dependent. 

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. 

Selecting a sample

In the previous post we have discussed about Sampling errors and In today's session we are going to discuss about Selecting a sample.
Selecting a sample:
In this session, we will talk about selecting a sample from a group of samples for grade VI.
In terms of probability, sampling is a method that aids in random selection process.
The important condition is that all the events to be chosen must have same probability.
For example, the random numbers chosen by a computer program is a random selection process as all the numbers can be chosen with equal probability.
Sample size: sample size is the total sum of sizes of all its cases.
Before we continue, let us understand some basic notations,
N=total number of cases in the sampling space.
n=number of cases in a given sample
f=sampling fraction=n/N
Simple random sampling:
We have to select n units from N.
N is the total cases in sampling space.
All the n must have the equal probability to be chosen.
nCN=total number of subsets of n from N.
Let us make this concept clearer through an example.
Let us take an example that we have to do a survey of a company by selecting its past clients. We want 100 clients to be a part of the survey.
Company provides a list of 1000 employees whose records are in the database of the company.
Sampling fraction=n/N=100/1000=0.10
Hence sampling fraction is 10%.
We have several ways to select the 100 clients. An easy way is to put all the 1000 clients in a group, subdivide the group and randomly select any subgroup. This is a mechanical way to select but it is not as efficient as the quality of samples would depend on how we have subdivided the group and how randomly we choose the subgroups. (know more about  Sampling, here)
The computerized method is more efficient as compared to the mechanical method.
Principally, our main motive is to understand the selection of sample out of many. To know more about cbse syllabus.

The main point here to keep in mind is that the samples must have equal probability to be chosen.
If the selecting probability depends on the previous selection, then it is said to be conditional probability.
In the next topic, we are going to discuss Sampling errors.

Sampling errors

In sampling errors we take a number of samples of the given mode. The samples are the models on which an analyst is working to find the errors from the number of terms which are under examination. We use the numbers of samples and then find the mean to reduce the sampling errors of the data model. In this way we define sampling errors.
For example, population of the state (increasing or decreasing); now if we want the mean height of 5th standard youngsters then we measure all the heights of sample of 5th graders in the state.
The best parameter to estimate the population is sample mean. But, there is difference between the mean sample or observed sample and the true population mean. So that, the sampling method is good or bad, if the rate of sampling is bad then likely should be some errors occur in the sample static.

The sampling errors are not easy to reduce. For example, any state wants to contact people to know how many people are homeless, the number of senior citizens, etc. The state government wants to find the parameter information but this is not easy. Then there is an error due to imperfect data collection. To reduce the sampling errors we take a number of samples of the model and then find the mean value of these samples. There are some other errors like non sampling, standard error. (know more about icse syllabus 2013, here)

The non sampling error is caused by human error by which a statistical analysis is done. These errors are not limited and not eliminated. Standard error helps us to measure the sample accuracy of the sample model. The representative sample is an unbiased indication of the data model. This is the sampling errors for grade VI. In the next session we will discuss about Selecting a sample.

Estimation of Solutions in Grade VI

In this session we are going to discuss Estimation of Solutions. Before we proceed for any project we need to find the estimated budget for the project to be attained. This is done by rounding the values to nearest tens, hundreds or thousands.  Suppose we go to buy some fruits and other purchase items. We make a rough budget of the articles to be purchased and take Rs 200 in my purse. This is called estimating solutions. Now when we buy the fruits, the seller tells the following costs:  Apples of Rs 84.00, Bananas of Rs 35 and grapes of Rs 18.
  The shopkeeper gives us the bill of Rs 84.00
                                                          Rs 35.00
                                                    +   Rs 18.00
                                                        _____________
                                                             137.00
We simply round off the figure to nearest tens and pay Rs 140 to him. Another way to make the payment will be to round off the above figure in nearest hundred and pay Rs 150.00 estimation of solutions is done in order to make any project a success, may it be a window shopping, budgeting for the parties big or small about how many expected guest will be attending the party or even organizing big projects.
In Grade VI We follow the following methods for estimating solutions:
To round off the value to nearest tens, we see the ones place digit, if it is less than 5, we make ones place 0. If it is greater than 5 we add 1 to tens place and make ones place 0. E.g.:
      47 round off to tens becomes 50
     32  round off  to tens becomes 30
    65 round off to tens becomes 70
In the next topic we are going to discuss Percentages