Effects of Magnetic Fields Produced from Long Wires

Effects of Magnetic Fields Produced from Long Wires Faradays Law Laboratory Exercise An investigation into the effects of magnetic fields produced from long wires and comparison of theoretical and experimental results through the use of Amperes Law and Faradays Law Contents 1. Summary 2. Introduction 2.1 Introduction to Method 2.1.1 Apparatus 2.1.2 Procedure 3. Results 3.1 Single Wire Experiment 3.2 Single wire experiment with Ferrite Core 3.3 Double Wire Experiment 4. Discussion 5. Conclusion 6. References Appendix A Raw Data Electromagnets and the magnetic fields that they produce provide the foundations for the development of various major industries in modern society, including medicine, transport and robotics. However, there can be inaccuracies with their use caused by a phenomenon known as Electromagnetic Interference (EMI). In this experiment, a search coil was placed near a fixed wire with a current flowing through it, and the induced voltage across the coil was measured and recorded as the coil was moved away from the wire to investigate the effect of distance on the magnitude of the magnetic flux while the effects of a ferrite core on the magnetic field produced were also explored. The experimental and theoretical results highlighted the same trends, confirming the expectation that an increase in distance would cause a decrease in the magnitude of magnetic flux. The differences in results can be considered due to EMI from the return connection, which can induce unwanted voltages in the circuit. A magnetic field is the region in the neighbourhood of a magnet, electric current or changing electric field in which magnetic forces are observable. (1) An electromagnetic field is the form of magnetic field generated by the flow of electric current; it is caused by the movement and acceleration of the electrons. (2) Electromagnets play an important role in the continued development of many major industries, while there are already numerous useful applications of them in modern society. The electromagnetic fields they produce are vital in: medical practises such as MRI scans where they are used to alter the alignment of hydrogen atoms in the body (3); the production of high-speed Maglev trains which eliminates friction by allowing the train to levitate (4) and the continued scientific research into superconductors and rapid acceleration which provides the basis for particle accelerators. (5) However, constantly changing electromagnetic fields, especially in electric circuits, can cause a phenomenon known as Electromagnetic Interference (EMI) which can induce unwanted voltages and affect the performance of electronic devices. The area of engineering which aims to eradicate the problems caused by these disturbances is known as Electromagnetic Compatibility (EMC). (6)(7) Two equations which form the fundamental basis for electromagnetism and its understanding are Amperes Circuital Law and Faradays Law. Amperes Law states that the magnetic field, B, caused by an electric current is proportional to the size of the electric current. (8) (equation 1) However, in this experiment, the current, I, flowing through the circuit remains constant, as does the permeability of free space, , and 2à Ã¢â€š ¬, and therefore the magnetic field, B, is expected to be inversely proportional to the distance from the wire. Faradays Law states that any change in the magnetic environment of a wire will cause a voltage to be induced in the wire. (9) (equation 2) If = BA and a sinusoidal variation of the magnetic field is assumed: (equation 3) where is the induced voltage, N is the turns on the coil, A is the area of the coil and is the angular frequency. As N, A and are constant, the magnetic field, B, should be directly proportional to the induced voltage, E, in this investigation. 2.1 Introduction to Method 2.1.1 Apparatus Agilent signal generator to vary the frequency of the signal provided to the circuit. Twin wire board as shown in figures 1 and 2, containing a fixed wire, an adjustable return connection wire and a 50ÃŽÂ © resistor in series with the circuit. Rectangular air cored coil of dimensions 30mm x 30mm and containing 50 turns, used to measure the changing B field from the wire. Ferrite core to alter the effects of the B field on the coil. Digital Multimeter to record the voltages across the resistor and the search coil, measuring with an uncertainty of +0.0005mV. 2.1.2 Procedure The long wire board was connected to the Agilent signal generator, ensuring that the 50ÃŽÂ © resistor was in series with the circuit. One connection was made using the fixed wire on the board; the other was made using a long connection lead kept the farthest distance away from the experiment as possible, as demonstrated in figure 1. A sign wave signal of frequency 60kHz was selected and the voltage across the resistor recorded, allowing a current to be calculated. The rectangular search coil was then placed against the fixed wire 2cm away from the centre line and the voltage across the coil measured. The coil was then moved at a right angle away from the fixed wire in increments of 1cm and the voltage across the coil measured at each of these points. The