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How to Calculate p Value

In the previous post we have discussed about statistical graphs and In today's session we are going to discuss about How to Calculate p Value. In mathematics, we will see How to Calculate p Value. First we will see small introduction about p value. Statistically p – value is used for evaluating the Probability or for testing hypotheses. In every statistical study you would calculate two possible types of hypothesis and they are: the null hypothesis and the alternate hypothesis. The null hypothesis made on any assumption is actually the nil difference among the two calculations that have been taken in our probability study. The substitute hypothesis says that the considered calculation is significantly different from the one such that the hypothetical study is being used. The p-value is that solved significance of the test. Smaller the value of p or variation in p – value, more chances of avoiding the null value are there. But do you know how to calculate p value? First we will see the table of P - value through we can easily solve the problem. The table is shown below:

P – write in %

01 (88) (2712)

----

02 (18) (565)

----

03 (4) (21)

----

For understanding this, make use of the k - distribution table to solve the degrees of freedom, matching the value of ‘k’ that you compute. In distribution table, the degree of freedom is obtained on the left-most column. Further solve the k-value on right row of the distribution. Let’s see at the top most column of the chart; there are two subscripts for the k-value. Here we will see one taken for the degrees of freedom, or can be represented as 'n' and the second subscript denoted the quantile for k - value. Subtract the value of quantile from 1. Repeat the same pattern for other columns also and record values of both columns and values of their identical quantile values.

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statistical graphs

In the previous post we have discussed about How to Find Variance and In today's session we are going to discuss about statistical graphs. In mathematics, there are various solutions are provided to deals with real world problem in an easier manner. Statistical Graphs are one of them which are popularly used for representing the data values in the form of 2 – D diagrams. Statistical graph is not a kind of graph; it’s just a picture that deals with representing the statistical data in the form of picture. Mathematics provides lots of different ways that helps the user for efficient representation of data. This kind of statistical graph helps the user for representing number data or values in an easier manner with easier intelligibility and greatly influence the observer’s mind. The basic reason behind using concept of statistical graph is that for representing vast amount of data in an easier manner.

If we discuss about different category of statistical Graphs then we can say that they can be divided into some groups that are given as Bar graphs, Box plot, Pie chart, Stem & Leaf plot and histogram and so on. These are most popular ways that helps the statistician for successfully plotting a numerical data in the form of picture. In the below we give you little bit detail about these statistical Graphs.

Bar Graphs are used for representing Single sided data with their labels in the form of bars where each bars having a space between each other. Pie chart is a circular representation of numerical data that are popularly used in the govt. survey and in news channel media. Stem and leaf plots are another kind of representing quantitative data in the form of distribution shape of display. Histogram is another graphical representation of data that deals with dual sided of data values. It also shows data values in the form of bars but they do not have any space between bars.

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How to Find Variance

In the previous post we have discussed about How to Make a Bar Graph and In today's session we are going to discuss about How to Find Variance. In statistics, if you don’t know how to find variance then you should need to know about variance first. Variance is used to check how far a set of numbers are spread out. It calculates the actual value that how far the numbers lie on the expect values (which is called mean). For this we used systematic approach in probability distribution. It is basically recognize through Greek symbol sigma σ. According to statistics variance is the average of the squared differences of mean. To calculate the variance we have to follow some rules:- (know more about How to Find Variance, here)

· First we calculate the mean for given numbers.

· After that we subtract the mean and square the result for each number.

· And in last we calculate the average of those squared differences.

To understand that more deeply we take an example where we have just measured the heights of plants in millimeters. The heights of plants are 340, 500, 270, 250, 180. So the mean of these heights:

Mean = ( 340 + 500 + 270 + 250 + 180)/ 5 = 1540/ 5 = 308.

Therefore the mean height is 308. Now we can easily calculate the variance, for that we take each difference and square them. So the variance:

Variance= [ (340 -308)2 + (500 - 208)2 + (270 – 308)2 + (250 – 308)2 + (180 – 308)2 ] / 5,

= [(322 + 2922 + (-38)2 + (-58)2 + (-128)2 )]/ 5,

= [(1024 + 85264 + 1444 + 3364 + 16384)] / 5 = 107480 / 5 = 21496.

