Statistics and ProbabilityIn this chapter we will learn about statistics and probability.StatisticsStatistics is the branch of Mathematics which deals with data collected for specific purpose.Central Tendencies of DataThe central tendency gives us an idea that represents the entire data. There are three types of central tendencies which are:
Mean
Median
Mode
MeanIt is also known as arithmetic mean of the given observations and is equal to ratio of sum of all the observations and total number of observations, i.e., \[Mean\text{ =}\frac{Sum\text{ }of\text{ }all\text{ }the\text{ }observations}{Total\text{ }number\text{ }of\text{ }observations}\] If \[{{x}_{1}},{{x}_{2}},---{{x}_{n}}\] are n observations then its mean is \[A.M.\text{ =}\,\overline{x}\,\text{= }\frac{{{x}_{1}}+{{x}_{2}}+......+{{x}_{n}}}{n}\text{ }=\frac{\sum\limits_{{}}^{{}}{xi}}{n}\]Arithmetic Mean for Frequency DistributionLet f1, f2, ....... fn be corresponding frequencies of x1, x2, x3, .......... xn then \[A.M.\text{ = }\frac{{{x}_{1}}{{f}_{1}}+{{x}_{2}}{{f}_{2}}+......+{{x}_{n}}{{f}_{n}}}{{{f}_{1}}+{{f}_{2}}+.....{{f}_{n}}}\text{ }=\frac{\sum\limits_{i\,=\,1}^{n}{{{x}_{i}}}{{f}_{i}}}{\sum\limits_{i\,=\,1}^{n}{{{f}_{i}}}}\]Arithmetic Mean for Grouped DataFor a classified data, we take the class marks x1, x2,?...., xn of the classes as variabies, then arithmetic by(i) Direct method is \[A.M.\text{ =}\frac{\sum\limits_{i=1}^{n}{xf}}{\sum\limits_{i=1}^{n}{f}}\](ii) Deviation method is \[A.M.\text{ =}{{\text{A}}_{\text{1}}}\text{+}\left( \text{ }\frac{\sum\limits_{i=1}^{n}{{{f}_{i}}{{d}_{i}}}}{\sum\limits_{i=1}^{n}{{{f}_{i}}}} \right)\times \text{ }h\] more...
LogarithmsEarlier you have studied that if two powers of the same base are equal (when base in not equal to \[-\]1, 0 or 1) then the indices are equal. For example if \[{{3}^{x}}={{3}^{y}}\] then\[x=y\]. But we cannot calculate the value of \[x\] when\[{{3}^{x}}={{7}^{3}}\]. The necessity of the concept of logarithms arises for such problems. Logarithms are useful in long calculations of multiplication and division.Logarithms are mathematical statements which are used to answer a slightly different question for exponents whose base is a positive real number. Thus if a is a positive real number other than 1 and \[{{a}^{x}}=n,\] then \[x\] is called the logarithm of n to the base a, and written as log n.Note: If no base is mentioned in a logarithm then it is taken as 10. Logarithms to the base 10 are known as common logarithms.Properties of Logarithms
Word Problems Based on MathematicsIn this chapter we will learn life problems related to mathematics.Problems Based on Time and WorkTime and work are always indirectly proportional.\[\therefore \] A person can take a time to do any work \[\alpha \frac{1}{capability\text{ }of\text{ }person\text{ }to\text{ }do\text{ }that\text{ }work}\]Thus, we know that if a person have lot of capability to do a work, then he takes less time to do that work and if a person have less capability to do a work, then he takes more time to do that work. Note: It is assumed that the person works at uniform rate until and unless specified.Problems Based on Time and DistanceLength of the path covered by an object is called distance. Speed is the distance travelled by an object in unit time. \[\therefore \text{ Speed = }\frac{distance}{time}\]Average speed is the ratio of the total distance and the total time taken by an object to cover that distance. \[\therefore \text{ Average speed = }\frac{\text{total distance covered}}{\text{total time taken}}\]Note:(a) When two trains are moving with velocities a km/hr and b km/hr respectively, then relative speed will be (where a > b)i.(a - b) km/hr, if they are moving in same direction. ii.(a + b) km/hr, if they are moving in opposite direction. (b) When the speed of boat in still water is a km/hr and speed of stream is b km/hr more...
Verbal and Non-verbal ReasoningReasoning and logic skills are an integral part of a wide range of subjects of mathematics. These skills are very useful in our daily lives. In this chapter we with solve problems related to verbal and non-verbal reasoning.Odd-One Out Types of ProblemsIn these types of problems, letters of the alphabet are classified into a group by applying a particular rule or pattern.