input sign wave frequency was then altered to 30kHz and the experimental procedure was repeated. The input sign wave frequency was then returned to 60Hz and a round ferrite core inserted into the search coil; the experiment was th en repeated again. The long connection lead was then changed to provide a short connection as shown in figure 2. A sign wave signal of frequency 60kHz was again selected and the current calculated. The rectangular search coil was then placed against the short connection wire 2cm away from the centre line and the voltage across the coil measured. The coil was then moved in the same manner as above and the voltages recorded. The input sign wave frequency was again altered to 30kHz and the experiment was repeated. The current through the circuit was calculated using Ohms law: where V is the measured voltage across the resistor (3.385 V) and R is the known resistor value 50ÃŽÂ ©, giving = 191mA. For the single wire and double wire at both frequencies, and the single wire at 60kHz with the ferrite core, the distance of the search coil away from the wire, d, and the RMS voltage across the search coil, E, were recorded and collected in three tables which can be found in Appendix A. The RMS voltages measured were then converted into peak-to-peak voltage values for use in equation 3. The resultant experimental B fields for the respective frequencies were then calculated using equation 3, using N = 50 and A = 9x and included in the tables. 3.1 Single Wire Experiment For the single wire experiment, theoretical values for the magnetic flux density at each distance were then calculated using equation 1. A graph of B against the distance from the wire was then plotted for both frequencies and a comparison between experimental and theoretical values made on both graphs. 3.2 Single wire experiment with Ferrite Core With the ferrite core introduced into the search coil, at a frequency of 60kHz, the voltage across the search coil was measured and a graph of the induced EMF, V, against distance plotted. The induced EMF without the ferrite core is also plotted for reference. 3.3 Double Wire Experiment For the double wire experiment, two theoretical values for the magnetic flux density were calculated; one for the magnetic flux induced by the fixed wire and one for the magnetic flux induced by the short connection wire. These were both calculated using equation 1, using a reference of +0cm for the short connection and +15cm for the fixed wire. These values were then combined using the principle of superposition and an overall theoretical value for magnetic flux density at each distance calculated. Again, a graph of B against the distance from the wire was plotted for both frequencies and a comparison between experimental and theoretical values made on both graphs. It was expected that as the distance of the search coil away from the fixed wire increased, the voltage induced across the coil would decrease and therefore the magnetic flux density, B, would also decrease. A comparison of the experimental and theoretical data points from figures 3 and 4 shows a clear correlation between the two calculations, confirming the theory discussed in section 2 of the report. The slight discrepancies between the experimental and theoretical values can be accredited to possible electromagnetic interference (EMI) from the long connection lead, inducing unwanted voltages across the coil and affecting the accuracy of the results. The scale of magnetic flux is affected by the angle at which the flux density and the surface interact such that , where ÃŽÂ ¸ is angle between the magnetic flux, B, and the normal to the surface. When the normal to the coil is parallel to the wire, ÃŽÂ ¸ = 90 ° and therefore cos(ÃŽÂ ¸) = 0, proposing that the theoretical value of magnetic flux is 0. When the coil was placed perpendicular to the fixed wire, a voltage of 0.541mV was measured, which can be approximated to 0V. The small induced voltage can be considered due to the presence of a background magnetic field. With the ferrite introduced into the search coil, the emf induced in the coil is measured to be significantly larger than with no ferrite present, as can be seen from figure 5. Due to the high magnetic permeability of a compound such as a ferrite, the magnetic field produced by the coil is concentrated in the core material, reducing the effects of EMI and increasing the induced emf in the coil. (10) In the double wire experiment, the voltage induced in the search coil is created through a combination of the magnetic fields produced from both the fixed wire and the short wire. Because it is a series circuit, the current is flowing in opposite directions in each of the wires and consequently, from the right-hand rule, the magnetic fields from each wire are also acting in opposite directions, demonstrated in figure 8. Therefore, it would be expected that the induced voltage across the coil, and subsequently the magnetic flux, B, would be smaller than those measured in the single wire experiment and this is confirmed through the values shown in Appendix A. As the coil is moved away from the wires, the magnetic field weakens but at a decreased rate as the distance increases; therefore, we