How to Calculate a Sample Standard Deviation

A common way to quantify the spread of a set of data is to use the sample standard deviation. Your calculator may have a built in standard deviation button, which typically has a sx on it.   Sometimes it’s nice to know what your calculator is doing behind the scenes. The steps below break down the formula for a standard deviation into a process. If youre ever asked to do a problem like this on a test, know that sometimes it’s easier to remember a step by step process rather than memorizing a formula. After we look at the process we will see how to use it to calculate a standard deviation. The Process Calculate the mean of your data set.Subtract the mean from each of the data values and list the differences.Square each of the differences from the previous step and make a list of the squares.In other words, multiply each number by itself.Be careful with negatives. A negative times a negative makes a positive.Add the squares from the previous step together.Subtract one from the number of data values you started with.Divide the sum from step four by the number from step five.Take the square root of the number from the previous step. This is the standard deviation.You may need to use a basic calculator to find the square root.Be sure to use significant figures when rounding your answer. A Worked Example Suppose youre given the data set 1,2,2,4,6. Work through each of the steps to find the standard deviation. Calculate the mean of your data set.The the mean of the data is (12246)/5 15/5 3.Subtract the mean from each of the data values and list the differences.Subtract 3 from each of the values 1,2,2,4,61-3 -22-3 -12-3 -14-3 16-3 3Your list of differences is -2,-1,-1,1,3Square each of the differences from the previous step and make a list of the squares.You need to square each of the numbers -2,-1,-1,1,3Your list of differences is -2,-1,-1,1,3(-2)2 4(-1)21(-1)21121329Your list of squares is 4,1,1,1,9Add the squares from the previous step together.You need to add 4111916Subtract one from the number of data values you started with.You began this process (it may seem like awhile ago) with five data values. One less than this is 5-1 4.Divide the sum from step four by the number from step five.The sum was 16, and the number from the previous step was 4. You divide these two numbers 16/4 4.Take the square root of the number from the previous step. This is the standard deviation.Your st andard deviation is the square root of 4, which is 2. Tip: It’s sometimes helpful to keep everything organized in a table, like the one shown below. Data Data-Mean (Data-Mean)2 1 -2 4 2 -1 1 2 -1 1 4 1 1 6 3 9 We next add up all of entries in the right column. This is the sum of the squared deviations. Next divide by one less than the number of data values. Finally, we take the square root of this quotient and we are done.

The Awakening Of The Third Eye - 759 Words

Poetry Poetry has always been way instrumental in my life. It’s a way for me to express how I feel to myself; it is a beautiful paradise, and poetry is the awakening of the third eye. The ability to view thing as the are, although they may not appear to be that way to the natural eye Also because of its traits of presenting imagery, its ability to make things out of an object that may not seem to be tangible, known as poetry in motion, Rappers, speakers and also singers may be identified as poets depending on the degree of truth, they shown their talks, raps or music. Poetry has the ability to make ugly truths look beautiful; for example, outsiders looking in may say rappers perpetuate the violence that has been seen in certain communities, schools and events that happen. On the other hand rappers believe that the violence that they have encountered in these communities, schools and events creates the music, speeches or songs. Since the beginning of time poets has been known a s storytellers, teachers and messengers. Poets would carry messages from different tribes to tribe reporting different knowledge also news to the world they knew. The reason being I want, well I am going to be one of the most prolific poets in this generation is, I want to never die, I want to always be immortal. Doctor Martin Luther King once said that you want to leave more on this earth than you took from it. Although Martin Luther King may not be here with us in his earthly body, his words willShow MoreRelatedChopin: External Narration695 Words   |  3 Pages1 Lecturer: Dr David Coughlan Tutor: Dr Jason King Date: 02 November 2009 Giving examples from Chopin’s The Awakening, explain what you understand by internal and external narration, restricted and unrestricted narration, and focalisation. How does the narrative point of view in The Awakening contribute to its theme of â€Å"an awakening†? 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Should Marijuana Be Legalized - 1057 Words

