range

It is defined as it contains all data and it is also length of the smallest intervals. It is based on two observations that are poor and weak and it is calculated by subtracting the lowest to the highest sample which includes statistical dispersion. Range, is the simplest method of measuring the variability and it is used only for highest score minus the lowest score. Range is equal to or greater than standard deviation which comes under cbse syllabus for class 10.
In range the difference between highest and lowest scores is known as crude range. The smallest and greatest observation is called observed range. For example range can be present in entire row or column and multiple row, column.
Range Of Probability (introduction to probability worksheet), is defined as an event is impossible when its probability is zero and when event is there its probability is one. The value of probability is Pr (impossible event) = 0
The probability of event A is denoted by P(A) and it is range from 0 to 1.
The range of distribution and value of function is equal to zero and it is a random variable which is used to differentiate between maximum value and minimum value which is equal to zero.
The three kinds of averages are mean, median and mode. The median is the middle value in the numbers. For example find the mean, median mode and range of the following values:
3,5,8,6
Answer: (3+ 5+8+6)/ 4 = 22/4 = 5.5
The mean is 3.5
median is 8+6= 14/2= 7
mode= none
range = 5
The largest value is 8, the smallest is 3 and their difference is 5.
so, the range is 5.
The output value of a function is called range of a function.
Domain ->function->Range.
In the next session we will discuss about Predictions from data and You can visit our website for getting information about physics tutor .

mode

Hello students, Previously we have discussed about what is cartesian product and In today's session we are going to discuss about mode which comes under cbse books, Mathematics covers many topics, statistics is one of them. In mathematics statistics plays a very important role to summarize the data by the various types. Mean, median and mode are the three measures of central tendency. But here we have to discuss the mode.

Mode in an ungrouped data, the most occurring term gives the data and if some terms have frequencies more than 1, then the term having the largest frequency is the mode.

 In a grouped data we have

Mode = L1+ (f-f1) / (2f – f1 - f2) * (L2 - L1), where L is the lower limit of model class, f is the frequency of model class and f1 and f2 are the respective frequencies of the preceding and succeeding classes of the model class.

Let’s take some example of mode:

Example 1: What is the mode of 5, 7, 9, 12, 10, 15, 7, 8, 7, 25?

Solution: Since 7 occurs most often, so mode = 7

Example 2: Find the mode of the following frequency distribution

Term               25        35        45        55        65

Frequency      4          9          16        13        6

Solution: Since 45 occurs most often, so mode = 45

Example 3: Find the mode from the data given below

Marks obtained          0-5      5-10   10-15             15-20             20-25             25-30

            Number of students  18        20          25                    30                    16                    14

Solution: The maximum frequency is 30. So mode class is 15-20

 L1 =15 L2 =20, f = 30, f1 = 25 and f2 = 16.

Mode = L1+ (f-f1) / (2f – f1 - f2) * (L2 - L1) = = 15+ (30 - 25) / (60 – 25 - 16) * (20 - 15) = 16.3

So exact values is 16.3

In the next session we will discuss about range and You can visit our website for getting information about calculus tutor.

standard deviation

standard deviation is defined for the given set of data in which data is spread or it is also called as data is distributed in the data set .It is defined for the distributed data set for defining the diversity of the set of data .standard deviation is the part of statistics in which we can understand that how data is deviated from its mean value or sometimes it will be denoted as the average value. You can also find the standard deviation for the given probability distribution.
According to definition of standard deviation which is given in cbse text books, it will used for finding the deviation of the data in the data set from the standard average value or mean value for that set of data .It will defined the dispersion of the data in form of variance that is sometimes called as the populated standard deviation .
sigma symbol (s) is used for specify the standard deviation and it is known as known as the standard deviation and there is one more way for defining the standard deviation that is square root of variance and it will be define as the (s 2) .
We can understand the standard deviation by specific expression that helps to understand the standard deviation very effectively:
If there in the data set a random variable (a) , for that mean value is define as m and it is denoted as in form of average or mean E | a | = m .
Where E denotes the average value of a .
so the formula for standard deviation is that is based on the mean value E is defined as
( s ) = √ E (a - m ) 2 .
Standard deviation is also expressed by formula of variance that is defined as square root of the variance and In the next session we will discuss about mode and you can also take chemistry tutoring from our website.

variance

Previously we have discussed about verifying trigonometric identities and In today's session we are going to discuss about variance which comes under board of intermediate education andhra pradesh syllabus, In statistics (statistics tutor), Variance is used for measurement between the data of a data set and its mean value. Sometimes it is defined as the moment of the distribution. It is also used in the probability distribution for distinguish it and it is expressed as the parameter that describe the probability distribution for every situation.
Variance is defined as the square of the standard deviation that is denoted by the symbol sigma (s) and variance is shown as (s)².
Variance is the measure of the farness of the data in the given data set from its mean value .so variance is based on the mean value of the data set and also defined in the expression as for a given data set standard deviation is define the distribution .
In a given data set for any random variable ‘x’, mean value is define as ‘m’ and it is denoted as E |x| = mand here ‘E’ denotes the average value of random variable ‘x’.
Here formula for variance is defined as (s)²= E (x - m)².
So, formula for standard deviation is square root of variance (s) = √ E (x - m )².
Here in above expression (s)defines the Standard deviation by the square root of the variance of random variable ‘x’ or if we have the value of standard deviation and we want to calculate the variance that is define as the square of the standard deviation as s²_.
If there are a given data set as there defines the variable as:
Variable: a₁ a₂ a₃ a₄ a₅ a₆
Value: 3 4 4 5 6 8
Then find the variance?
So, mean m = å ⁶_{i= 1}a_i / n = 30 / 6 = 5,
Variance as s²= å (x - m )²/ n.
By using formula we calculate the value of variance s² = 2.67.
In the next session we will discuss about standard deviation.

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.