How to Calculate Standard Deviation

Standard deviation (usually denoted by the lowercase Greek letter ÏÆ') is the average or means of all the averages for multiple sets of data. Standard deviation is an important calculation for math and sciences, particularly for lab reports. Scientists and statisticians use standard deviation to determine how closely sets of data are to the mean of all the sets. Fortunately, its an easy calculation to perform. Many calculators have a standard deviation function. However, you can perform the calculation by hand and should understand how to do it. Different Ways to Calculate Standard Deviation There are two main ways to calculate standard deviation: population standard deviation and sample standard deviation. If you collect data from all members of a population or set, you apply the population standard deviation. If you take data that represents a sample of a larger population, you apply the sample standard deviation formula. The equations/calculations are nearly the same with two exceptions: for the population standard deviation, the variance is divided by the number of data points (N), while for the sample ​standard deviation, its divided by the number of data points minus one (N-1, degrees of freedom). Which Equation Do I Use? In general, if youre analyzing data that represents a larger set, choose the sample standard deviation. If you gather data from every member of a set, choose the population standard deviation. Here are some examples: Population Standard Deviation—Analyzing test scores of a class.Population Standard Deviation—Analyzing the age of respondents on a national census.Sample Standard Deviation—Analyzing the effect of caffeine on reaction time on people ages 18 to 25.Sample Standard Deviation—Analyzing the amount of copper in the public water supply. Calculate the Sample Standard Deviation Here are step-by-step instructions for calculating standard deviation by hand: Calculate the mean or average of each data set. To do this, add up all the numbers in a data set and divide by the total number of pieces of data. For example, if you have four numbers in a data set, divide the sum by four. This is the mean of the data set.Subtract the deviance of each piece of data by subtracting the mean from each number. Note that the variance for each piece of data may be a positive or negative number.Square each of the deviations.Add up all of the squared deviations.Divide this number by one less than the number of items in the data set. For example, if you had four numbers, divide by three.Calculate the square root of the resulting value. This is the sample standard deviation. Calculate the Population Standard Deviation Calculate the mean or average of each data set. Add up all the numbers in a data set and divide by the total number of pieces of data. For example, if you have four numbers in a data set, divide the sum by four. This is the mean of the data set.Subtract the deviance of each piece of data by subtracting the mean from each number. Note that the variance for each piece of data may be a positive or negative number.Square each of the deviations.Add up all of the squared deviations.Divide this value by the number of items in the data set. For example, if you had four numbers, divide by four.Calculate the square root of the resulting value. This is the population standard deviation.