would expect a graph displaying a reciprocal nature, achieved in figures 3 and 4. To conclude, the experiment outlined in this report was successful in demonstrating the effects of magnetic fields produced by long wires and the effects of ferrite on the emf induced in a coil, successfully validating the theory from section 2 that the magnitude of the magnetic flux field, B, is proportional to the reciprocal of the distance of the coil from the wire. However, the consistently higher experimental values compared to the theoretical values clearly demonstrates the possible disturbances arising from the interaction between two different magnetic fields and highlights the need to minimise these to achieve accurate results. Through the introduction of a ferrite core, this experiment was successful in demonstrating a simple method for this. The findings from this experiment are statistically insignificant due to the nature of the apparatus used and the various possible sources of error, both systematic, because of EMI, and human, arising from the low level of accuracy when measuring distances and ensuring the coil remains parallel to the wire. However, the experiment was useful in showing the basic relationship between distance and the strength of magnetic flux, as well as highlighting the importance of finding solutions to reduce the effects of EMI on induced voltages and introducing a simple method for realizing this. [1] Encyclopaedia Britannica, Magnetic Field, Encyclopaedia Brittanica, [Online]. Available: https://www.britannica.com/science/magnetic-field. [Accessed 19 October 2016]. [2] M. Rouse, Electromagnetic Field, March 2010. [Online]. Available: http://whatis.techtarget.com/definition/electromagnetic-field. [Accessed 20 October 2016]. [3] Institute of Physics, Magnetic Resonance Imaging, 2012. [Online]. Available: www.iop.org/education/teacher/resources/teaching-medical-physics/magnetic/file_56290.pdf. [Accessed 20 October 2016]. [4] K. Bonsor, Maglev Train, 13 October 2000. [Online]. Available: http://science.howstuffworks.com/transport/engines-equipment/maglev-train.htm. [Accessed 19 October 2016]. [5] M. Williams, Use of Electromagnets, 13 January 2016. [Online]. Available: http://www.universetoday.com/39295/uses-of-electromagnets/. [Accessed 21 October 2016]. [6] Andi, What is electromagnetic interference and how does it affect us?, [Online]. Available: https://www.westfloridacomponents.com/blog/what-is-electromagnetic-interference-emi-and-how-does-it-affect-us/. [Accessed 21 October 2016]. [7] M. Soleimani, Faradays Law, University of Bath, 2016. [8] D. Wood, Amperes Law: Definiton Examples, [Online]. Available: http://study.com/academy/lesson/amperes-law-definition-examples.html. [Accessed 22 October 2016]. [9] Hyper Physics, Faradays Law, [Online]. Available: http://webcache.googleusercontent.com/search?q=cache:85jQ17DaK1wJ:hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html+cd=2hl=enct=clnkgl=uk. [Accessed 21 October 2016]. [10] Wikipedia, Magnetic Core, [Online]. Available: https://en.wikipedia.org/wiki/Magnetic_core. [Accessed 23 October 2016]. Single Wire Single Wire with Ferrite Core Double Wire

Gather facts interview

In most cases, information systems are formal, computer based systems that play an integral role in organizations. Some information systems include: transaction processing systems, which simply record the routine transactions needed to conduct business, like payroll, shipping, or sales orders: and office automation systems, which are intended to increase the productivity of office errors and include such systems like word processing, electronic mail, and digital filing. The various types of information systems in an organization are interconnected to allow for information sharing.Inventory management to a layman may be defined as a system used in a firm to control the firm investment in inventory. According to (T LUCY 1 996) it involves the recording and monitoring of stock levels, forecasting future demands and decides when and how many to order. 1. 1 Background of the Study Divine supermarket is located in Nassau town along Him road, it deals in grocery. It uses the manual system o f sales transactions and purchases. Sales recording, when a product is being sold the records are just written on papers and books manually.This leads to poor data Storage and retrieval. Customer registration, the details of the customers are recorded whenever they enters the supermarket and this is done manually with a pen and the book where the same details can be recorded many times leading to data redundancy. Stocks updating, in order for the staff to know the amount of stock available, the manager just count the products one by one. This takes a lot of time and onetime leads to counting errors hence producing poor results.The finding shows the challenges facing the manual system of inventory management system; the manual system requires everyday counting of items in the inventory, human errors are very prevalent during counting and recording and in case of disaster like fire or flood or poor communication, all the manual inventory records will be damaged and irretrievable. The accountant manually computes and totals the amount of monthly sales, purchases and expenses. In manual inventory, missing receipts, sales, expenses and inventory records are hard to track back. 1. 