How to Estimate Standard Deviations (SD)

The standard deviation and range are both measures of the spread of a data set. Each number tells us in its own way how spaced out the data are, as they are both a measure of variation.  Although there is not an explicit relationship between the range and standard deviation, there is a rule of thumb that can be useful to relate these two statistics.  This relationship is sometimes referred to as the range rule for standard deviation. The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s (Maximum – Minimum)/4. This is a very straightforward formula to use, and should only be used as a very rough estimate of the standard deviation. An Example To see an example of how the range rule works, we will look at the following example. Suppose we start with the data values of 12, 12, 14, 15, 16, 18, 18, 20, 20, 25. These values have a mean of 17 and a standard deviation of about 4.1. If instead we first calculate the range of our data as 25 – 12 13 and then divide this number by four we have our estimate of the standard deviation as 13/4 3.25. This number is relatively close to the true standard deviation and good for a rough estimate. Why Does It Work? It may seem like the range rule is a bit strange. Why does it work? Doesn’t it seem completely arbitrary to just divide the range by four? Why wouldn’t we divide by a different number? There is actually some mathematical justification going on behind the scenes. Recall the properties of the bell curve and the probabilities from a standard normal distribution. One feature has to do with the amount of data that falls within a certain number of standard deviations: Approximately 68% of the data is within one standard deviation (higher or lower) from the mean.Approximately 95% of the data is within two standard deviations (higher or lower) from the mean.Approximately 99% is within three standard deviations (higher or lower) from the mean. The number that we will use has to do with 95%. We can say that 95% from two standard deviations below the mean to two standard deviations above the mean, we have 95% of our data. Thus nearly all of our normal distribution would stretch out over a line segment that is a total of four standard deviations long. Not all data is normally distributed and bell curve shaped. But most data is well-behaved enough that going two standard deviations away from the mean captures nearly all of the data. We estimate and say that four standard deviations are approximately the size of the range, and so the range divided by four is a rough approximation of the standard deviation. Uses for the Range Rule The range rule is helpful in a number of settings. First, it is a very quick estimate of the standard deviation. The standard deviation requires us to first find the mean, then subtract this mean from each data point, square the differences, add these, divide by one less than the number of data points, then (finally) take the square root. On the other hand, the range rule only requires one subtraction and one division. Other places where the range rule is helpful is when we have incomplete information. Formulas such as that to determine sample size require three pieces of information: the desired margin of error, the level of confidence and the standard deviation of the population we are investigating. Many times it is impossible to know what the population standard deviation is. With the range rule, we can estimate this statistic, and then know how large we should make our sample.

Book Report for Underground Railroad - 1337 Words

William Wang Mrs. Smart Book Report Midterm Report Underground Railroad Dramatic First-Hand Accounts 1. Alabama a. Narrative of Peter Still i. This narrative appears in stills Underground Railroad Records ii. One of the greatest documents of the underground railroad iii. The life, struggles, and success of Peter and his Family were ably brought before the public in â€Å"The Kidnapped and the Ransoms† iv. His Parents Levin and Sidney were both slaves on the Eastern shore of Maryland v. The father was able to buy his freedom at a low sum vi. But the wife and mother remained a slave vii. The wife had four children, two girls and two boys viii.†¦show more content†¦Narrative of John Brown lxiv. Went to Kansas and brought many weapons lxv. Found his sons in an unsheltered area lxvi. Created a posse to fight against Missouri pro slavery militia occupying Kansas lxvii. During the battles one of John Brown’s son was killed lxviii. Many Missouri men had robbed Kansas houses during battle lxix. Created one of the first sparks of the Civil W ar 5. South Carolina lxx. Large portions of the slaves lived near the water lxxi. Many seek northern captains to pilot them north lxxii. Dr. Alexander M. Ross traveled through South Carolina for the purpose of spreading the word about Canada and the routes slaves could take to reach Canada g. Narrative of John Jackson lxxiii. Was able to live with the masters children as a playmate lxxiv. Started to work in the fields when he was 7 or 8 lxxv. Only had 2 meals a day lxxvi. The overseers whipped him in front of his father lxxvii. Was married and had a baby boy lxxviii. Was whipped to give up his wife lxxix. Decided to run away to the north and have his wife bought back lxxx. There was a north bound ship which John Jackson hid in for 4 days lxxxi. Out of hunger he dig a hole in the wooden planks that signaled the Captain lxxxii. 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Daniel Shays As An American Officer - 1730 Words

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Ma Assignment free essay sample