The topic of marijuana is so widely discussed and argued upon. Those that go against legalizing the use of marijuana instinctively believe people just want to casually smoke it and achieve the â€Å"high† sensation. Those that choose not associate themselves with marijuana all together are undoubtedly in favor of keeping it illegal. Opposing views on the issue of decriminalizing the plant has caused much debate over the past century and still establishes itself as an important matter. The legalization of marijuana in the Unites States would drastically reduce crime in our cities and form a more productive society through its positive uses. The war on drugs deals with every level of society. Annually, the U.S. government uses a hefty†¦show more content†¦Over twenty years later, Buckley s words still stay true today. Just eight years later an author speaking on the legalization of marijuana summed up the feelings of anti-pot laws activists by saying, Decriminalization is supported by an increasing number of responsible persons who are seeking a rational and humane solution to an issue too long dominated by myth, emotion and misunderstanding (Price). A professor of psychology, Ethen A. Nadelmann, is for the legalization of marijuana in America because he feels that the present marijuana control policies are expensive and inefficient in preventing drug problems. He disputes in the book Clashing Views, that more emphasis should be put on addictive drug treatment other than on marijuana prohibition. In terms of a criminal justice approach to the drug problem, everything we have done in the past, are doing now, and are talking about in the future is inherently limited in its effectiveness against the fundamental problem of drug abuse (Nadelmann). Government spending is the main reason for the many Americans that are assertive towards getting pot legalized. The National Clearinghouse on Smoking and Health states, The federal government spent $1 billion on marijuana enforcement in 1980 and about $5 billion in 1990. State and local spent between $3 and 4 billion in 1980 which means they may now be spending $10 billion presently (Goldberg).

In Hamlet, are Gertrude and Ophelia weak willed and morally suspect Essay Example For Students