Example:
Choose the group of letters which is different from the others:BEI, MPT, RVZ, LOS (a) BEI (b) MPT (c) RVZ (d) LOS (e) None of theseAns. (c)Explanation: \[B\underrightarrow{+3}\text{ }E\underrightarrow{+4}\text{ I, M}\underrightarrow{+3}\text{ P}\underrightarrow{+4}\text{ T, R}\underrightarrow{+4}\text{ }V\underrightarrow{+4}\text{ Z, L}\underrightarrow{+3}\text{ }O\underrightarrow{+4}\text{ }S\]Clearly, RVZ is different from others.Problems Related to Missing Number in the SeriesIn these types of problems, we have to find the missing number of the given series, where the given series follow a certain type of pattern.
Example:
Find the missing number in place of the question mark.80 143 224 ? 440 (a) 420 (b) 258 (c) 228 (d) 323 (e) None of these more...
Classification of Computer Based on Size and Capability
Introduction
Classification of computers are based on their architecture, speed of executing commands or instructions, peripheral used and also their uses. Microcomputers are usually used in home and offices and only a single user can perform the task using a microcomputer. Its storage and data handling capacity are limited as per the requirement for home and office work. The another type of computer is called minicomputer which has usually larger storage and can handle multiuser at a time. This chapter includes the classification of computers.
Computer's Classification
Computers are classified on different parameters, such as, storage capacity, processing speed and component (CPU) used in computers. Depending upon the components used and features of different computers, they are classified into four groups, Microcomputers, Minicomputers, Mainframe computers and Supercomputers.
Micro Computers
Micro Computer is a computer whose CPU (Central Processing Unit) is a microprocessor. All the components of a microprocessor are on a single integrated circuit chip. Micro computer can be categorized as the desktop, programmable and workstation. The microprocessor based computers are called third generation computers. They are the backbone of the modern computer era. The first and second generation computers are based on vacuum tubes and bipolar junction transistors.
Desktop Computers
Desktop computer is a type of microcomputer. A desktop computer has a keyboard for input data, a LCD or CRT monitor to display information and Central processing unit tower contains storage, memory, different types of drives, such as, CD drive, hard drive, etc. A desktop computer is mainly used at home and office applications.
Programmable Computers (PDA)
Personal digital assistance is a type of hand held programmable digital computer. It is used as notepads, address books and can connect to world web wave to share information. A PDA is equipped with mobile phone hence, called smallest computer.
Workstation
A workstation computer has greater memory capability and more extensive mathematical abilities. It is connected with other workstation computers or personal computer to exchange data and mostly used for scientific applications. It also supports multitasking applications.
Mini Computers
Minicomputers were introduced in early 1960s. They were faster than micro computers. Basically these computers were mainly multi-user systems, where many users work on the systems. Generally these types of computers had larger memories and greater storage capacity. They had large instruction set and address field. These kinds of computers have efficient storage for handling of text, in comparison to lower bit machines. Due to more efficient processor, speed and memory size, minicomputer was used in variety of applications and could support business applications along with the scientific applications. Minicomputer was a multi-user system which means more than one user could use this system simultaneously.
Comparison of Micro and Mini computers
Operating System
Introduction
An Operating System is a master control program. Basically it is system software that manages the operation of a computer. Without an operating system computer cannot work. The computer is useless unless it is provided with essential software that makes it ready to use. As we have seen that an operating system is software, which makes the computer ready to use by a process called booting. Basically booting is a process which loads operating system from disk to RAM.
About twenty years ago Steve Jobs and Wozniak, the founders of Apple, came up with the very strange idea of selling information processing machines for use at the home. The business took off, and its founders made a lot of money and received the credit they deserved for being daring visionaries. But around the same time, Bill Gates and Paul Alien came up with an idea even stranger and more fantastically: selling computer operating systems. This was much wider than the idea of Jobs and Wozniak. A computer at least had some sort of physical reality to it. It came in a box, you could open it up and plug it in and watch lights blink. An operating system had no tangible incarnation at all. It arrived on a disk, of course, but the disk was, in effect, nothing more than the box that the OS came in. The product itself was a very long string of ones and zeroes .that, when properly installed and coddled, gave you the ability to manipulate other very long strings of ones and zeroes. Yet, now the company that Gates and Alien founded is selling operating systems like Hindustan Lever Limited sells detergents. New releases of operating systems were launched as if they were Bollywood blockbusters, with celebrity endorsements, talk show appearances and world tours. The market for them is vast enough that people worry about whether it has been monopolized by one company. Even the least technically minded people in our society now have at least a hazy idea of what operating systems do; what is more, they have strong opinions about their relative merits. To be more elaborative on the topic, every general-purpose computer requires some type of operating system that tells the computer how to operate and how to utilize other software and hardware that are installed on to the computer. All software programs developed today require some type of Operating System to operate properly. MSDOS, Unix and Windows are all examples of operating systems. Because the history of computer operating systems parallels that of computer hardware, it can be generally divided into five distinct time periods, called generations, that are characterized by hardware component technology, software development and mode of delivery of computer services.