Essay on Summary of I Know Why the Caged Bird Sings

Summary of I Know Why the Caged Bird Sings Maya recalls an Easter Sunday at the Colored Methodist Episcopal Church in Arkansas. Her mother makes her a special Easter dress from lavender taffeta, and Maya thinks the dress will make her look like the blond-haired blue-eyed movie star that she wishes, deep down, to be. But, the dress turns out to be drab and ugly, as Maya laments that she is black, and unattractive as well. She leaves her church pew to go to the bathroom, and doesnt make it; she runs from the church, ashamed, but glad to be out of church and away from the children who torment her, and make her childhood even harder than it already is. Analysis: One of the main themes of this chapter is race and appearance; Maya†¦show more content†¦Analysis: Angelou tells of the little sensory details that make her life working and living in the store an adventure for a young girl. She recalls the smells, and unfamiliarity of the place, and the constant stream of people who made the place seem exciting and almost magical. However, the theme of romance vs. reality soon becomes plain; for even as the cotton pickers come in each morning, happy and boastful, each afternoon they come back bitter and wondering how to make enough money to make ends meet. Angelou notes the difference between the wonderful mornings and the hard reality of the afternoons, knowing that however things might seem, there are always the harsh facts of life to face. The difficulty of being black in the South is a theme that is important throughout the work; financially, it is difficult to make ends meet, and black people also face social hardship. Even in the intro to the work, Angelou reminds us that living in the segregated South during this time is never easy; not even to a child, and not even with wonderful sights and sounds around at the store. Chapter 2: Summary: Maya and her brother recite their times tables for their Uncle Willie, who was crippled as a child and whose left side of his body is shriveled and deformed. Maya and her brother are disturbed by his disability, though his mother, Mayas grandmother, blames God but accepts her son. Things are more difficult forShow MoreRelatedSummary Of I Know Why The Caged Bird Sings 1184 Words   |  5 PagesBY: Nitesh Goel I Know Why the Caged Bird Sings 1) She is described that she is poor and she is black. This proven by the quote she is a too-big Negro girl with nappy black hair, broad feet and a space between her teeth that would hold a number-two pencil. 2) Mr. Steward, the white former sheriff, comes to warn Momma that the whites were on the path to hurt or kill a black because they say a black man has â€Å"messed with† a white woman. 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In addition to a strong introductionRead MoreEssay on I Know Why The Caged Bird Sings1319 Words   |  6 Pages 1) Summary of Character Traits amp;nbsp;a) School smart (Maya is smart. When she moves to San Francisco from Stamps, Arkansas, she is skipped a grade.) amp;nbsp;b) Caring sister (she always talks of her devotion to Baily) amp;nbsp;c) Determined (she wants to get a job with the streetcar company and she keeps bugging them until they finally give her a job) amp;nbsp;d) Proud (she lives with the junkyard kids instead of going back to her father’s; she slaps Dolores for calling her mother a whore)Read MoreSister Flowers Summary Essay examples996 Words   |  4 PagesSister Flowers Summary â€Å"Sister Flowers,† is a descriptive narrative by Maya Angelou. This piece was taken from her first of six autobiographies, Why the Caged Bird Sings (1970). Angelou, with much admiration and respect, describes a woman by the name of Sister Flowers as, â€Å"the aristocrat of Black Stamps†(87), â€Å"the measure of what a human being can be†(88), and educated. Angelou, who became mute almost a year earlier after being raped at the age of eight, was at a low point in her life. She describesRead MoreRhetorical Analysis Of I Know Why The Caged Bird Cannot Sing794 Words   |  4 PagesIn Francine Prose’s essay â€Å"I Know Why the Caged Bird Cannot Sing† Prose tends to evoke her unsureness on why schools use certain books to teach students their moral values. Prose argues that certain books should be taught in English classes, that in fact, teach students their values. Prose uses several literary examples, such as Frankenstein, How To a Kill A Mocki ngbird, The Great Gatsby, etc. She also provides several controversial opinions, such as using different books to try and teach studentsRead MoreMaya Angelous I Know Why the Caged Bird Sings Essay1687 Words   |  7 PagesMaya Angelous I Know Why the Caged Bird Sings Maya shields herself against the confusion of St. Louis by reading fairy-tales and telling herself that she does not intend on staying there anyway. Vivian works in a gambling parlor at nightRead MoreEssay on Banning Books4604 Words   |  19 PagesCatcher in the Rye from high school classes after a protester reported that she had counted ‘785 profanities’ (Donelson 1985). With the offensive talk, one is clearly able to see why this book wi th the profanity alone is banned in many schools, even today. Moreover, sexuality appears to be another issue regarding why Salinger’s The Catcher in the Rye was banned in the United States. Many parts within the book dealt with sexuality in Holden’s life. For example, Holden observes the man and women

Mcdonals Kotlers Changes - 4578 Words

McDonald’s Strive for a Healthier Image by Means of Organizational Change Students: | I.D: | Merav Lezmy (Faber) | 302917042 | Yona Golran | 000799000 | Rotem Shayovitch | 302264635 | Table of Contents Table of Contents 2 Introduction 3 1) Choosing the Organization 3 2) McDonald’s Area of Expertise 3 3) McDonald’s Customer’s 4 4) McDonald’s as a Company 4 McDonald’s Transformation 5 Kotter’s 8 Steps to Organizational Transformation within McDonald’s 6 1) Creating a Sense of Urgency 6 2) Forming a Powerful Guiding Coalition 7 3) Creating a Vision 8 4) Communicating the Vision 8 5) Empowering Others to Act on the Vision 9 6) Planning For and Creating Short-Term Wins 10 7) Consolidating Improvements†¦show more content†¦2) McDonald’s Area of Expertise The McDonald’s corporation is the largest chain of hamburger fast food restaurants in the world. It is the leading global foodservice retailor with more than 35,000 chains of restaurants serving nearly 70 million people in 119 countries every day, while employing 1.8 million workers. McDonald’s primarily sell their famous hamburgers, cheeseburgers, chicken, french fries, breakfast items, soft drinks, coffee, milkshakes and desserts. In response to changing consumer tastes and growing health concerns (which we will address), the company expanded their menu to include items such as salads, fish, wraps, smoothies and fruit. Globalization has allowed McDonald’s to serve their dominant original menu, while various countries have expanded this menu and added regional market foods to the menu. For example, here in Israel, most McDonald’s chains are Kosher and it is easy to spot domestic foods while taking a quick glance at the menu. These foods include pita and f alafel. In China the menu will include many meals with rice, and in India on the other hand, because of the religious prohibition of beef consumption, the menu will be strictly dairy. 3) McDonald’s Customer’s When entering a McDonald’s chain, one can find costumers from all segments of the population. They include anywhere from young children to elderly, every race and religion, and of all kinds of economic backgrounds. The chain has gained great popularity by focusing