So, the variance after calculating mean is 21946. So we can easily write this

variance σ2 = 21496

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How to Make a Bar Graph

In the previous post we have discussed about how to do standard deviation and In today's session we are going to discuss about How to Make a Bar Graph. In mathematics, we will go through different graph such as histogram graph, double bar graph. Here we will talk about bar graph. Generally bar graph are used to distinguish the different information, situations by using bars in the graph. Sometimes it is also called as bar charts. Here we will talk about How to Make a Bar Graph. Some steps to be followed while ploting bar graph are mention below:

Step 1: To construct a bar graph first draw the axis in the graph. As we know that two axis are present in a graph that is named as x – axis and y - axis.

Step 2: Then after chooose an appropriate scale and construct equal intervals.

Step 3: Now with the help of information of given data items label the horizontal axis.

Step 4: According to data items plot the bars.

Step 5: At last named the title of a graph.

Now we have to apply these steps in example.

For example: Using the table mention below plot a bar chart.

(know more about Bar Graph, here)

Scores on the practice Test and the Test

Student Practice Test Test

John

Peter

Jeff

Mariya

Solution:

First of all select or named the title from above mention table. As we see in the table that the title of above table is 'Score on practice Test and Test'.

After that choose vertical bars.

Here scores are different from one another mostly by 5, 10, 15 or 20. It means select a scale of 10.

If we find any variation between scores then scores are like 1, 2, 3, 4, or 5, then it is better to select a scale of 1 or 2.

After marking names on x – axis and scores on y – axis. Suppose if we decide to plot horizontal bars then put names on y – axis and scores on x – axis.

At last plot the bars. Double bar graph is shown below:

This is how we plot double bar graph using above steps.

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how to do standard deviation

In the previous post we have discussed about Range in Math and In today's session we are going to discuss about how to do standard deviation. If we want to extent the deviation of data then standard deviation can be used to show the deviation of different data from its mean. It is equals to square root of variance. Basically standard deviation shows that how many data items are pointed top and below the mean. Let’s show that how to do standard deviation. The formula is also given to find the standard deviation from its mean value:

S = √∑(x – x’2)

N – 1

Here‘s’ denotes the standard deviation, ‘X’ denotes each value in the sample, X’ denotes the mean of the values, ‘N’ denotes the number of the values (the simple size). Now we will see how to do standard deviation. Some steps are givne to solve the standard deviation. (know more about standard deviation, here)

Step 1: To find the standard deviation first of all we have to find the mean of the given data’s.

Step 2: After doing so, we have to subtract the mean value from each value present in data set.

Step 3: Then we have to calculate the expected mean of values which we obtained in step 2.

Step 4: After then solve the square root of value we obtained from step 3, the value which we get is the standard deviation. Some identites are also defined for the standard deviation which are: For a constant variable ‘c’ the random variable ‘S’ and ‘T’ can be written as: Stdev (c) = 0,

Stdev (S + c) = stdev (S), and Stdev (cS) = | c | stdev (S), The word ‘std’ denotes the standard deviation. Then the relation between the standard deviation and covariance can be writeen as: Stdev (S + T) = √ var (S) + var (T) +2 cov (S, T), Where var = stdev2 and cov stands for the variance and covariance respectively. Simple Linear Regression is a used to fit a given strainght line using the set of n points. cbse sample papers 12 is help us in the examination hall.

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Range in Math

In mathematics, function has two parts either x – coordinate or y – coordinates. The values of x – coordinates are known as the domain of the function and y – coordinate are known as range of the function. Function is a relation in which entire value of input is provides one value of output. It is basically written as f (b) where ‘b’ is the value you assign it. Suppose f (b) = b / 5 (f of ‘b’ is ‘b’ divided by 5") is a function, because for every value of ‘b’ you get another value ‘b / 5’. So if we put the value of ‘b’ as 5 then we get the value of function as 1: f (5) = 5 / 5 = 1,

Now we will see how to define Range in Math. In function, entire ‘y’ coordinate values are said to be range of a function. In the same way, entire possible ‘x’ coordinate value is known as domain of a function. Let we have some values (6, -9), (-1, 5), (6, -4), (-5, 2), then range of function is all the ‘y’ coordinate values. (know more about Range, here)

Domain = 6, -1, 6, -5.

