Sample Standard Deviation Example Problem

This is a simple example of how to calculate sample variance and sample standard deviation. First, lets review the steps for calculating the sample standard deviation: Calculate the mean (simple average of the numbers).For each number: subtract the mean. Square the result.Add up all of the squared results.Divide this sum by one less than the number of data points (N - 1). This gives you the sample variance.Take the square root of this value to obtain the sample standard deviation. Example Problem You grow 20 crystals from a solution and measure the length of each crystal in millimeters. Here is your data: 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4 Calculate the sample standard deviation of the length of the crystals. Calculate the mean of the data. Add up all the numbers and divide by the total number of data points.(925412781193741254109694) / 20 140/20 7Subtract the mean from each data point (or the other way around, if you prefer... you will be squaring this number, so it does not matter if it is positive or negative).(9 - 7)2 (2)2 4(2 - 7)2 (-5)2 25(5 - 7)2 (-2)2 4(4 - 7)2 (-3)2 9(12 - 7)2 (5)2 25(7 - 7)2 (0)2 0(8 - 7)2 (1)2 1(11 - 7)2 (4)22 16(9 - 7)2 (2)2 4(3 - 7)2 (-4)22 16(7 - 7)2 (0)2 0(4 - 7)2 (-3)2 9(12 - 7)2 (5)2 25(5 - 7)2 (-2)2 4(4 - 7)2 (-3)2 9(10 - 7)2 (3)2 9(9 - 7)2 (2)2 4(6 - 7)2 (-1)2 1(9 - 7)2 (2)2 4(4 - 7)2 (-3)22 9Calculate the mean of the squared differences.(4254925011641609254994149) / 19 178/19 9.368This value is the sample variance. The sample variance is 9.368The population standard deviation is the square root of the variance. Use a calculator to obtain this number.(9.368)1/2 3.061The population standard deviation is 3.061 Compare this with the variance and population standard deviation for the same data.

The Museum Of Modern Art - 2070 Words

Before the 19th century, artists mainly made artwork for the wealthy people and the religious groups. They were controlled by the academy and painted in a way that mainstream society recognized. Many of their paintings depicted scenes of mythology and church. However in the 19th century, industrialization brought many new technologies to ordinary people, making the impossible possible. Many artists began to create artworks to explore the concept of symbolism. Many of their subjects were daily things such as ordinary people, normal places and the things they had direct experience on. They challenged the traditional concept that artists must depict realistic worlds. Instead, they used a wide range of colors, materials and techniques to†¦show more content†¦Van Gogh depicted clouds and stars in whirly shape in order to direct the viewer ´s eye around the painting. When standing in front the painting, one would spontaneously be attracted by those swirls and would follow one sw irl to another. These elements make the painting seems to be fluid and abstract. The yellow crescent moon at the upper right corner is blight and mild. It softens the painting to convey a sense of serenity. Compared to other Impressionist paintings, Starry Night is somehow different: van Gogh used very expressive color and distorted form to give the viewers a very bright picture. Van Gogh wrote a letter to his brother to point out that compared to other Impressionist artists of that time, he utilized â€Å"exaggeration in terms of composition.† He uses techniques such as surrealism to draw those swirls. In Starry Night the landscape seems to be a way to convey the artist’s emotion. I believe that the fight van Gogh had against his mental illness is reflected in the painting. When looking at the upper sky in the painting, there is a strong contrast between the sky and the stars, similar to what van Gogh experienced that time: his illness and his hope to recover. Van Gog h painted the village in dark color but on the contrary, he used bright color to draw the windows. I think this contrast gave people the idea that finally human should have hope and try their best to overcome the