Looking Inside The Hollow Men Essay Example For Students

Looking Inside The Hollow Men Essay A Look Inside â€Å"The Hollow Men†Eliot, a master of the written craft, carefully thought out each aspect of his 1925 poem â€Å"The Hollow Men.† Many differences in interpretation exist for Eliot’s complex poetry. One issue never debated is the extensive range of things to consider in his TS Eliot’s writing. Because TS Eliot often intertwined his writing by having one piece relate to another â€Å"The Hollow Men† is sometimes considered a mere appendage to The Waste Land. â€Å"The Hollow Men,† however, proves to have many offerings for a reader in and among itself. The epigraph contains two pertinent references (http). First, â€Å"Mistah Kurtz – he dead† is an allusion to Conrad’s Heart of Darkness. In his novella, Conrad portrays the empty nature of men. Mistah Kurtz is a character that lacks a soul, thus, a true â€Å"Hollow Man.† In the second quotation the epigraph alludes to England’s November 5 tradition of Guy Fawkes Day. In 1605, Guy Fawkes unsuccessfully tried to blow up the parliament building. Eliot’s quote â€Å"A penny for the old guy† is called out by children on this holiday who are attempting to buy fireworks in order to blow up straw figures of Fawkes. Within the first stanza Eliot establishes the speaker, setting, theme and begins a rhythmic pattern that will hold true for four of the five sections of the poem. The speaker in the poem is not human, or at least prefers to be thought of as a scarecrow over a â€Å"†¦lost / Violent soul†¦Ã¢â‚¬  (lines 15-16). The powerful comparison between the worthlessness of â€Å"rats’ feet over broken glass†¦Ã¢â‚¬  (line 9) to their â€Å"dry voices† (line 5) illustrates how meaningless they (the Hollow Men) truly are. Two lines detached from the first stanza contain a series of paradoxes which further the idea of meaninglessness, â€Å"Shape without form, shade without color, / Paralyzed force, gesture without motion† (11-12). Although difficult to discern exactly what is going on and where in the poem, the reader easily perceives the overall feeling of the hopelessness in just the opening lines, â€Å"We are the hollow men / We are the stuffed men†(lines 1-2) establish a grim feeling of emptiness. Images like â€Å"This is the dead land / This is cactus land†¦Under the twinkle of a fading star† (lines 39-44) create a bleak, dry, desert land setting. The theme of the poem parallels those of Conrad’s Heart of Darkness (Smith). The degradation of ritual (religious or otherwise) and the emptiness or reduction of human to childish behavior is parallel concepts in both pieces. Part I of the poem describes the insignificance of the â€Å"hollow men.† Part I gives the vague setting and shows the request of the hollow men to be viewed as empty; â€Å"Remember us†¦not as lost / Violent souls which Kurtz and Fawkes both were, but only / As the hollow men† (lines 15-18). It also introduces two motifs, that of eyes and kingdom. â€Å"Those who have crossed / With direct eyes, to death’s other Kingdom† (line 13-14) is an allusion to Dante’s Paradiso (Bowler). Kingdom with a capita lized K may refer to Heaven (although all references to a â€Å"kingdom† do not), and those with â€Å"direct eyes† are allowed to go there and become blessed. â€Å"Eyes† in the poem refer to those of Charon in Dante’s Inferno (Williamson, 157). With the line, â€Å"Eyes I dare not meet in dreams† (line 19) the speaker states that the â€Å"eyes† are a source of fear. Playing a connective role in the poem, the first two lines in the first four sections have a specific rhythm. Section I’s, â€Å"We are the hollow men / We are the stuffed men† (lines 1-2) is like II’s â€Å"Eyes I dare not meet in dreams / In death’s dream kingdom†(19-20), Part III’s â€Å"This is the dead land / This is the cactus land† (39-40) and IV’s â€Å"The eyes are not here / There are no eyes here.† This language serves as a rhythmic refrain tying each section together while setting off the last. The use of literary devices in â€Å"The Hollow Men† is seemingly endless. Rhyme also plays and important role. In I, like all of the other parts (except the fifth) the final line of