Why may financial information alone be insufficient for the ongoing informational needs of operators/workers, managers and executives? Financial information’s are the measurement of the effectiveness and efficiency of operator’s actions, and it’s mainly for the use of external users. However financial information did not reflect the non-financial information such as performances of workers etc. But operators need direct measurement on variables of outputs and inputs resources so they can control the quality of their work. The variables include time requirement relevant process to produce the output. Hence it is important for the operators to enhance their quality, productivity, and time spending on their task. As a brief concluding, operators needs measurements of performance to achieve better efficiency and effectiveness of their existing operations, which financial information did not provides. For managers, financial information alone is insufficient for decision makings because it cannot assists in controlling and directing the operational activities of the firm manufacturing process. We will write a custom essay sample on Ma Assignment or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Controlling and processing the operational activities will ensure the long run and profitability of a firm. Also, budgeting and planning the work of a firm will motivate the managers to direct their subordinates for improvement of task. The manager of a firm must assure the appropriate use of its resource. In contrast to financial information, the manager of an entity also need primarily looking forward information based on abstraction to support their makings of decisions.. It is to ensure that the resource of the company is fully utilized, and reduce the wastage to minimum level. Nowadays, competition among industries has reached an intensive stage, it’s crucial for manager to make effective decisions to survive the competition. As for executives, non financial information such as market information is important for retention or acquisition of investment and shares. In other way, customer feedback on firm performance is also a sticking point for decisions making. Customer satisfaction reflects the quality of the firm services and products. Executive could also customize their output to reach increment in customer satisfaction. An executive should be sensitive to the firm operating information such as employee morality, safety and timeliness of key business provides to succeed in their strategic proposal and the efficiency of internal operations. ( B ). Describe the differences between the management accounting information needed in manufacturing organizations and that are needed in service organizations? Normally, there are slight difference between the management information needed in manufacturing organization and service organization. Accurate cost information is required in both organization in decision making for distinguishing between profitable and unprofitable activities in addition, the required information for planning, control, performance measurement and continuous improvement. The difference in information needs are planning, that is a very essential tool in every manufacturing firm and these information assists the firm to make cost-benefit analysis of each alternative and the decision taken whereas service organization need those information while communicating directly with customer Manufacturing organization will gather and analyze data in their sales quantity, profit gain, and cost of production before manufacturing a new product however service organization focus on individual service such like after-sale service. Moreover, manufacturing organization are base on process costing but service organization are base on job-order costing. Product of manufacturing organization are homogeneous but the product of service organization are base on customer‘s demand. Furthermore, service organization needed management information such as customer feedback, survey taking, complaint and convey these information to manufacturing organization ,this help them in improvement of quality and quantity of product. Manufacturing organization needs inventories management information because it requires inventories keeping, however does not emphasize on inventories keeping because it mainly produce service which is the main product. Another point of view, service organization mainly consist of labor work while manufacturing may only need machinery supervising or labor for other purpose. As a conclusion, it is quite clear that the manufacturing cost which is also call production cost in broader terms, are losing relevance when comparing to service company to a traditional manufacturing company. ( C ) Consider the operation of a fast food company while hundreds of retail outlets scattered about the country. Identify the management accounting information needed for the followings. ( i ) The manager of a local fast food outlets that prepares food and serves it to customer who walk in and pick it up at a drive-through window. The manager of a local fast food outlets that prepares food and serves its to customer who walk in and pick it up at a drive-through window will need the information of the following, such as quality control of food served, the time taken to prepare and serve the customer, cleanliness of the outlet and employees attitude and morality. These are important factors as the company will be defamed. Also, the manager of the outlet should know the average operating expenses and revenues, the availability of stock, food or material scrapped and customer flow of that particular province. In addition, the manager must be aware of customer satisfaction toward the outlet products and services in order to improve the outlet compatibility in the future. ( ii ) The regional manager who supervises the operations of all the retail outlets in a three-state region. The regional manager will need to know the operating report of particular outlets consisting total revenues, total operating cost, total material cost, total products being sold. This manager will have to know the profitability of each outlets and average customer served. The manager should carry out survey on outlets upon their quality of services and products. Sometimes, the manager would send inspector to various outlets to report cleanliness and quality of food serve and service provided. Also, it is crucial for the manager to control the quality of each outlets. ( iii ) Senior management located at the company’s corporate headquarters. Consider specifically the information needs of the president as well as the vice president of operations and marketing. The vice president of operations will likely wish to see the report revenue and expenses and statistic of efficiency and productivity of each outlet. This particular manager will also required to know the report of cleanliness, services and customer feedback. The vice president of the marketing department will need to know the ordering rate of each product, customer flow of each outlets, average revenues and expenses of each product and service. In addition, information on competitors in relevant industries would be desirable in order to compete and survive the harsh compete. As for the president of both marketing and operating department, they would require the revenue and expenses summary obtain by the vice president, not to mention that average report on various outlet about their operating results and problems and the stock turn. With this information, the president could make the most precise decisions to help improve the outlets performance and profitability.