2 Problem StatementProcesses at Divine are managed manually which results into poor record keeping and management, time wastage in retrieving information, data redundancy, monetary loss resulting from poor calculations, duplication of data and data insecurity. 1. 3 Objectives of the Study 1. 3 . 1 Main objective To develop an automated inventory management system that saves time, reduce costs, and provide quality services for customers. 1. 3. 2 Specific objectives I. To study and analyses the current system. Ii. To design the system iii. To implement the system iv. To test the system 1. 4 Research Questions I. How does the current system work? I. What are requirements for designing an inventory management system? Iii. How the system is implemented? Iv. What are the methods used for testing the system? 1. 5 Scope of the Study 1. 5. 1 Geographical scope This research work covers stock control, sales management, customer registration, purchases and tends to correct anomalies in the supermarket database. It analyses stock updates and ability to view existing stock. It provides quick way of operation by capturing the manual processes and automates them. 1-5. 2 Time scope The study covered a period of five months from September 2014 to January 2015 1. Significance of the Study . To provide an effective supermarket database that handles sales, purchases and overall stock control to save time, prevent congestion of customers and provide data recovery program for effectiveness of the supermarket operations. Ii. To act as a ground for the future scholars or academics in future research in the field of improving inventory management. Iii. To reduce the costs of information storage and retrieval. CHAPTER MO LITERATURE REVIEW 2. 0 Introduction This chapter gives a view of the sel ected existing system from literature on inventory management.It covers the overview of the types of inventory kept ND system design and implementation. According to (S. C Sahara (1999). P. 509, 512). Inventory is considered as a systematic location, storage and recording of goods in such away that desired degree of service can be made to the operating shops at a minimum ultimate cost According to (Pander 1990) inventory management is stock of the product a firm is manufacturing for sale and the components that makes up a product. Firm hold inventory in a form of raw material, work in progress, finished goods and supplies.These inventories facilitates production and sales operation, guard against the risk f unpredictable changes in usage and delivery time and take advantage of quality discount and price frustration. Donnelly (1990) states that inventory management and control process are very useful in determining the optimum level of inventories and finding answers to the problem o f economic order quality, the re-order point and safety stock. 2. 1 Inventory Control and Management Inventory management is defined as the system in a firm to control the firm's investment in inventory.It involves the recording and monitoring of stock level, fostering future demand and deciding on when and how to order. The objective of inventory management is to minimize in total, the cost associated with inventory (T Lucy, 1996). According to Salem (1 997), inventory control refers to a planned method of purchasing and storing materials at the lowest possible cost without affecting the production distribution schedule. Inventory control therefore is a scientific method of determining what, when and how much to have in stock for a given period of time. 2. Importance of inventory Management Systems Inventory management is an important part of a business because inventories are usually the largest expenses incurred from business operations. Most companies will use an inventory manag ement system that will track and maintain the inventories required to meet customer demand. Most systems used by companies are linked to meet the management or accounting information systems increasing the effectiveness of their operations. (Kumara Nixon 2006) 2. 2. 1 Inventory Orders Inventory management system help business order inventory by accurately recording consumer sales.Electronic inventory systems can track sales in a real time- time format, ordering inventory automatically when current stock hits a predetermined minimum levels. Electronic ordering known as electronic Data interchange (EDI), allows companies to maintain the proper amount of stock by not increasing costs through over- ordering of inventory . EDI also ensures placed orders are placed immediately, ensuring shortly amounts o lead times to receive new inventory(junkyards Nixon 2006) . 2. 2. 2 Stock Maintenance Computerized inventory management system allows companies to properly order and maintain several diff erent types of goods.Different styles, colors or size can easily be managed to ensure that consumers demand is met through offering a variety of goods. Most companies use inventory management to pep stock items separate from similar goods this allows management to determine which items are selling and which items need to be reduced from inventory based on poor sales. (Saxons 2003) 2. 