Calculating the Mean Absolute Deviation

There are many measurements of spread or dispersion in statistics. Although the range and standard deviation are most commonly used, there are other ways to quantify dispersion.  We will look at how to calculate the mean absolute deviation for a data set.   Definition We begin with the definition of the mean absolute deviation, which is also referred to as the average absolute deviation. The formula displayed with this article is the formal definition of the mean absolute deviation. It may make more sense to consider this formula as a process, or series of steps, that we can use to obtain our statistic. We start with an average, or measurement of the center, of a data set, which we will denote by m.  Next, we find how much each of the data values deviates from m.  This means that we take the difference between each of the data values and m.  After this, we take the absolute value of each of the difference from the previous step. In other words, we drop any negative signs for any of the differences.  The reason for doing this is that there are positive and negative deviations from m.  If we do not figure out a way to eliminate the negative signs, all of the deviations will cancel one another out if we add them together.Now we add together all of these absolute values.Finally, we divide this sum by n, which is the total number of data values.  The result is the mean absolute deviation. Variations There are several variations for the above process.  Note that we did not specify exactly what m is. The reason for this is that we could use a variety of statistics for m.  Typically this is the center of our data set, and so any of the measurements of central tendency can be used. The most common statistical measurements of the center of a data set are the mean, median and the mode.  Thus any of these could be used as m in the calculation of the mean absolute deviation. This is why it is common to refer to the mean absolute deviation about the mean or the mean absolute deviation about the median. We will see several examples of this. Example:  Mean Absolute Deviation About the Mean Suppose that we start with the following data set: 1, 2, 2, 3, 5, 7, 7, 7, 7, 9. The mean of this data set is 5.  The following table will organize our work in calculating the mean absolute deviation about the mean.   Data Value Deviation from mean Absolute Value of Deviation 1 1 - 5 = -4 |-4| = 4 2 2 - 5 = -3 |-3| = 3 2 2 - 5 = -3 |-3| = 3 3 3 - 5 = -2 |-2| = 2 5 5 - 5 = 0 |0| = 0 7 7 - 5 = 2 |2| = 2 7 7 - 5 = 2 |2| = 2 7 7 - 5 = 2 |2| = 2 7 7 - 5 = 2 |2| = 2 9 9 - 5 = 4 |4| = 4 Total of Absolute Deviations: 24 We now divide this sum by 10, since there are a total of ten data values.  The mean absolute deviation about the mean is 24/10 2.4. Example:  Mean Absolute Deviation About the Mean Now we start with a different data set: 1, 1, 4, 5, 5, 5, 5, 7, 7, 10. Just like the previous data set, the mean of this data set is 5.   Data Value Deviation from mean Absolute Value of Deviation 1 1 - 5 = -4 |-4| = 4 1 1 - 5 = -4 |-4| = 4 4 4 - 5 = -1 |-1| = 1 5 5 - 5 = 0 |0| = 0 5 5 - 5 = 0 |0| = 0 5 5 - 5 = 0 |0| = 0 5 5 - 5 = 0 |0| = 0 7 7 - 5 = 2 |2| = 2 7 7 - 5 = 2 |2| = 2 10 10 - 5 = 5 |5| = 5 Total of Absolute Deviations: 18 Thus the mean absolute deviation about the mean is 18/10 1.8.  We compare this result to the first example.  Although the mean was identical for each of these examples, the data in the first example was more spread out. We see from these two examples that the mean absolute deviation from the first example is greater than the mean absolute deviation from the second example. The greater the mean absolute deviation, the greater the dispersion of our data. Example:  Mean Absolute Deviation About the Median Start with the same data set as the first example: 1, 2, 2, 3, 5, 7, 7, 7, 7, 9. The median of the data set is 6.  In the following table,  we show the details of the calculation of the mean absolute deviation about the median. Data Value Deviation from median Absolute Value of Deviation 1 1 - 6 = -5 |-5| = 5 2 2 - 6 = -4 |-4| = 4 2 2 - 6 = -4 |-4| = 4 3 3 - 6 = -3 |-3| = 3 5 5 - 6 = -1 |-1| = 1 7 7 - 6 = 1 |1| = 1 7 7 - 6 = 1 |1| = 1 7 7 - 6 = 1 |1| = 1 7 7 - 6 = 1 |1| = 1 9 9 - 6 = 3 |3| = 3 Total of Absolute Deviations: 24 Again we divide the total by 10 and obtain a mean average deviation about the median as 24/10 2.4. Example:  Mean Absolute Deviation About the Median Start with the same data set as before: 1, 2, 2, 3, 5, 7, 7, 7, 7, 9. This time we find the mode of this data set to be 7.  