Structure of OS
The internal structure of operating system is divided into layers. The outermost layer is called user interface and innermost layer is hardware.
The following are the main layers more...
Introduction to Logic Gates and Number System
Introduction
A logic gate is an idealized or physical device implementing a Boolean function, that take inputs and produces a single logic output.
Computer are made up of logic gates. Logic gates take information coming in and output different information depending on what type of gate they are.
In 1938, Claude E. Shannon introduced a two ? valued Boolean algebra called Switching Algebra, which applied the concept of Boolean Algebra to the design of electrical circuits.
Truth Table and Logic Gates
Truth Table
A truth table is a representation of all possible combinations of Input values and their result in a tabular format. If the result of a logical expression of logical statement is always true or 1, it is known as Tautology. If the result expression or logical statement is always false or 0, it is known as Fallacy.
Briefing on Internet and Networking
Introduction
In the world of Information Technology, some set of rules are defined and these are known as protocols. Basically the set of protocols enables two systems to communicate and transfer data on the network. Any electronic device which is having a capability of sending and receiving data is a system. Protocols are generally implemented by software, hardware or a combination of the two.
The information which identifies the protocols are the following:
vTo identify the corrupt messages, error checking is to be used.
vWhile receiving messages, it generally indicates the receiving devices.
vWhile sending messages, it indicates the sending devices.
vTo compress the data transmitted through the network, the method data compression is used.
The following table lists some important networking protocols:
Network Protocol
NetBIOS Enhanced User Interface (NetBEUI) is the fastest protocol and does not require any configuration to implement. NetBEUI is simple to use.
AppleTalk is a routable protocol and is mainly used to communicate with Macintosh computers on the network.
Transmission Control Protocol/Internet Protocol (TCP/IP) is also a routable protocol. TCP/IP is supported by most of the OS. It is more reliable than other protocols.
NWLink is used in Novell NetWare networks. This protocol is easy to install and also a routable protocol. The NWLink protocol is faster than TCP/IP but slower than the NetBEUI.
Internet
The Internet goes back to early 1960's. J.C.R. Licklider of MIT (Massachusetts Institute of Technology), first proposed a global network of computers in 1962 and moved forward to the DARPA (defense Advanced Research Projects Agency) in late 1962 to head the work for its development.
In old days Internet was known as ARPANET (Advanced Research Projects Agency Network). It was started online in 1969 under a contract led by the renamed ARPA (Advanced Research Projects Agency), which initially connected four major computers at universities in the southwestern US UCLA (University of California, Los Angeles), Stanford Research Institute, UCSB (University of California, Santa Barbara) and the University of Utah). Internet is the best example of WAN (Wide Area Network). A WAN is one of the computer networks which was established on a large geographical area. While connecting the Internet with your computer you need modem. Basically modem is one of the most important parts for using Internet services. This works as a key because it receives the packet of data or signals through the service provider and thus after receiving it, it allows user to use the packet of data for surfing. Without modem surfing is unable to proceed.
The following are the advantages of the Internet:
Email
Using Internet you can send any information, greeting and any type of file, such as picture to any location of the more...
Introduction to MS-Access 2013
Introduction
Our lives revolve around to obtain, upgrade and maintain data and to a great extend depends upon it. From the normal daily life to working in an organization to the growth of any nation, everything depends upon on information.
However, data in its raw and unprocessed form is meaningless, but when such data is converted into information it is useful. Hence it is essential to provide a structure to the available data and organise it, which can be achieved with of a database. Database is an organised collection of information that can be easily be accessed, managed and updated.
Need of Database
Earlier, it was difficult to maintain a database which consists of hundreds and thousands of records. However, when a piece of information was to be updated, it had to be done separately in all related files. These problems created the need for designing a database which could handle vast amount of data. A database management system (DBMS) is a powerful tool used to store data, secure it, protect it and make it quickly available to people who need it. We need DBMS for the following reasons:
Data Storing: Large amount of data can only be managed with the help of efficient DBMS. For example most medium and large banks rely on databases to store customer information. Because this information is accessible wherever they need all over the world through internet, customers don't have to go to a local banking branch, for example, to access their account information.