3 The existing inventory management system This is the manual system where the customer buys a product by moving around the stock looking for the product without specific directions and after words goes to the cashier and pays for the product.A t this stage the accountant just write using a pen and a book to record the transaction and the total amount for sales and purchases are computed manually using a calculator. And lastly a receipt is issued. This consumes a lot of time and even leads to data redundancy Customer registration is done manually whenever he/she enters the supermarket using books for re cord keeping which leads to redundancy of data. When stock is added, they just use man counting around stock to know the current status. 2. 3. Difficulties in the Manual Inventory System The current system operates manual inventory system, from stocks, products, ordering and purchases etc recorded in a book. This is faced with errors, incompleteness, and insufficient data for analysis. Information regarding tock, products, sales and purchases are still in black and white which is not properly organized and managed. From the wholesalers to retailer bills, tickets, vouchers, receipts of products are recorded in a book but further operations are not being properly handled. As a result it is difficult in processing, updating and managing.The factors for these difficulties are: Time Consumption, Manual inventory systems are time consuming, as the business owner must keep track of inventory sales on a daily basis, while updating the system manually at the end of the day. Poor Communicatio n, A annual inventory requires employees and managers to write down each time an item is removed from the inventory. If one employee forgets to mention that the last coffee product has been removed from the inventory, a manager expects the item to still be available for a customer during a sale.Compared with a technical inventory system, a manual inventory system does not help the communication in the workplace. Physical Counts, A manual inventory system does not provide any number, as all numbers from the inventory are gained through physical inventory counts. One of the difficulties of running a annual inventory system is that physical inventory counts must be performed frequently to control the items in the inventory. This is time consuming and can cost the business money, if employees must come in to help out outside of business hours.Daily Purchases, Keeping track of daily purchases is another difficult controlling measure with manual inventory systems. A manual inventory syste m requires the employees to write down the items sold during a single work day. This can be a difficult task, as one employee may lose the list of items sold or another may forget to write down a sale. Ordering Supplies, A manual inventory system does not update at the end of the day with updated inventory counts. This means you must go through the inventory items each time you need to place an order for new raw materials, products or supplies for the inventory.This can be a time consuming process, as you will physically have to go through each product box and browse through the items. 2. 4 The proposed inventory management system This is an automated inventory management system where all transactions are done electronically. In this, when a customer picks a product from stock takes it to the checkout assistants. Then the checkout assistants use bar code readers to scan purchases which are linked to the application program that uses a bar code reader to find the price of the item fr om the product database and then the stock is automatically reduced by the system.The program then reduces the number of such items in a stock and displays the price on the cash register. And customers' details are recorded. Most companies use inventory management to keep stock items separate from similar goods this allows management to determine which items are selling and which items need to be reduced from inventory based on poor sales. Saxons 2003) 2. 4. 1 Benefits of the proposed system I. Optimize the security and validity of the number of supplies, sales, purchases, expenses every month. Ii. Easier tracking down the purchases, expenses and inventory records. Ii. Support for inventory management that helps record and track materials on the basis of both quantity and value. Iv. Uses less of time for the accessing data or information. V. All data or information that currently stored in the drawers or racks will be transfer to the database system that will be safely saved in the computer. CHAPTER THREE RESEARCH METHODOLOGY 3. 0 Introduction This chapter contains the research design, population study, sampling design, data collection and system analysis. A qualitative research will be used by the research. . 1 System investigation This will involve investigating the weaknesses of the system where the system investigation techniques like case diagrams will be used. Case diagrams depict the system's operation where they demonstrate system processes. Questionnaires given to a large number of users Formal interviews with selected key personnel Observing a sample of users as they go about their daily tasks with the current system Analyzing existing documents to understand what data is created and how it is then manipulated by the system. . 