Range is all ‘y’ coordinate values,

Range = -9, 5, -4, 2.

Let's see how to define range in math. To find the range of a function we have to follow some steps:

Step1: To find the range of a function first of all assume a function which has ‘x’ and ‘y’ coordinates.

Step2: Then we know that , range of a function is the entire ‘y’ coordinates values.

Step3: In a given function the values of ‘x’ and ‘y’ coordinate are present then we can easily find the range and domain of a function.

This is how we can find the range of a function. Equations of Motion is used to show the behavior of a system in terms of motion. To get more information about the equation of motion then prefer on-line tutor of icse syllabus 2013 and In the next session we will discuss about how to do standard deviation.

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Descriptive Statistics

In this blog we are going to discuss about the descriptive statistics .Descriptive study is used to define the relation between the data that is define in the data set for describe all the general trends. It is basically used to define all the features of the data .It helps in providing the samples and their measures that are based on the samples. Descriptive statistics are not only for defining the samples and

trends but also this is used to test the data and defining the errors that are associated with the result that are based on the data set. We can also define it by a simple example as if you want to go on a trip to meet with your friend and you have a quick estimation of time that is taken to go to your friend's home or sometime you give the time period of meeting to your friend. This type of estimation is based on the previous experience that defines through the estimation of the standard deviation or estimation of standard error. (know more about Descriptive statistics, here)

Descriptive studies are defined what is showed by the data and sometimes it is different from the inferential studies. Descriptive studies are used to define the quantitative description of the data that is defining it into the manageable format. it is used for managing the large amount of data in a way that anyone can understand it in a sensible manner. It is understand through the very simple example of the grade of the student as a single grade point average defines that overall performance of the student. Grade point average is defined as a single number that contains the several numbers of different subjects.

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Relative Standard Deviation

In this blog we are going to discuss about the topic of relative standard deviation. In statistics relative standard deviation is define as the absolute value of coefficient of variation. The basic use of relative standard deviation is on analytical chemistry. We can calculate the relative standard deviation by using the formula that is as follows: (know more about Relative standard deviation , here)

If there is a sample standard deviation s = √ 1 / N -1 ∑ ( xi – x') 2 where i is from 1 to N.

Then relative standard deviation is calculated as RSD = s / x' .

Where s = sample standard deviation and RSD = relative standard deviation.

X define the sample data and x' define the mean value for the sample data set.

N defines the size of the set.

When we used it in the analytical chemistry it defines to express precision. It present in the form of percentage as define by the formula (standard deviation of the data set) / (average of data set) * 100. there is difference between the normal standard deviation and relative standard deviation is that standard deviation is define how much data is spread in terms of mean but relative standard deviation defines as the absolute value of the coefficient of variation.

The RSD allows to make the easy comparison for different types of measurements for standard deviations.

We can take an example for defining it as measuring the concentration of two compounds p and q then the result is 0.5 (+/-) 0.4 ng / mL for compound p and 10 (+/-) 2 ng/mL for compound q. when we calculate the RSD that define their new values for compound p and q are 0.5 (+/-) 80% and 10 (+/-) 20% respectively, so we can see that the measurement for compound q is more precise. During the probability study sometime a question arises that what is an Independent Variable. According to the CBSE pattern, CBSE geography syllabus provides the basic guideline for geography subject for preparation of examination and In the next session we will discuss about Descriptive Statistics.

