Representations of data

Previously we have discussed about differential equations formulas and In today's session we are going to discuss about Representations of data which comes under cbse 12th syllabus, It means presenting the data in form of graphs, diagram, maps or chart besides the tabular form. In this type of representation of data, visualization is provided in forms of graphs and charts. There are some basic needs for the representation of data:

. Sometimes it is difficult to understand the descriptive data as it is not easy to draw the results.

. Easily draw the visual impression of the data

. Makes comparison easy

. Characteristics can be represented in a simplified way

. Some kind of patterns are made easy as population growth or distribution and density or age – sex composition , etc .

There are some rules that must be followed before designing the graphs,charts or diagrams

1. first of all a suitable graphical method is selected .

    
        Then after selecting the graphical method a scale is selected that is suitable to the data
        On the basis of Title,Index and Direction design must be followed.

There are several diagrams that are used for representing the data that can be categorized

in the following types :

. Some examples like Line graph, polygraph, histogram, pyramid and bar diagram etc. examples of One dimensional diagram.

. There are rectangular diagram and pie diagram examples of Two dimensional diagrams.

. Diagram as cube and spherical diagram examples of Three dimensional diagram.

Representation of data are done in many ways that are flow chart,line graphs,bar diagrams,pie diagrams , wind rose and star diagram etc .These are some examples of popular diagrams that are mostly used in representing the data.

Rainfall,Population growth,Temperature are examples of series of time, For representing the series of time e and series like birth rates and death rates etc are represented by drawing the Line graphs .

Two or more variables on a same diagram is represented by a Polygraph that is also a line graph ,that are shown by different line as example for showing the growth rate of different crops and These diagrams are also used for show the birth and death rates .

So there are different types of graphs and diagrams that are used for show the different type of representing data .In the next session we are going to discuss Sampling techniques.

In the next session we will discuss about online math tutor and You can visit our website for online tutoring for free.

Simple random sampling

Previously we have discussed about application of differential calculus  and In today's session we are going to discuss about Simple random sampling  which is fronm cbse previous year question papers class 12.

Some points to understand Simple random sampling:-

• The set of total observations that can be calculated in the experiment is called population.

• Sample can be defined as a set of observations drawn from the population.

• Statistics is related to sample which is a measurable characteristic of the samples like standard deviation.

• Sampling method is the procedure of selecting sample elements from the population that were made.

• Random number is a matter of chance having no relationship with the occurrence of other number.

• Simple random sampling related to sample method having following properties

1.  In Simple random sampling population can have n number of objects.

2.  Simple random sample that is chosen can also have N number of objects, here n ≠ N.

3.  All possible samples of N objects have same probability to occur.

Samples chosen with the help of simple random sampling are refers to the population this is the measure profit of choosing simple random sampling, it means that the conclusion will be valid.

There are several methods to get simple random sample for example lottery ticket is the example of simple random sampling in which a unique number is assigned to each member of N population. These numbers are placed in a bowl and then thoroughly mixed then a blind folded researcher selects n numbers from the bowl. The selected n numbers are called the samples taken from the population.

There are two other terms too; sampling with replacements and sampling without replacements.

In the above example of lottery ticket when a number is picked from the bowl; if it putted aside by the blind folded researcher then the probability of occurrence of this number is only once and if this number is putted back in the bowl then the number can be selected further too.

This is sampling with or without replacements.

If a population element has the chance to be selected more than one time then it is called sampling with replacements.

If a population element only can be selected one time then this sampling is called sampling without replacements.

In the next session we will discuss about Representations of data and You can visit our website for getting help from online tutors.

Sampling techniques

Sampling techniques:

Previously we have discussed about definite integral examples and In today's session we are going to discuss about Sampling techniques which comes under cbse books for class 11,  Sampling is required when information is being processed for the transmission from one place to another place. The information is divided into samples and then the information is transmitted. It’s easy to remove noise or other factors from the samples in spite of the whole information directly.

If there are a lot items in a population set then the analysis process would be too costly and time consuming for that population. Like if the customer base id too large then  it would be too costly to determine the satisfaction level of each customer. The sampling process defines the same thing in short.

Sampling is the risk that it's not representative of the population from which it is made . Basically sampling  is the main step in analyzing any analytical process after that its not actually possible to remove errors.

The main processes for the sampling techniques are

·         Determine objectives and population then

·         Determining the sample size that would be created

·         Selection of the sampling method

·         Then the last step is to analyze the sampling errors regarding the projection or other

Sample size can be defined as

                                Sample size = reliability factor/Precision

There are several advantages of the sampling

·         The actual air sample can be collected without any breakthrough

·         No degradation problem of trapping material

·         Moisture has no effect on sampling

·         Duplicate analysis of the sample can be performed.

In mathematics it can be defined as to take a function f and recreate it with the help of only certain values.