In Hamlet, are Gertrude and Ophelia weak willed and morally suspect Essay In William Shakespeares time women had a very uncertain place in society, differing greatly from the standards of today, which were brought about partly by the Womens liberation and suffragette movement in the early 20th century. In Elizabethan times women were seen as subservient to men, insignificant and as many have argued second class citizens, with their rightful places being only to bring up children and housekeep in all cases except the rich and the aristocracy. In fact if a woman did not raise children and marry they were more than likely a prostitute or whore. This is very apparent throughout Shakespeares work as the roles of women were traditionally played by men and even more apparent is the fact that even the most important female characters appear to have had significantly fewer lines than those of their equivalent male counterparts. In Hamlet the predominant female characters are indeed the only female parts in the entire play, one being the strong regal Gertrude the Queen of Denmark and the other, weak, insecure Ophelia, daughter of Polonius and Hamlets uncertain lover. Gertrude can be viewed both as a confident, powerful figurehead and as a loving mother, although in saying this, I may create the illusion that she has a split personality which is not the case. The truth is superbly demonstrated in her relationship with Hamlet, as it is not that of a stereotypical mother and son, but more as an incestuous lovers relationship. Shakespeare was by no means the first to touch upon the idea of incest in his works, as it had been a popular theme widely used since the ancient Greek tragedies, such as Oedipus Rex. Their relationship is very like that of two lovers, it has its passionate highs and numb lows, its violent turmoil and gentle, intimate moments. Every aspect of their unusual interaction is portrayed graphically in director Franco Zefferellis interpretation of Act 3 Scene 4, which is staged in Gertrudes chamber and at its opening sees Hamlet and his mother engrossed in a passionate argument, which through Gertrudes effort is soon defused into a gentle intimate, more platonic exchange of comforting words in Gertrudes effort to heal the emotionally scared Hamlet. The peace, however is soon disturbed again when Hamlet launches a verbal attack on his mother, questioning her morals and the reasons she could possibly give for marrying his uncle so soon after the late kings death as he describes his disgust at her actions: Such an act That blurs the grace and blush of modesty, Calls virtue hypocrite, takes off the rose From fair a forehead of an innocent love, And sets a blister there, The aforementioned verbal attack is demonstrated with immense force in the very violent and somewhat sexual grapple that takes place between Gertude and Hamlet, underneath the canopy of the grand and luxurious four-poster bed. Due to the abuse Hamlet so vexingly administers to his mother, toward the end  of the scene the usually invulnerable Gertrude is reduced to a quivering wreck, filled with remorse and self-pity she begs Hamlet to stop, Oh Hamlet speak no more, Thou turnst mine eyes into my very soul, And there I see such black and grained spots as will not leave their tinct. In my opinion a reasonable explanation for Gertrudes actions and her haste to marry again so soon after King Hamlets death may be that she craves sexual fulfilment, the royal status of Queen, the continuation of the royal line and, to a lesser extent, stability and succession for her son. I arrived at this conclusion after Hamlets profuse insistence that his mother should remain abstinent and not engage in any voluntary intimacy with Claudius, which leads me to believe that Gertrudes exuberant libido and greed for a luxurious lifestyle is her greatest weakness. Gertrudes hastened remarriage could also help to paint her in a new light, as a vulnerable woman devoid of any obvious male protection following her husbands death. Her aforementioned re-marriage as a monarch to the deceased kings brother, would not have been much of a taboo to the Elizabethan audience, who had witnessed a similarly quick royal marriage in recent history, when the Tudor, king Henry VIII married his late brothe rs widow; Catherine of Aragon less than 100 years before in 1503. Hamlet - A Comparison To Humanity EssayAs a would draw it. Long stayed he so; At last, a little shaking of mine arm, And thrice his head thus waving up and down, He raised a sigh so piteous and profound As it did seem to shatter all his bulk, And end his being; that done, he lets me go, And with his head over his shoulder turned, He seemed to find his way without eyes, For out a-doors he went without their helps, And to the last bended their light on me. Hamlets madness can be viewed as nothing more than a ploy to avoid the affections of the sexually innocent Ophelia and in affect reject her, in this way as well as inflicting physical pain he leaves emotional scares which lead to Ophelias eventual madness Ophelias suicide only being implied suggests to me that Shakespeare has introduced a clever underlying sub-plot filled with suggested ideas of conspiracy within the royal court. My interpretation of this sub-plot is that, opposed to the more predominant theme, which suggests Ophelias mumblings and apparent insanity resulted in her untimely death, her sudden explosion of passionate anger was in reality the release of pent up frustrations brought about by years forced to be a non-individual, moulded very much of her father and brothers design. Her build up of aggression may not have resulted in madness but in the release of her own opinions and her rebellious questioning of the civilised royal society. This build up of aggression can be interpreted from her quick-witted exchange with Hamlet in Act3 Scene2 as she is disconcerted by and retorts to Hamlets sexual backchat using quick and abrasive replies: I think nothing my, lord And: Ay my lord. It is apparent that she may have inclinations to make a stand against the morals of her superiors as within her twisted and encrypted ramblings she makes profound statements regarding amongst other things disgust at the treatment of her fathers death as she bitterly retorts I would give you some violets, but they withered all when my father died, In response to this, I think the members of the court decided that the chance of any more damaging comments should be stopped, and Ophelia silenced. Such a conclusion may seem very far fetched and not evidentially based in the text, but further reading into the subsequent scenes following Ophelias death, show that many aspects of her death, the discovery of her body and her eventual burial are shrouded in mystery. This mystery is apparent in the conversation that takes place between the two gravediggers in Act5, Scene 1, as the two men question why, Ophelia, who supposedly committed suicide and in turn disobeyed God should be buried on sanctified ground: Is she to be buried in christian burial when she wilfully seeks her own salvation? Later in their conversation the two further question whether in fact her death was a suicide at all and even imply that she may have been drowned: If the man go to this water and drown himself, it is, will he, nill he, he goes, mark you that. But if the water come to him, and drown him, he drowns not himself; argal, he that is not guilty of his own death, shortens not his own life. In conclusion, I think that however different Ophelia and Gertrude  may appear from the outset, they both cannot help but to conform to the ideas of the different social standings for men and women of the age. Ophelia being under the control of her father, brother and the chauvinistic Hamlet and Gertrude, although she makes great efforts to appear strong, under the control of King Claudius. In this way, Ophelia like Gertrude is very stereotypical of the age in the way she serves and is oppressed by the men in her life. This is apparent throughout her relationship with Hamlet, of which Hamlet is definitely in control. Also, she is obviously been under the control of her father and brother since her mothers death.