What Is Statistical Sampling

Many times researchers want to know the answers to questions that are large in scope.  For example: What did everyone in a particular country watch on television last night?Who does an electorate intend to vote for in an upcoming election?How many birds return from migration at a certain location?What percentage of the workforce is unemployed? These kinds of questions are huge in the sense that they require us to keep track of millions of individuals. Statistics simplifies these problems by using a technique called sampling. By conducting a statistical sample, our workload can be cut down immensely. Rather than tracking the behaviors of billions or millions, we only need to examine those of thousands or hundreds. As we will see, this simplification comes at a price. Populations and Censuses The population of a statistical study is what we’re trying to find out something about. It consists of all of the individuals who are being examined. A population can really be anything. Californians, caribous, computers, cars or counties could all be considered populations, depending on the statistical question. Although most populations being researched are large, they do not necessarily have to be. One strategy to research the population is to conduct a census. In a census, we examine each and every member of the population in our study. A prime example of this is the U.S. Census. Every ten years the Census Bureau sends a questionnaire to everyone in the country. Those who do not return the form are visited by census workers Censuses are fraught with difficulties. They are typically expensive in terms of time and resources. In addition to this, it’s difficult to guarantee that everyone in the population has been reached. Other populations are even more difficult to conduct a census with. If we wanted to study the habits of stray dogs in the state of New York, good luck rounding up all of those transient canines. Samples Since it’s normally either impossible or impractical to track down every member of a population, the next option available is to sample the population. A sample is any subset of a population, so its size can be small or large. We want a sample small enough to be manageable by our computing power, yet large enough to give us statistically significant results. If a polling firm is trying to determine voter satisfaction with Congress, and its sample size is one, then the results are going to be meaningless (but easy to obtain). On the other hand, asking millions of people is going to consume too many resources. To strike a balance, polls of this type typically have sample sizes of around 1000. Random Samples But having the right sample size is not enough to ensure good results. We want a sample that is representative of the population. Suppose we want to find out how many books the average American reads annually. We ask 2000 college students to keep track of what they read over the year, then check back with them after a year has gone by. We find the mean number of books read is 12, and then conclude that the average American reads 12 books a year. The problem with this scenario is with the sample. A majority of college students are between 18-25 years old and are required by their instructors to read textbooks and novels. This is a poor representation of the average American. A good sample would contain people of different ages, from all walks of life, and from different regions of the country. To acquire such a sample we would need to compose it randomly so that every American has an equal probability of being in the sample. Types of Samples The gold standard of statistical experiments is the simple random sample. In such a sample of size n individuals, every member of the population has the same likelihood of being selected for the sample, and every group of n individuals has the same likelihood of being selected. There are a variety of ways to sample a population. Some of the most common are: Random sampleSimple random sampleVoluntary response sampleConvenience sampleSystematic sampleCluster sampleStratified sample Some Words of Advice As the saying goes, â€Å"Well begun is half done.† To ensure that our statistical studies and experiments have good results, we need to plan and start them carefully. It’s easy to come up with bad statistical samples. Good simple random samples require some work to obtain. If our data has been obtained haphazardly and in a cavalier manner, then no matter how sophisticated our analysis, statistical techniques will not give us any worthwhile conclusions.