Data Summarizing & Data Classification: Arranging the data and providing the facility to get the data on the basis of some criteria or category is again the main advantage of DBMS. Through this feature only we are able to get the summary of our bank statement based on some criteria whenever we need.
Data Retrieval: Efficient DBMS helps us to instantly retrieve the data from the database. Despite having millions of records of account holders in a bank database, it retrieves the data at lightning speed. Therefore, a DBMS not only stores large of data but also helps in quick retrieval of the same.
To reduce Data Redundancy and Inconsistency: DBMS helps in controlling data redundancy which in turn reduces data inconsistency. Data redundancy occurs when data is duplicated unnecessary which results in multi mismatching of copies of the same data.
Data Concurrency and Data Integrity: DBMS allows multiple transactions to access and modify the shared data at the same time, without violating data integrity.
Enforcement of Data standards: In DBMS, data is stored in a standard formats which helps to maintain integrity and exchange of data between the database system.
Ensure Data Security: Confidential data needs to be protected from unauthorized access. DBMS facilities to secure sensitive data by performing authorization checks and enforcing selective access to users.
Backup and Recovery Management: DBMS applies its theory for protecting a database against data loss and the process of more...
Introduction to CSS
Introduction
Cascading. Style Sheets, fondly referred to as CSS, is a simple design language intended to simplify the process of making web pages presentable. CSS handles the look and feel part of a web page. Using CSS, you can control the color of the text, the style of fonts, the spacing between paragraphs, how columns are sized and laid out, what background images or colors are used, as well as a variety of other effects. CSS is easy to learn and understand but it provides powerful control over the presentation of an HTML document. Most commonly, CSS is combined with the markup languages HTML or XHTML.
Advantages of CSS
Consistency
The main benefit of CSS is that style is applied consistently across a number of web pages. One command line can control several areas at one time, which is quite advantageous if there are changes that need to be made. You only need to alter one thing and the rest will follow. Because you don't have to change each page one at a time, web designers can be very efficient in creating and changing a website with only a few lines of code.
Improved Website Speed
Web designers only need to use a small amount of lines of programming for each page. And if there are less code, there are fewer lines to read, resulting in a faster load time for every page. With online users not willing to wait for a website to load, improving site speed will be most advantageous. Owners who bank on website performance to improve search engine rankings and customer base will benefit from CSS.
Easy to Maintain
Cascading style sheet not only simplifies website development, but also maintenance. All the codes are placed on one page, which means making improvements or changing a few lines will not involve going through several pages. And since a change with a single line of code is applied across the website, maintenance time and effort are significantly reduced.
Appearance
CSS makes it easy to improve the appearance of a website by allowing you to create a much more stylish website since CSS offers a wide array of expressive style capableness. With CSS, you will actually obtain more control over your website's visual aspect. Now, designers can orchestrate the styles and design of several web pages in a flash.
Maintainability
One of the convenient features that CSS produces is the consistency it provides when you want to make changes to a website. When a change is made to your websites CSS Style sheet, you will have the ability to automatically correct or change every page throughout your website-all at once. You do not have to go in to each individual web page to make a particular change as CSS will instantly do it for you. If your website is rather large, this one simple feature will save you ample time more...
Desktop Computers
Desktop computer is a type of microcomputer. A desktop computer has a keyboard for input data, a LCD or CRT monitor to display information and Central processing unit tower contains storage, memory, different types of drives, such as, CD drive, hard drive, etc. A desktop computer is mainly used at home and office applications.
Programmable Computers (PDA)
Personal digital assistance is a type of hand held programmable digital computer. It is used as notepads, address books and can connect to world web wave to share information. A PDA is equipped with mobile phone hence, called smallest computer.
Workstation
A workstation computer has greater memory capability and more extensive mathematical abilities. It is connected with other workstation computers or personal computer to exchange data and mostly used for scientific applications. It also supports multitasking applications.
Mini Computers
Minicomputers were introduced in early 1960s. They were faster than micro computers. Basically these computers were mainly multi-user systems, where many users work on the systems. Generally these types of computers had larger memories and greater storage capacity. They had large instruction set and address field. These kinds of computers have efficient storage for handling of text, in comparison to lower bit machines. Due to more efficient processor, speed and memory size, minicomputer was used in variety of applications and could support business applications along with the scientific applications. Minicomputer was a multi-user system which means more than one user could use this system simultaneously.
Comparison of Micro and Mini computers