2 Population study The study area was Divine supermarket and the study population consisted of the manager, and staff and customers. The sample size 30 respondents were interviewed with the use interviews, questionnaires and ob servations 3. 3 Data gathering techniques 33. 1 Interview This will involve face to face direct conversation were questions and answers where he main theme. The researcher will approach the users directly in order to obtain comments and notes about the current supermarket inventory management system.The interview questions will be designed in line with the objectives Of the study . The interviewees mentioned the problems that where encountered in the use manual system and also gave the possible causes of the problems which where faced. It is unlikely that a single interview with a user will cover everything the analyst needs to know. Therefore part of the plan should include 3 interview types I. An initial interview This interview is to scope out the overall problem that the new system is to solve and any shortcomings in the current system.This interview provides the analyst with a context for the project. This information is recorded in the definition part of the the requirements d ocument ii. Gather facts interview The initial interview allowed the analyst to have a view of the project and begin to understand what needs to be done. This second interview is intended to gather detailed information about the system. This information helps build up the draft requirements document iii. Final interview The draft requirements document has been written.This interview goes through the relevant part of it with the interviewee (who could be user, management or customer). They confirm that the requirement document is correct or they provide feedback if any changes need to be made. 3. 3. 2 Observations. This will include observation of the services of the current system. The researcher will use this process to verify the data collected from the above methods and also to capture some more data that could have been ignored. And will be done by looking at the systems performance of the supermarket. Methods of observation could be either direct or indirect. . Direct. As in si tting next to the user and viewing work done. This has the advantage f being able to ask questions as you go along but has the disadvantage of users being uncomfortable with someone looking over their shoulder. This may lead to people carrying out the task as it ‘should' be done rather than how they really do it. Ii. Indirect With their permission, users could be viewed with remote video cameras. This avoids the awkwardness of being right next to them but it has the disadvantage of being less able to ask questions on the spot.It is also more costly to set up and may be impractical in open-air environments (for example fire-brigade or ambulance systems perhaps). 3. 3. Questionnaires The questionnaires were closed ended to enable the respondents to understand them and answer them appropriately with ease. It will include the liker scale that is Agree, strongly agree, not sure, disagree, and strongly disagree. I. Closed questions (multiple choice), These are easy to analyze but th e choices provided must be different enough to make it simple for the user to select one. They must also include the most relevant choices. I. Open questions, these offer the chance to obtain more detailed answers and to seek opinions. They are however more difficult to analyze than closed questions and people may not provide useful answers. 3. 4 System analysis This will involve careful analysis and study to understand how the designed system would differ from the old system. It describes what system should do so as to satisfy the needs of the user. It will also involve study of sets of interacting entities, including computer systems analysis. This field is closely related to requirements analysis or operations research.It is also â€Å"an explicit formal inquiry carried out to help someone (referred to as the decision maker) identify a better course of action and make a better decision than he eight otherwise have made. † This will be done in form of expressing responses a s squares correlation of the population and by use of frequency distribution tables and SPAS. 3. 5 System design This will involve a detailed specification of the computer-based solution to the above-mentioned requirements. Context diagram, Data flow diagrams and entity relationships diagrams will be used for designing the proposed system. . 5. 1 Data Flow Diagram The DEED Diagram for Inventory Management System is a data flow diagram of graphical representation and commonly used also for the visualization of tortured design data processing through an information system, it's an important technique for modeling process aspects with a system's high-level detail by showing what kinds Of data will be/how to input and Output from the system, where the data will come from and go to by sequentially, and where the data result will be stored through functional transformations.