Sampling techniques can be understood in probability or non probability preference. In probability method each member of the population has a non zero probability of being selected. This includes random, stratified and systemic sampling. In non probability method members are selected from the population in a random manner. It includes convent sampling, quota sampling, snowball sampling etc., techniques of sampling or methods for sampling are described below.

In Simple random sampling each member has an equal chance for being selected. It’s the purest method of sampling.

In systemic sampling every nth record is selected from the population.

Stratified sampling reduces the number of errors and used when one or more stratums have a low incidence relative to other.

Convenience sampling is used when inexpensive approximation of truth is required.

Judgment sampling is an extension of convenience sampling as the name indicates samples are made on the judgment basis.

Snowball sampling is used when desired sample characteristic is rare. It’s a difficult method and cost prohibitive too.

In the next session we are going to discuss Simple random sampling and You can visit our website for getting math help for free.

Range in Grade VIII

Range in Class VIII.
Hello children! Previously we have discussed about column multiplication. Now we will study about the topic Range which comes under gujarat education board.
In statistics, range means to find the difference between the largest and the lowest frequency of the given data.
So, for finding range we first need to arrange the given data in ascending or descending order in order to get the accurate information.
The formula for range is:
Range = highest value - lowest value.
It actually gives the length of the smallest interval which contains all the information of the given data. It gives the variation of the spread of the data.
 Let us understand it more clearly through some examples.
The ages of the ten teachers in the school, they are 35, 28, 36, 26, 45, 30, 29, 35, 26, and 30. Now for finding range of age of teachers in a school, we first arrange the given data in ascending order. We get: 26, 26, 28, 29, 30, 30, 35, 35, 36, and 45.
We observe that the teacher with least age is 26 and the teacher with largest age is 45.
So Range = Maximum age - minimum age
                  = 45 - 26 = 19 years.
Which means that range of age of teachers in the school is 19 years.

In the next topic we are going to discuss Sampling techniques and You can visit our website for getting information about physics problem solver.

Mode in Grade VIII

Previously we have discussed about calculus problem solver and In today's session we are going to discuss about Mode which comes under gujarat board textbooks online, Its mathematical term that comes in statistics. It can be defined as particular value that occurs most number of the times in a list. In simple words mode is a most frequent value in a data set or most common value in a group. Mode or statistical mode is same thing. Let us understand mode with an easy example:-

We have a list of numbers :- 3, 5, 7, 2, 8, 9, 2, 4, 2

The first step to find mode is to arrange the list in ascending order than we will get.

2, 2, 2, 3, 4, 5, 7, 8, 9

The next step to find out particular number that has occurred most number of times.

Here the particular number is 2.

So the mode will be 2.

Mode is used to collect information about non-deterministic numbers, also called random numbers in a single quantity.

Now let us discuss how calculate mode when list is fractional with an example:-

Now we are talking a example of fraction list :- 3.2, 3.7, 4.1, 3.2, 5.6, 2.4, 3.2, 2.4

First of all arrange the list in an ascending order:- 2.4, 2.4, 3.2, 3.2, 3.2, 3.7, 4.1, 5.6

3.2 is a number that has occurred most number of times in the above list.

So the mode is 3.2

Advantage of mode

-provide support to mean,median to solve statistical problems.

-to identify wether an event has occurred more than one time or not.

-used for counting the number of times

Note:- A mode will not exist if there is no repetition of any number in a list. A list contain may be more than one mode if two numbers sharing same occurrence of time

The above described mode information will be truly helpful for grade VIII students.

In the next topic we are going to discuss Range in Grade VIII and You can visit our website for getting information about free online math help.

Math Blog on Median

In reference with data handling to be studied in Grade VIII  of CBSE math Syllabus today we are going to learn about median.
We have already learned about math questions on mean, which help us to find the average of the given collection of data.
As you have studied earlier that the raw data collected is to be arranged in the ascending or descending order in order to retrieve some information from it.
In this Blog we will discuss about median in math. Median is the mid value of the collected data. Suppose we have collected the age of 5 teachers in the school.
They are 35, 24, 45, 22 and 36.(Know more about Median in broad manner here,)
 To find the median, we will first arrange this data in ascending order:
We get:
  22, 24, 35, 36 45
We observe that 35 is the median.
Now we look at the data when the number of data is even, in such cases we select middle two terms of the data.
Then we find the average of these two values.
To sum up, we produce the formula for the same:
To find the median, the following steps are to be followed:
1. Arrange the data in ascending order; let the number of entries be n
2. Then we will find if the number of entries is even or odd
3 If the number of entries is odd then
    Median = (n+1) / 2 th term
And if the number of terms is even then
    Median = [ (n/2) th term + (n/2) +1th term ] /2
 So children we first check the number of entries in the given set of raw data and then accordingly proceed to find the median.

In the next blog we are going to discuss Mode in Grade VIII and if anyone want to know about How to calculate Median in grade 9th then they can refer to Internet and text books for understanding it more precisely and also know about some interesting questions like is square root of 7 a rational number.