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Descriptive Statistics Definition

In the previous post we have discussed about Box Plots and In today's session we are going to discuss about Descriptive Statistics Definition. In the study of statistic, descriptive statistics definition can be expressed as a numerical summarization for collection of data. It means to say that descriptive statistic is used for representing the basic feature in a numerical form for a group of data. As the name specifies that the basic role of descriptive statistics in the mathematical statistic is to provide quantitative analysis of data. Normally in mathematics we generally deal with the inferential statistic. In the inferential statistics we generally deal with the data to get the result or conclusion from the dataset. In the same aspect, according to descriptive statistic definition, we can simply perform the description of dataset. In the other words we can say that the concepts of descriptive statistic are not based on the probability theory. (know more about Descriptive statistics, here)

Descriptive statistics definition represents the summarization of data values that can be obtained from various observation of any event. In the descriptive statistics the summarization of dataset can be represented in a visualize form by using different types of descriptive statistics. We can easily perform the descriptive analysis on the given dataset by using the concept, which is known as measure of central tendency.

In the central tendency we generally deal with the data set to find the central or most common value.

This process can be obtained by using different statistical concept like mean, median and mode.

Mean – Here we are going to discussing about the arithmetic mean, which is simply used for performing the sum of the measurements which is divided by the number of measurements.

Median – This concept helps in finding the value that is half the measurements in between left and half right.

Mode – In this concept we generally deals with those values that are occurring most.

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Box Plots

In mathematics we graphed our numerical data in many ways. By graphing the data we can easily understand the solution of the problem. For this we have so many types of graphs like bar charts, histogram and many more. Box plots are one of them. It is also known as a box and whisker diagram. Box plots in statistics are the appropriate way by which we can represent the group of numerical data in a graphical manner through their five number summaries.

Now the question arises is; what are the five number summaries, so the answer is:

1. Minimum

2. Maximum

3. Lower quartile

4. upper quartile

5. Median

All the above are the measures of distribution that gives the whole descriptions about the series. We can make box plots either horizontally or vertically. Box plots are useful to display the difference between populations. Box plots are useful to measure the shape, middle value and variability. Although box plots do not gives the detail descriptions like histogram and stem and leaf graph gives. Box plots are useful when we have large numbers of values in a given set.

To draw the box plot first we have to arranger the numbers in an order than we find the maximum, minimum and quartiles. The first value and last value will be the minimum and maximum respectively. To find maximum, minimum and quartiles we have formulas.

For first quartile that is lower quartile Q1 = (n + 1th) item / 4

For second quartile that is median Q1 = (n + 1th) item / 2

For third quartile that is upper quartile Q3 = 3(n + 1th) item / 4

By theses formulas we can easily find the all measures of distribution and construct the graph easily.

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How to find Median

In the previous post we have discussed about How to find Standard Deviation and today we are going to discuss about the topic median, as the name suggest median is the middle point of any data. Median is also a parameter to find measure of central tendency, as we well know that there are three measures of central tendency mean mode and median. All the three parameters are used for but for the same thing. but as we know there are different type of data available, so if data is skewed then we use median , if in the data we have terms very close to each other we will be using mode and if the data is continuous we will be using mean. For finding median of any data we need to remember the point given below,

· First thing we need to do is to arrange the data in ascending order

· check the number of terms in the data, if terms are odd then use the formula

Median = n+1/2

Here n is the number of terms

If number of terms are even then use the formula given below,

Median = ((n/2)th + (n/2)th +1)/2

By using these two formula we can find the median of any data , if we have a data like 2,3,,6,5,7,8 and we are asked to find the median of that data then we will be arranging this data to ascending order first, so after converting the data in ascending order the data will look like 2,3,5,6,7,8 , now we need to check the number of term, here number of term are 6 so we will be using the second formula , so on putting the value in second formula we will get

Median = (6/2th + 6/2th +1)/2

Median = 3rd + 4th/2

Median = 5+6/2

Median = 5.5

This is the required median for the data.

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How to find Standard Deviation

In the previous post we have discussed about Mean and In today's session we are going to discuss about Standard deviation which lies under the topic of statistics. Generally it is represented by the symbol (σ) which is pronounced as sigma. Standard deviation in mathematics can be defined as the deviation of data from mean or the average. Variance is the square of standard deviation. Now we will see the process of finding out standard deviation

The formula for standard deviation is given by

S = √∑(x – x’)2,

Where the ‘s’ represent the standard deviation. And ‘x’ represent the each and every value of the sample. And x’ represent the average of the value whereas the n represents the number of the value.