The Issue Of Slavery During The Westward Expansion

Between Constitutional ratification and southern secession, the United States increasingly developed sectional tensions between North and South. Regional differences and territorial expansion created the conflict of interests between the states. Proslavery southern and antislavery northern states envisioned their economical and political future in different ways. The question of slavery during the westward expansion was decisive for politics of both sides because more slave states would create voting advantages for the slaveholding states in the Congress. Northwestern territories were occupied by the new settlers from New England who established urbanized culture and infrastructure in Upstate New York and the Upper Northwest. New settlers in the Lower South organized farms and plantations to develop agricultural sector. Slavery was the main labor force in the South. With technological and transportation development, it became easier to migrate in the search of new territories. In th e first half of the nineteenth century, the North supported industrialization and manufacturing, while the South was mostly focused on the agricultural development. The whole economy of the southern states depended largely on the cotton production. For many years, the issues of slavery, human rights and racial inequality were the main topics for discussion by people, and the expansion of borders in the beginning of the nineteenth century intensified discussions around these questions. TheShow MoreRelatedThe Impact Of The Westward Expansion On Women And African Americans991 Words   |  4 Pages The Impact of the Westward Expansion on Women and African Americans The Westward Expansion started prior to The Revolutionary War, settlers were migrating westward to what states are now modern day Kentucky and Tennessee in hopes for a fruitful life and larger job opportunity. This Westward Expansion was aided through the Louisiana purchase in 1803, in which the United States purchased territory from France, resulting in doubling in size of the country. This Louisiana purchase was stretchedRead MoreWestward Expansion and the Civil War Frq1276 Words   |  6 Pages12/17/12 Block 6 Westward Expansion and the Civil War By the mid nineteenth century, the United States was expanding westward rapidly. And as America expanded, so did the sectionalism. The rifts between the North and the South, caused by conflicting views on Westward Expansion were becoming more evident. Not only were the debates over westward expansion tedious; the ever growing social debate was also becoming alarmingly prevalent. And in 1860, the Civil War broke out, ultimately because of economicRead MoreWestward Expansion Of The United States1477 Words   |  6 Pagesnation consisting of only thirteen states. Over time the leaders of this county recognized that in order to prosper the nation would need to expand beyond the current set borders. Westward Expansion was the only solution, to adopt such a large endeavor meant that the population had to have a reason to migrate west. Expansion had appeal to the Southern land owners for the fact that the Missouri Compromise did not affect territories that were not part of the Louisiana P urchase, while those who did notRead MoreThe Doctrine Of Manifest Destiny By John Louis O Sullivan1686 Words   |  7 PagesDuring the first half of the 19th century, the United States experienced westward expansion into territories, like Oregon, Texas, and California. The main incitement for the expansion was the Doctrine of Manifest Destiny. In 1845 an American columnist, John Louis O’Sullivan, introduced the term â€Å"Manifest Destiny,† which applied to the idea that America was destined to expand. According to the doctrine, America had a God given right to expand its democratic institution because Americans were morallyRead MoreThe Impact Of Westward Expansion On The United States1571 Words   |  7 Pagesopened the door to westward expansion. Thomas Jefferson purchased this extensive plot of land with the hopes of strengthening and expanding the Republic, unaware that it would have the opposite effect. Jefferson’s fateful decision to expand the United S tates nearly destroyed the Republic that Americans worked so hard to build. It triggered the rise of divisions amongst Americans. These small cracks continued to grow and tear at the seams of the nation. Although westward expansion between 1800 and 1848Read MoreThe Expansion of America and The Homestead Act of 18621180 Words   |  5 Pagescountry to keep up with the increasing amount of people and become more powerful, the US expanded westward. 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As the country matured from its initial beginnings in the latter part of the 18th century, the issues of sectarian differences evolved to include key aspects of sectional proclivities between the North and the South, and the impact of those differences on the burgeoning western portion of the U.S. The South favored slavery and the economic prosperity it brought to thatRead MoreSlavery During The American Revolution Essay1523 Words   |  7 PagesSlavery was held out until 1865, but during this time period abolitionist are trying to do anything to stop slavery. The reason being is because slavery wasn’t slavery anymore. Slavery was beginning to become more advance due to technological innovation. The Abolitionist are people that were against slavery and would boycott anything to get rid of slavery. The argument that the Abolitionist had during this time period was its conditions as violating Christian’s principals and rights to equality