In the following table,  we show the details of the calculation of the mean absolute deviation about the mode. Data Deviation from mode Absolute Value of Deviation 1 1 - 7 = -6 |-5| = 6 2 2 - 7 = -5 |-5| = 5 2 2 - 7 = -5 |-5| = 5 3 3 - 7 = -4 |-4| = 4 5 5 - 7 = -2 |-2| = 2 7 7 - 7 = 0 |0| = 0 7 7 - 7 = 0 |0| = 0 7 7 - 7 = 0 |0| = 0 7 7 - 7 = 0 |0| = 0 9 9 - 7 = 2 |2| = 2 Total of Absolute Deviations: 22 We divide the sum of the absolute deviations and see that we have a mean absolute deviation about the mode of 22/10 2.2. Fast Facts There are a few basic properties concerning mean absolute deviations The mean absolute deviation about the median is always less than or equal to the mean absolute deviation about the mean.The standard deviation is greater than or equal to the mean absolute deviation about the mean.The mean absolute deviation is sometimes abbreviated by MAD.  Unfortunately, this can be ambiguous as MAD may alternately refer to the median absolute deviation.The mean absolute deviation for a normal distribution is approximately 0.8 times the size of the standard deviation. Common Uses The mean absolute deviation has a few applications.  The first application is that this statistic may be used to teach some of the ideas behind the standard deviation. The mean absolute deviation about the mean is much easier to calculate than the standard deviation. It does not require us to square the deviations, and we do not need to find a square root at the end of our calculation. Furthermore, the mean absolute deviation is more intuitively connected to the spread of the data set than what the standard deviation is. This is why the mean absolute deviation is sometimes taught first, before introducing the standard deviation. Some have gone so far as to argue that the standard deviation should be replaced by the mean absolute deviation.  Although the standard deviation is important for scientific and mathematical applications, it is not as intuitive as the mean absolute deviation. For day-to-day applications, the mean absolute deviation is a more tangible way to measure how spread out data are.

Metaphors In Sonnet 116 - 724 Words

William Shakespeare’s â€Å"Sonnet 116† illustrates an image of what true love is and what it is not. Through the use of imagery, the speaker defines love as unchanging and persevering, but if it isn’t, then it can’t be considered true love. Although this may be true, the speaker concludes that if he is wrong and is proven so, then his idea of love is false and no man has ever loved. The speaker begins by saying, â€Å"Let me not to the marriage of true minds / Admitimpediments† (1-2). In these lines, the speaker says he won’t impose on two lovers who possess true love for one another and prevent them from marrying. These lines are a play on the words from the Episcopal Book of Common Prayer, â€Å"If any of you know cause or just impediment†,which†¦show more content†¦In the last line, the speaker says love that isn’t real will erase if a person is willing to erase it. But even if they try to stop themselves from loving someone, real love will never disappear, or be removed. Furthermore, the speaker says, â€Å"O no! it is an ever-fixed mark / That looks on tempests and is never shaken† (5-6). In other words, the speaker is saying love isimmovable and withstands even the strongest storms. At this point in the sonnet, the speaker then goes on to explain what he thinks love really is. The overall mood of the poem changes from negative to positive. In the first line, the exclamation of â€Å"O† signifies a change in tone. Thespeaker denies that real love isn’t what he’s proclaimed until this point, but is something different. The ever-fixed mark is the North Star, which served as a guide for sailors on the sea. Like this star, love is a guide and is unmoved by the hands of time. Even though time may pass, true love will stay strong despite changes like physical beauty. Love is never shaken by obstaclesor hindrances that pose as a threat. Like a rock, it’s strong and solid. To conclude, the overall theme of the sonnet is mutual love that is unchanging. The opening remarks of marriage within the first line set the tone and overall meaning of the speaker’s definition of true love by showing how bound lovers are to each other. In Shakespeare’s time, the average life expectancy was 30 to 40 years,Show MoreRelatedComparing And Contrasting Two Sonnets1141 Words   |  5 Pages Comparing and Contrasting Two Sonnets ‘Sonnet 116’ by William Shakespeare and ‘What Lips My Lips Have Kissed, And Where, And Why† by Edna St. Vincent Millay are both sonnets that discuss companionship and a glimpse of each poet’s experiences. In ‘Sonnet 116’, Shakespeare illustrates how capability is weakened by its metaphysical stereotype and ideals such as, love, while on the contrary, in ‘What Lips My Lips Have Kissed, And Where, And Why† Millay feeds on the chaos between the idealRead MoreWilliam Shakespeare s Sonnet 116944 Words   |  4 Pages ‘Sonnet 116’ by William Shakespeare and ‘What Lips My Lips