Active And Passive Euthanasia free essay sample

Euthanasia is the act of ending another person’s life, either with or without their consent or assistance, performed generally in order to end one’s suffering.   It manifests in two main forms; â€Å"active euthanasia† is the act of directly causing someone’s death, either with or without their permission, while â€Å"passive euthanasia† relies on inaction rather than action – usually ending treatment that could prolong a patient’s life and allowing death to occur naturally.   The former is basically â€Å"mercy killing,† while the latter can be considered â€Å"letting nature take its course.† Physician-assisted suicide differs from active euthanasia because the former gives patients control of the process that results in their death.   With physician-assisted suicide, the choice rests with the patient, who voluntarily commits suicide and enlists a doctor’s help only to provide the means without performing the act.   Euthanasia is different because the patients do not actually kill themselves, but are allowed to die (in the passive case) or put to death by others (in the active variety). Two schools of thought exist on the moral differences between active and passive euthanasia.   Conventional morality tolerates some degree of the latter, while the former is considered unconditionally wrong, little better than murder itself.   The American legal and medical professions tend to agree and enforce this doctrine; according to the AMA, â€Å"Whether a specific case of euthanasia is ‘active’ or ‘passive’ has nothing to do with whether or not the patient consented to it,† which seems to make a case against euthanasia in general because patients’ consent has no bearing (AMA).   Also, the United States Supreme Court makes no distinctions between the types. However, advocates of euthanasia, like James Rachels, claim that active euthanasia is acceptable, even desirable; he writes that â€Å"active euthanasia is in many cases more humane than passive euthanasia† (Rachels).   Instead, he claims that passive euthanasia is morally the same as watching someone die in an accident while refusing to save them, and that withholding life-sustaining treatment only prolongs the patient’s agony, so actively ending that person’s life is actually morally more acceptable. Rachels also argues that the grounds for such arguments are themselves outmoded and inherently incorrect.   This view assumes that one agrees that the best action causes the greatest benefit (or, if nothing else, the least unhappiness for patients and relatives alike). Between the two, I find active euthanasia more morally acceptable, since it is often quick and painless.   Simply ceasing treatment and allowing a patient to die naturally can be callous because, in many cases, the patient will continue to suffer until death.   I do not necessarily agree with Rachels’ notion that passive euthanasia is the same as watching someone drown and refusing to assist, though, since the former act is generally not done out of cruelty or indifference.   However, I agree with Rachels’ point of view, which argues that active euthanasia is at times more favorable and even more humane than the passive type (which can prolong a patient’s suffering). In cases of permanently comatose or brain-dead patients, it seems more humane to allow them to die with dignity than to live artificially However, I am ambivalent about the issue because I am aware that many consider any for of euthanasia little more than murder. I believe my reasons for advocating active euthanasia are consequential, since they center on the most relevant concern – the patient’s welfare and dignity.   A brain-dead patient has no quality of life to speak of, while the terminally ill generally suffer greatly.   Keeping them alive with no legitimate hope of recovery, as James Rachels claims, does seem cruel because it prolongs their suffering.   Allowing their lives to end quickly and painlessly appears more humane.   However, I am aware of the law’s position on euthanasia, as well as the religious considerations.   Also, there is the possibility of euthanasia being applied unnecessarily or against the patient’s will, or in cases where the patient is not as ill as initially thought. Permanently comatose (or â€Å"brain-dead†) patients pose another dilemma, because they are unable to actively participate in the act of euthanasia.   They cannot issue orders or make decisions, leaving them wholly at the mercy of physicians or family members who consider death a more dignified state than being a vegetable.   (In this case, euthanasia can be only active, and places much more responsibility for the death in the caregivers’ hands.) This was the case in the Terri Schiavo controversy, in which the permanently brain-damaged patient’s family and husband took opposite stances on whether her life should be ended.   Her devoutly Catholic relatives objected on primarily religious grounds and did not concede that she was as brain-damaged as some experts maintained, and the matter became a sort of national referendum on euthanasia itself, with right-to-die advocates siding against the religious right and briefly involving Congress. SOURCES Anonymous.   â€Å"Active and Passive Euthanasia.†Ã‚   BBC – Religion and Ethics.   2005.   http://www.bbc.co.uk/religion/ethics/euthanasia/active_passive.shtml. Anonymous.   â€Å"Euthanasia Assisted Suicide.†Ã‚   Constance Perry. Ph.D.   http://www.pages.drexel.edu/~cp28/euth1.htm. Rachels, James.   â€Å"Active and Passive Euthanasia.†Ã‚   2002.   Perspectives on Death and Dying.   http://www2.sunysuffolk.edu/pecorip/SCCCWEB/ETEXTS/DeathandDying_TEXT/Rachels_Active_Passive.htm.