Analysis Of The Movie Georgina - 893 Words

5. According to Goffman, patients commonly create narratives about themselves in order to make more desirable self-presentations of themselves to others. In other words, patients will commonly make up past achievements about themselves in order to create a better self-image. In the movie, Georgina, who was Susanna’s roommate, was a pathological liar. Throughout the film, she continuously told lies in order to better her self-presentation. For instance, she threatens another patient when she says â€Å"My dad is the head of the CIA and he could have you dead in minutes†. She used this lie to portray herself as having powerful and influential family members and to depict herself in a better way to the other patients. Furthermore, Goffman writes, â€Å"One typically finds that he constructs an image of his life course – past, present, and future – which selects, abstracts, and distorts in such a way as to provide him with a view of himself which he can usefu lly expound in current situations† (Goffman 1961:498). This is seen through another character in the film, Polly. Polly is a disfigured patient checked into the mental hospital because of her schizophrenia and depression. She has various burns on her face and body and tells the other patients she was part of a bad fire. This causes the other patients to feel bad for her and show her sympathy. However, in reality Polly was not trapped in a fire, but rather she set herself on fire. If she told the other patients this, they would viewShow MoreRelatedAnalysis of Girl Interrupted2171 Words   |  9 PagesMovie Analysis: Girl, Interrupted. Brittany Clontz Nursing 114 Girl interrupted is a gripping tale of a girl’s maladaptation to the challenges of life. The movie focuses on a young girl named Suzanna Kaysen growing up in the 1960s and struggling with the world around her. Suzanna is admitted to Clarmoore institution after she consumes a whole bottle of aspirin and alcohol to deal with her pain. When admitted to Clarmoore she claims she was not trying to commit suicide, but that she just had a headache

How To Calculate the Variance and Standard Deviation

Variance and standard deviation are two closely related measures of variation that you will hear about a lot in studies, journals, or statistics class. They are two basic and fundamental concepts in statistics that must be understood in order to understand most other statistical concepts or procedures. Below, we’ll review what they are and how to find the variance and standard deviation. Key Takeaways: Variance and Standard Deviation The variance and standard deviation show us how much the scores in a distribution vary from the average.The standard deviation is the square root of the variance.For small data sets, the variance can be calculated by hand, but statistical programs can be used for larger data sets. Definition By definition, variance and standard deviation are both measures of variation for interval-ratio variables. They describe how much variation or diversity there is in a distribution. Both the variance and standard deviation increase or decrease based on how closely the scores cluster around the mean. Variance is defined as the average of the squared deviations from the mean. To calculate the variance, you first subtract the mean from each number and then square the results to find the squared differences. You then find the average of those squared differences. The result is the variance. The standard deviation is a measure of how spread out the numbers in a distribution are. It indicates how much, on average, each of the values in the distribution deviates from the mean, or center, of the distribution. It is calculated by taking the square root of the variance. A Conceptual Example The variance and standard deviation are important because they tell us things about the data set that we can’t learn just by looking at the mean, or average. As an example, imagine that you have three younger siblings: one sibling who is 13, and twins who are 10. In this case, the average age of your siblings would be 11. Now imagine that you have three siblings, ages 17, 12, and 4. In this case, the average age of your siblings would still be 11, but the variance and standard deviation would be larger. A Quantitative Example Let’s say we want to find the variance and standard deviation of the age among your group of 5 close friends. The ages of you and your friends are 25, 26, 27, 30, and 32. First, we must find the mean age: (25 26 27 30 32) / 5 28. Then, we need to calculate the differences from the mean for each of the 5 friends. 25 – 28 -326 – 28 -227 – 28 -130 – 28 232 – 28 4 Next, to calculate the variance, we take each difference from the mean, square it, then average the result. Variance ( (-3)2 (-2)2 (-1)2 22 42)/ 5 (9 4 1 4 16 ) / 5 6.8 So, the variance is 6.8. And the standard deviation is the square root of the variance, which is 2.61. What this means is that, on average, you and your friends are 2.61 years apart in age. Although it’s possible to calculate the variance by hand for smaller data sets such as this one, statistical software programs can also be used to calculate the variance and standard deviation. Sample Versus Population When conducting statistical tests, it’s important to be aware of the difference between a population and a sample. To calculate the standard deviation (or variance) of a population, you would need to collect measurements for everyone in the group you’re studying; for a sample, you would only collect measurements from a subset of the population. In the example above, we assumed that the group of five friends was a population; if we had treated it as a sample instead, calculating the sample standard deviation and sample variance would be slightly different (instead of dividing by the sample size to find the variance, we would have first subtracted one from the sample size and then divided by this smaller number). Importance of the Variance and Standard Deviation The variance and standard deviation are important in statistics, because they serve as the basis for other types of statistical calculations. For example, the standard deviation is necessary for converting test scores into Z-scores. The variance and standard deviation also play an important role when conducting statistical tests such as t-tests. References Frankfort-Nachmias, C. Leon-Guerrero, A. (2006). Social Statistics for a Diverse Society. Thousand Oaks, CA: Pine Forge Press.