Have Kissed, And Where, And Why† by Edna St. Vincent Millay are both sonnets that discuss companionship and a glimpse of the poets’ experiences. In ‘Sonnet 116’, Shakespeare illustrates how capability is weakened by its metaphysical stereotype and ideals such as, love which never seems to wither away according to Shakespeare while on the contrary, in ‘What Lips My Lips Have Kissed, And Where, And Why† Millay feeds on the chaos betweenRead MoreShakespeare Sonnet Compare and Contrast Essay777 Words   |  4 PagesSonnet Compare and Contrast Essay Love can be expressed and described in many different ways. Shakespeare`s sonnets â€Å"116† and â€Å"18† justify that love has the ability to create extremely powerful feelings between two people, which can help them achieve the ultimate sense of happiness. To that end, when people experience true love they live a more joyful and content life. When a person finds love their lives are filled with joy and pleasure that bring true happiness into ones life. In sonnet â€Å"116†Read MoreShakespeare - Sonnet 116 Analysis and Interpretation887 Words   |  4 PagesShakespeare – Sonnet 116 Analysis and interpretation Sonnet 116 was written by William Shakespeare and published in 1609. William Shakespeare was an English writer and poet, and has written a lot of famous plays, amongst them Macbeth and Romeo and Juliet. Shakespeare lived in the Elizabethan era. At that time, the literature and art was in bloom, and his works are clearly characterized by that era both as language and theme goes. A sonnet is a poem consisting of 14 lines, three quatrainsRead MoreIs Love An Unattainable Ideal? Essay1388 Words   |  6 Pagespoints in â€Å"Sonnet 116† and â€Å"Sonnet 138.† Firstly, in â€Å"Sonnet 116†, Shakespeare analyzes love in a rhetorical manner, meaning that he is not discussing a specific relationship of his, but theorizing on the concept of love as a whole, in abstract terms. Conversely, in â€Å"Sonnet 138†, Shakespeare analyzes love in a specific manner. He looks inward to inspect a relationship between him and a woman, also known as The Dark Lady, and paints a much different picture of love than in â€Å"Sonnet 116†, in specificRead MoreImagery in Sonnet 116 by William Shakespeare627 Words   |  3 PagesThe romantic poet William Shakespeare speaks about love in his poem â€Å"Sonnet 116†. He starts out by saying what love is not; love never stops, changes, or dies. He then goes on to tell how love doesn’t termin ate with old age and loss of beauty, it guides people through tough times. Finally, Shakespeare threatens his own reputation by saying, â€Å"If this be error, and upon me proved, I never writ, nor no man ever loved†. The theme of this poem is that love is a truly powerful force that cannot be changedRead MoreThe Beauty Of Love In Shakespeares Sonnet 1161112 Words   |  5 PagesTwo of the most famous sonnets in its entire sequence of its time and modern day, are â€Å"Sonnet 130† and â€Å"Sonnet 116†. Both poems, written by William Shakespeare, revolve around the theme of love. â€Å"Sonnet 130†, compares the imperfect physical attributes of the speaker’s mistress in essence of his extraordinary love for her. â€Å"Sonnet 116†, expresses the speaker’s idea of infinite and genuine love through defining what love is and is not. Throughout both compositions, William Shakespeare communicatesRead MoreClose Reading of Sonnet Essay examp le1391 Words   |  6 PagesClose Reading of Sonnet 116 Written by William Shakespeare 2011 â€Å"Sonnet 116† written by William Shakespeare is focusing on the strength and true power of love. Love is a feeling that sustainable to alterations, that take place at certain points in life, and love is even stronger than a breakup because separation cannot eliminate feelings. The writer makes use of metaphors expressing love as a feeling of mind not just heart as young readers may see it. To Shakespeare love is an immortalRead MoreWilliam Shakespeare s Sonnet 116981 Words   |  4 Pagesform of 38 plays, 154 sonnets, and two narrative poems† (â€Å"The Life of William Shakespeare†). William Shakespeare’s plays, sonnets, and narrative poems are still appreciated and read today. One of his famous works is his sonnet, Let Me Not to the Marriage of True Minds, which is also referred to as sonnet 116. Sonnet 116 was first published in the year 1609. In his sonnet Let Me Not to the Marriage of True Minds, Shakespeare’s use of end rhyme, iambic pentameter, and metaphors which allows the readerRead MoreEssay about Copmaring Shakespeares Sonnets 116 and 1471489 Words   |  6 PagesCopmaring Shakespeares Sonnets 116 and 147 Light/Dark. Comfort/Despair. Love/Hate. These three pairs of words manage to sum up William Shakespeares Sonnet 116 and Sonnet 147, while also demonstrating the duality of Shakespeares heart. Sonnet 116 reveals to a careful reader the aspects of Shakespeares concept of what ideal love is. However, Sonnet 147 shows the danger of believing in this ideal form of love. These two sonnets perfectly complement and clarify each other