There are few steps which should be followed at the time of estimation of the standard deviation. The procedure is as under

First step is we must assume some data items for the valuation of standard deviation

Then our next step is to find the average of the data ( it can be calculated first by summing up and then dividing them with the number of terms.)

Then we will subtract the average from the original values

Then we will place them in the formula so that it will help us in computation of the standard deviation.

Suppose we are given with the data such as 10, 2 ,16 ,4 so to estimate the standard deviation we will follows these steps which we have already discussed

x1+ x2+ x3 + x4 …. + xN

= 10+ 2 + 16 + 4;

= 8

Here the average comes is 8

Now we will calculate x – x’ from the given data:

X1 – x’ = 10 – 8 = 2;

X2 – x’ = 2 – 8 = -6;

X3 – x’ = 16 – 8 = 8;

X4 – x’ = 4 – 8 = -4;

Now we will calculate ∑(X1 – x’)2;

∑(X1 – x’)2 = (X1 – x’)2 + (X2 – x’)2 +… (Xn – x’)2

= (2)2 + (-6)2 + (8)2 + (-4)2;

= 4 + 36 + 16+ 64 = 120;

Now substitute all the values in the formula:

S = √∑(x – x’)2,

= √120 / 4

= √30 = 5.47

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Mean

In the previous post we have discussed about free online tutoring and In today's session we are going to discuss about Mean, It is a statistical term in Mathematics. In other words, it is a term used in statistics. Now, what is Statistics? Statistics is also one of the branches of Mathematics in which we study data. It is concerned with collection, presentation, analysis & interpretation of data. Data, in turn, is a collection of numerical figures which give some information about a particular matter. We need data in the form of numbers, from different fields of life. A very simple & common example is about the lists of marks obtained by the students in a class in different subjects. We need this information to find out the highest, the lowest, and the most repeated marks & also to find out the percent of marks obtained by all the students to make the result. Thus, this is all dealt with in Statistics.

As stated in the beginning, mean is a statistical term. So, it is also related to some collection, presentation & interpretation of data. Mean, in statistical terms, is also called average or arithmetic mean. It can be defined as the average of all the observations or the data collected. In simple words, it can be defined as: Mean = sum of all the observations / number of observations.

For example : To find the mean marks obtained by 12 students of class VII , given marks as 20, 13, 15, 19, 13, 20, 18, 12, 10, 19, 11, 20. Here number of observations is 12.

The sum of observations is 20+13+15+19+13+20+14+11+10+19+11+15 = 180

So, mean = Sum of observations / Number of observations = 180/12= 15

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free online tutoring

We say that math help online, helps us to understand the different topics available on the internet related to the topics of math. We will understand the concept of geometry by free online tutoring. If we talk about the online tutoring, we start with the concept of line and the line segment. We say that the line is formed by joining the set of collinear points, such that it has no end points. So we represent the line by arrows at the end and the line has no fixed length. If we look at the line segment, we say that the line segment is the part of the line and has fixed end points.

On joining the line segments, we can form the closed figure and such closed figures are called the polygons. We say that the closed figure formed by joining 3 or more line segments is called polygons. We say that the polygons with three line segments are called a triangle. A triangle has three sides, three angles and three vertexes.

Similarly if the polygon is of four sides, then we say that it is a quadrilateral. Any 4 sided figures are called a quadrilateral, but we say that depending on the sides and the angles of the quadrilateral, we can give different names to the quadrilateral. So if all the four sides of the quadrilateral are equal and all the four angles of the quadrilateral are 90 degrees then we say it is a square. Similarly a quadrilateral with the pair of opposite sides equal is called rectangles. A kite has a pair of adjacent sides equal.

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math help

We can get math help online to understand the concepts of algebra word problems which is a part of cbse board. Algebra Word problems are the real life problems of Algebra which are solved by taking one or two variables. The equations are formed based on the statements given in the word problems and then we can solve these equations in order to get the solution to the given problems. Now we will see that how to form the algebraic equations for the given algebra word problems. We must recall that the operations addition, subtraction, multiplication and division can be performed on the algebraic equations in order to get the value of the variables. But forming equations is another concern and learning how to form the equations is must to get the solution to the given word problems in algebra.