Development of Jazz and Blues Free Essays

Jazz music traces its origin to a mixture of West Africa and European musical elements (Hoiberg, 2002, p. 641). It is said that slaves from West Africa took with them their music when they came to North America (p. We will write a custom essay sample on Development of Jazz and Blues or any similar topic only for you Order Now 641). There, their music was exposed to European music. Thus, it is believed that jazz evolved from a fusion of these two elements- West Africa with its rhythm and structure and from Europe, harmony and the use of other instruments such as trumpet, trombone, saxophone and piano (p. 641). The fact that its roots were in the United States and not from South America or Caribbean where there were also African Blacks is rather interesting. However, African Blacks in those regions were emancipated and thus, had the chance to practice and promote their African music tradition (p. 642). In the United States, however, there was slavery. Slaves were not able to retain their music tradition and had to rely to whatever was available to them at that time to make music. While it is unfortunate to think that such practice existed, had it not been for slave trade, we probably would not enjoy jazz music now. Jazz music was heard in various occasions, from funeral processions and parades, hymns and religious events, even for work songs (p. 642). When classically-trained black musicians could not find work, they turned to jazz and played in clubs. New Orleans was the place where jazz music evolved (Hoiberg, 2002, p. 642). At that time, musicians were limited to seven instruments- cornet, clarinet, trombone, bass or tuba, piano, banjo and drums (p. 642). Saxophone made its way into jazz music only after ten years (p. 642). In 1915, the place was teeming with jazz musicians. Among those who were well known were Buddy Bolden, Buddy Petit, and Bunk Johnson (p. 643). At this time, jazz has spilled over other places such as Kansas City, Colorado and had reached Los Angeles and New York City (p. 643). Jazz groups and orchestras had started to perform. Fate Marable’s orchestra, for instance, produced the great Louis Armstrong (p. 643). Armstrong invented swing but perhaps his greatest contribution to jazz music was introducing jazz to the entire world with his jazz recordings (p. 643). He was the â€Å"first superstar of jazz† (p. 643). He also introduced what is now known as â€Å"scat† or singing without words or texts (p.  643). Other jazz standouts were Fletcher Henderson, Duke Ellington, Benny Goodman, and King Oliver (pp. 643-644). Jazz at the end of the twentieth- century is changing. Others say that some elements of jazz have been chucked in favor of new styles (Hoiberg, 2002, p. 648) In the past, jazz had a distinct sound but it has now been replaced by â€Å"stylistic flexibility† (p. 648). Also, music schools have exposed jazz students and musicians to all aspect of music now whereas before, jazz musicians were mostly self-taught. Today, we study about music theory and styles, among other things At a time when the country was experiencing depression, jazz became an outlet of many people to release pent-up emotion. Dr. Martin Luther King, Jr. spoke about the importance of jazz music during the opening of the Berlin Jazz Festival in 1964 (Winkel, 2002). He exclaimed that jazz talks about life, that jazz deals with putting into music all the troubles in the world only to come up with something that evokes hope and triumph (2002). For King, music is â€Å"triumphant† (2002). He added that jazz contributed to the freedom movement in the United States, with rhythms and harmonies serving as encouragement and composure to the despondent (2002). Jazz was popularized by American Negroes in a time when they were struggling, when they were hopeless. Listening to jazz music soothed their tired spirits, uplifted their souls. King even compared the struggle of the American Negroes to that of the modern man. While their problems may be different, they all longed for the same thing- to find their own identities and meaning in life (2002). Music is about life and when a musician creates one, it is akin to creating life, bringing hope to anyone who can hear it. Jazz music, specifically has an undeniable magic that draws people to it. It evokes a sense of calm that sometimes you need not have to be in the presence of others to appreciate it. Unlike say rock music where listening with others make it sounds better, you appreciate rock music better when you’re in a crowded concert hall where people are in high spirits. Listening to jazz does the same effect but in the opposite way. One only needs to sit back, relax and absorb the music. While classical music can also unwind a person, the effect of jazz on the listener is more personal, more emotion. Classical music is pleasant to the ears but jazz targets one’s soul. Perhaps, it’s the way the instruments are played. In classical music, various instruments are played simultaneously to produce one distinct sound that is meant to be heard. But when one listens to jazz, one does not only hear the melody and harmony, but something more, something deeper. It’s like you can see and listen to the mood of the musician. Truly, jazz has more emotional depth. Perhaps, that is also one reason why jazz is more accessible to listeners that classical music. Also, unlike classical music, one does not need to go to opera hall to hear jazz music. Jazz can easily be heard in clubs and restaurants. Lately, jazz elements have been infused with other music forms. For instance, American pop artists like Norah Jones, Christina Aguilera and Amy Winehouse have incorporated jazz into their music. Rhythm and blues (R B) is an offshoot of jazz music that evinces funk and soul. Mariah Carey, Whitney Houston, Mary J. Blige, even Justin Timberlake are just some of the popular artists who use this style and judging by the sales of their albums, concerts, and the number of times their songs have been played over the radio and rocketing sales in music downloads, they have succeeded. It just goes to show that jazz music is really evolving. And when people continue to listen to it, jazz music will live on. How to cite Development of Jazz and Blues, Papers