The Sexual Objectification of Women Free Essays

The sexual objectification of women on the mass media is becoming an alarming affair. According to Faridah, et al.’s study, the uses of sex images of women in advertising by different companies who seek to promote their products are doing an injustice to women (Faridah, et al. We will write a custom essay sample on The Sexual Objectification of Women or any similar topic only for you Order Now 4). It is a challenge the in the modern democracies with regards to the objective of building an egalitarian society. It is worrying that the modern democracies would still promote women objectification. It seems that the leaders have remained so dormant and silent in pointing out the levels of discrimination exercised in the mass media in the name of advertisement (Berberick 12). Another thing is that mass media has been used as an instrument to advocate for equal rights among different genders in the society; while on the other hand, it is used to discriminate women sexually. This study is done through different means, which include social, psychological, philosophical and economic rights that examine the way sexual objectification of men infringes on their rights. In this milieu, the media should not be used to exploit women but should be used to promote their rights and the protection different people from the various levels of discrimination. Therefore, this study is important to address the issues of exploitation and discrimination perpetuated by the advertisement companies that promote various products in the market.Literature ReviewThe portrayal of women in the mass media makes them appear vulnerable to manipulation. Scholars such as Turner are worried that women are thinly represented in as actors in the existing news programs, but are instead used negatively in advertising certain products (Turner 2). They appear as young and slim in the advertising programs in the televisions as well as magazines for eye-catching purposes. The women on such advertisement platforms are explicated as instruments to inspire women to like certain products. Their main role is just to make men happy as sexual objects rather than people with value and personality. They are shown to embody every trait of beauty aimed to attract men in like those products. The society is tailored in a way that women are only perceived to look good to impress men, not for their own good. The products are advertised and made to imply that when used, the skin becomes flawless and beautiful that can be admired by men. It is a very unfortunate affair that should be discouraged by all means in the contemporary society for a sustainable greater posterity.Another thing to point out is that the decision to place anything in the media program is influenced by the current state of cultural and social values. In different societies, such values are greatly based on gender. Females in that respect are considered weak and lesser beings to their male counterparts. Through cultural and social norms, women’s rights have been violated, and that is why the same spirit spirals to the media advertisements, which portrays women as objects, not humans with values and images to protect. Punyanunt-Carter did a study on the African-American portrayals on the televisions and confirms that this group of people is more objectified in the American televisions (Punyanunt-Carter 245). Faridah, et al. on the other hand states that the movies produced around the periods of the fifties portrayed women as perfect objects of domesticity, while in the contemporary world, women are portrayed as sexual objects that make men happy and satisfy their sexual desires (Faridah et al. 7). The most important question to answer is why women must just be implicated negatively and vulnerable. Even if at times they are portrayed as professionals at times when out of their offices, they are given a negative image. They are only seen as those that can only be teased, admired, played upon and desired by men. In her study on women images in Polish and Malaysian print media, her findings pointed out that even if done in done in different cultures, the study about women portrayal has some profound similarities and commonalities in the findings.The regrettable thing addressed by the experts involved in the subject of women discrimination in the social media is that despite the efforts to establish a gender sensitive society where people are treated equally, there are still rampant cases of discrimination against women in various fronts. Faridah et al. is worried about the same, more so the words