Thus we must read the word problem thoroughly and then we will form the equations based on the statements in order to get the result for the equations so formed. Let us look at the following examples:

Example : If nine added to the thrice of the whole number gives 45, then what is the number.

Sol : Here we will first assume the number as x, which we need to calculate. Now as we say thrice a number, it means three times of a number, which is represented as 3x. So the equation will be formed as follows :

3x + 9 = 45

To get the value of x, we will first take the constant 9 to the right side of the equation, so we get :

3x = 45 – 9

Or 3x = 36

Or x = 36/ 3 = 12 Ans.

This is all about the math help and if anyone want to know about compound interest calculator then they can refer Internet and text books for understanding it more precisely and Read more maths topics of different grades such as algebra 2 help in the upcoming sessions here and In the next session we will discuss about free online tutoring.

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Notations

In statistics the population attributes are written in capital letters while the small letters are denoted for sample attributes. The statistical notations could be described as below-

‘P’ shows the meaning for population proportion while p refers the sample proportion.

‘X’ is used for a set of population elements while the ‘x’ is used for the sample elements.

‘N’ shows the meaning of population size while n refers the mean of sample size.

The following statistics notation refers for the population:

‘µ’ is generally used for the population mean.

‘σ’ refers the meaning of standard deviation for a population.

σ2 used for the variance of population.

‘P’ used for the proportion of the population elements having a particular attribute.

‘Q’ is used for the proportion of the population elements that does not have a particular attribute and usually this is referred as Q = 1 – P.

‘N’ is used as a statistical notation and refers the total number of elements in a population.

‘ρ’ is used as a population co relation coefficient that is based on the elements of population. (know more about icse board , here)

Some linear regression statistics notations are described as:

For a population regression line the statistical notation ‘B0’ is the intercept constant.

B1 is named as regression coefficient or slope in a population regression line.

For coefficient of determination R2 is used.

In sample regression line b0 is the intercept constant.

For slope in the sample regression line b1 is the regression coefficient.

The statistical notations below described are used for the sample statistics:

For a sample s have the meaning for the standard deviation.

‘r’ is used as a sample co relation coefficient that is based on the elements of a sample.

Number of elements in a sample is denoted by ‘n’.

‘q’ is used for the proportion of the sample elements having no particular attribute. This is written to define ‘q’ in mathematical form q = 1 – p and

In the next session we will discuss about

math help.

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organizing experiment data

As we all are very well aware that statistic is an most important part of mathematics that provide a field of study and describe how to collect and manage the data which are collected from the various experimental resources. These summarized and collected resources are used for performing the interpretation and statistical analysis of the data. According to the standard analysis of data, statistics can be defined as a analytical approach to collect the numerical, systematical facts and data to perform the systematical analysis of data.

In the field of statistics the collected data can be categorized in various categories like categorical and quantitative. In the category of categorical data we generally deals with handling the data which are not identified or counted by the any type of real number. To resolve the problem mathematician make the use of bar charts and pie charts to handle the data values in a systematic and summarize way.

In the same aspect quantitative data is a type of data collection system where data are being recorded or identified by the real number. This concept helps the mathematician to handle the data or to manage the data in frequent and summarized way. In the way of organizing experiment data in statistics can be performed by two popular ways that are stem and leaf plot and next one is histogram. (know more about cbse syllabus , here)

Suppose in mathematical, through an experiment on class the weight of all students are collected the how we manage the data in a systematic order? The solution is use the concept of stem and leaf plot. Through which we can easily perform the management and summarization of data in a systematic order. It is a table representation of data that handles the data by reducing them in small size.

There is another way to organize the statistical data ina pictorial form. The concepts of Organizing experiments in a pictorial form are known as Histogram. It is a type of graph that manages the collected data in the form of bars on the graph and In the next session we will discuss about Notations.

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