An Introduction To Management Science

Question: Explain about the Report for An Introduction To Management Science? Answer: 1: Here, Expected duration = (Best case + 4 * Most typical case + Worst case) / 6 Standard deviation = sqrt (((Best case Worst case)/6) ^2) Schedule mode Best case Most typical case Worst case Expected duration Variance Standard deviation ID speaker topics ASAP 1 3 5 3.000 0.444 0.667 Contact speakers ASAP 8 9 12 9.333 0.444 0.667 Select hotel ASAP 4 5 7 5.167 0.250 0.500 Arrange hotel accommodations ASAP 2 4 4 3.667 0.111 0.333 Arrange catering ASAP 4 5 7 5.167 0.250 0.500 Develop brochure ASAP 7 9 12 9.167 0.694 0.833 Print and mail brochure ASAP 4 8 8 7.333 0.444 0.667 Develop exhibit material ASAP 10 12 15 12.167 0.694 0.833 Develop workbook ASAP 4 5 7 5.167 0.250 0.500 Print and bind workbook ASAP 3 5 6 4.833 0.250 0.500 Final set-up for conference ALAP 2 3 5 3.167 0.250 0.500 2: According to the critical path analysis, the critical path of the project is as follow: Start - ID speaker topics - Contact speakers - Develop brochure - Print and mail brochure - Develop workbook - Print and bind workbook - Finish Hence, the duration of the project will be 3 + 9.333 + 9.167 + 7.333 + 5.167 + 4.833 = 39 3: The standard deviation of the critical path will be 0.667+ 0.667 + 0.833 + 0.500 + 0.500 = 3.167 4: Let the duration of the project is D1 when 1 is added. Since, about 68% of observations lie within 1 , we have z value is 1 Therefore, (D1 39) / 3.167 = 1 Or, D1 = 39 + 3.167 = 42.167 Let the duration of the project is D2 when 2 is added. Since, about 68% of observations lie within 2 , we have z value is 1.96 Therefore, (D1 39) / 3.167 = 1.96 Or, D1 = 39 + 6.21 = 45.21 5: Expected duration Latest Start Earliest Start Float ID speaker topics 3 0 0 0 Contact speakers 9 3 3 0 Select hotel 5 9 0 9 Arrange hotel accommodations 4 15 5 10 Arrange catering 5 18 9 9 Develop brochure 9 12 12 0 Print and mail brochure 7 21 21 0 Develop exhibit material 12 23 14 9 Develop workbook 5 29 29 0 Print and bind workbook 5 34 34 0 Final set-up for conference 3 36 26 10 6: Since, both Develop workbook and Print workbook are critical activities, any changes in these activities will influence the overall duration of the project. Note that the activity Develop workbook will start as soon as ID speaker topics is complete. Hence, it will reduce the overall duration. Initially the duration was 39 days. Now it reduced to 29 days. At the same time the critical path will also change. Bibliography Anderson, D., Sweeney, D., Williams, T., Camm, J. and Cochran, J., 2015.An Introduction To Management Science: quantitative approaches to decision making. Cengage Learning. Fama, C.C.G., Alencar, L.H. and de Almeida, A.T., 2015, December. Assignment of critical path for a building site based on multicriteria approach. InIndustrial Engineering and Engineering Management (IEEM), 2015 IEEE International Conference on(pp. 1307-1311). Kim, K.J., Cho, J.Y., Lee, D.Y. and Lee, M.J., 2015. Development of an automated As-planned schedule system for efficient scheduling.KSCE Journal of Civil Engineering, pp.1-7. Selvan, M.M., Ahuja, S., Parray, R.A., Rajaiah, P. and Rangasamy, K., 2015. Overhaul maintenance of modern bulldozers with software-based management techniques (PERT/CPM).The Indian Journal of Agricultural Sciences,85(4). Trietsch, D. and Baker, K.R., 2012. PERT 21: Fitting PERT/CPM for use in the 21st century.International journal of project management,30(4), pp.490-502. Willis, R.J., 1985. Critical path analysis and resource constrained project schedulingtheory and practice.European Journal of Operational Research,21(2), pp.149-155.