used to describe women when portrayed in the social media (Faridah et al. 5). She says that when the media decided to focus on women in the public space during the 1995 Fourth World Conference on Women in Beijing, the terms used were very unpleasant. In fact, she considers the words like ‘burning bras’, ‘hardcore feminists’, and ‘nude women running around the streets of Huarious’ among others to be devilish and uncalled for in the contemporary society. This is a weighty proof that the society still remains negative about women and only considers them objects of sexuality that cannot stand for anything good. Even if they try to do something significant, they are only seen to be irrelevant. Methodology The study relies greatly on the existing pieces of literature to paint the image of women portrayal in the televisions. It is part of the wider study of women and children’s representation in the contemporary media, which include unprinted and printed media. It is generally a qualitative study that relies on the literature about women negative portrayal on the televisions in the United States of America, which is used as a case study to represent some of the discriminations against women that are undertaken silently in the social media. The ideas by Faridah et al. and Punyanunt-Carter are significant since they explore different findings that have common issues worth addressing in women discrimination in the social media. The scholars are credible in their studies as they explore different pieces of information from different scholars to justify their arguments. They use longitudinal approach to expose the various stereotypical ways in which women are disregarded in the society. I chose the sources since they provide a thrust of the investigation, which is thought-provoking to the readers who are carried with their findings to be part of the fight against women discrimination in the social media. Positionality I do this study with an aim of addressing some of the injustices done on women in social media. The negative portrayal of women in different fronts like television, magazines, and internet makes them feel less valued in the society. It appears that the society is only happy when they are used. They are seen to best fit as objects to make men happy and satisfy their sexual needs. Sexual objectification lowers their self-esteem. The awful thing is that women from other cultures are more objectified than others are. Women from African-American communities are more portrayed negatively than those from other cultures. This means that social media are only used by the society to promote the cultural negativity about women, something that seems to be more embedded in people. This implies that there is a serious need for attitudinal change to ensure that that mindset is alleviated. Women deserve recognition and respect just as their male counterparts are. They should not be seen as second-class citizens but should be regarded with an utmost value they deserve.Studies show that the spirit of discrimination against women stems from the tradition that only regarded men to manage media. Women are meagerly represented in the employment positions. Faridah et al. states that only 33.3% of women are in full-time employment among the 59 countries they surveyed (Faridah et al. 3). It implies that women do not equal men when it comes to job competition and other important positions in the society. Another unfortunate thing is that different studies have been done on the subject of women discrimination in the social media, but nothing much has changed. It means that various experts need to be more vigorous in addressing the problem of women discrimination in the social media. The revolutionary change in technology has made it easy to sexually objectify women, something that needs to be addressed with sufficient attention to change negative attitude that makes it easy to discriminate women in the social media and other areas. The numbers of women that appear in the social media as main actors are few, but those that are shown on the negative side of the shows are many. Even though men are also objectified, their number is smaller. It means that there is much to be done to deal with the issue of women discrimination. It is also apparent from the study that women are highly discriminated in the social media. The negative portrayal of women on television is fueled by the social and cultural norms that consider men to be superior beings to their female counterparts. They are seen to best fit to make men happy by serving their sexual desire. This mindset does not believe that women can look good for their own sake, but that they do so to attract men. As a result, it is ostensible that it is a negative mindset, which kills women’s self-esteem, significance and values, as opposed to men who are seen to be important and worth the best in the society. It remains a serious matter that should not be allowed to thrive in the contemporary society. Conclusion This study confirms that it is utterly bad to continue the negative portrayal of women in the social media, more so in the contemporary world. As pointed out herein, the portrayal of women in the social media has been marred by a lot of discrimination. For instance, during the fifties, women were pictured as perfect objects of domesticity. Today, they are portrayed as sexual objects that can only be used to make men happy and satisfy their sexual desires. As a result, they are seen to be significant and less valued in the society apart from being there to make men happy. The most regrettable thing is that besides the numerous studies than on the same area, the discrimination against women still thrives. This means that social and cultural norms that disregard women should be attacked and changed. The best way to attack such norms is attitudinal change communication, which would make the society to see life more differently. Instead of being viewed as objects to make men happy, they should be seen as entities that should be incorporated in different avenues to help the society to grow. How to cite The Sexual Objectification of Women, Papers

Justice in Othello free essay sample

Justice is a powerful force, one that continuously motivates the actions of an individual. Each individual has a different understanding of what justice is, and many will go to extreme measures to receive justice. In Othello, William Shakespeare develops the idea that an individual will go to extreme measures in order to obtain his own sense of justice. However, the individual will go to such extremes in an attempt to receive justice that the repercussions of his actions will overpower the feeling of success he attains in his endeavour. When an individual feels as though he has been robbed of his rightful acknowledgements, he will go to extreme measures to obtain justicein fact, in working to attain justice, he will end up lapsing into a plot of revenge. Iago feels wronged by Othello when Cassio is chosen as Othello’s new lieutenant. He feels that this is clearly unjust, as Iago believes that he would be much better suited for the job. We will write a custom essay sample on Justice in Othello or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page In his planning to obtain justice for himself, he plots revenge on not only Othello, but on Cassio as well. Iago’s plans are all going well, and he would have gotten away with everything had his wife, Emilia, not spoken up after Desdemona’s death and told Othello what her husband had done. Iago’s actions, although his plans were well thought-out and cleanly executed, ultimately led him to his own demise, as Cassio was put in charge of Iago’s torture. Iago also feels that Othello is unjustly in a position of power and authority. He feels as though it is a personal offense to him that a â€Å"Moor† should be in a higher position than he is. Because Iago feels that Moors are below him, he acts out against this injustice. For Iago, justice is the same as enacting revenge on everyone who has wronged him, or treated him unjustly. An individual who seeks justice against a loved one will go to even greater extremes to obtain this justice. However, because the actions taken were more extreme, the consequences will also be worse. Othello suspects that Desdemona is being disloyal to him and sets out to gain justice. In his eyes, he cannot obtain his justice while the person who has wronged him is still living. However, after learning that Iago tricked him into mistrusting Desdemona, the magnitude of what he has done becomes apparent to him, and he kills himself. Othello is an individual who strongly supports the idea that when an individual treats another unjustly, he should be subject to whatever punishment the wronged individual sees fit in order to obtain his sense of justice. The search for justice has a significant impact on the play as a whole. This search is ultimately the driving force behind the story. Although revenge plays a role, the revenge is prompted by the desire for justice after having been wronged. Without the characters’ separate quests for justice, the play would have no driving force behind it, and the characters themselves would have not motivation to prompt their actions. When an individual searches for justice, he will find that the extremity of his actions lead to severe repercussions that ultimately outweigh the success of attaining his justice. Seeking revenge as an attempt to feel as though justice has been served eventually leads to the downfall of the individual, whether by his own feelings of guilt or by the actions of others.