Also, the 52 percent comes from the sample, so it is important to ask if the sample was large enough, unbiased, and review randomly chosen. One also needs to be aware of margins of error and confidence intervals. If the margin of error for this survey is 5 percent than this means that the percentage of car owners in the United States who prefer Chevrolet could actually be between 47 and 57 percent (5 percent higher or lower than the 52 percent). Similar questions are important to consider when we try to understand polls. During the 2000 presidential race, the evening news and newspapers were often filled with poll reports. For example, one poll stated 51 percent of Americans preferred george. Bush, 46 percent preferred Al Gore, and 3 percent were undecided, with a margin of error of plus or minus 5 percent.
If this is the case then there is a 5 percent chance that this sample data does not typify make or carry over to the population of the United States. The margin of error represents the range of this 95-percent confidence interval (the range that represents plus or minus two standard deviations from the mean ). Understanding and Interpreting Data figuring out what data means is just as important as collecting. Even if the data collection process is sound, data can be misinterpreted. When interpreting data, the data user must not only attempt to discern the differences between causality and coincidence, but also must consider all possible factors that may have led to a result. After considering the design of a survey, consumers should look at the reported data interpretation. Suppose a report states that 52 percent of all Americans prefer Chevrolet to other car manufacturers. The surveyors want you to think that more than half of all Americans prefer Chevrolet, but is this really the case? Perhaps not all those surveyed were Americans.
Considering Margin of Error. Margin of error is important to consider when statistics are reported. For example, we might read that the high school dropout rate declined from 18 percent to 16 percent with a margin of error of 3 percent. Because the 2-percentage point decline is smaller than the margin of error (3 percent the new dropout rate may fall between 13 percent to 19 percent. We cannot be entirely sure that the high school dropout rate actually declined at all. Confidence intervals, a term usually employed by statisticians, and related to margins of error, is reported by a percentage and is constructed to relay how confident one can be that the sample is representative of the population. The producers of this survey may only be 95 percent confident that their sample is representative of the population.
Data representation - integers, Floating
Informed citizens who are assessing survey results must consider the type of questions that are asked when a survey is conducted. Were the questions leading? Were they easy or difficult to understand? For example, suppose a study carried out by a local ice cream manufacturer states that 75 percent of Americans prefer ice cream. It seems self-evident that an ice cream company would not report a study that showed Americans do not like ice cream. So perhaps the question in the study was leading: for example, "do you prefer ice cream or spinach?" It is therefore important to find out exactly what questions were asked and of whom. Giving a proper Interpretation.
Data are often interpreted with a bias, and the results can therefore be misleading or incomplete. For example, a bath soap company claims that its soap is 99 percent pure. This statement is misleading because the soap manufacturer does not explain what "pure". When reading an unclarified percentage such as in the previous example, one needs to ask such questions. An example of another incomplete or misleading interpretation is that the average child watches approximately 5 hours of television a day. The reader should question what an "average child".
Multiplying that figure by 35 percent (the number of households that did not return the forms) gives the staggering figure.875 million forms that were not returned. Of the.875 million households that did not return forms, census takers were unable to track down 20 percent,.375 million households. Why is this biased sampling? It is believed that of the more than 4 million households not counted, the overwhelming majority was from poorer sections of large cities. This implies that certain parts of the country may be over-represented in Congress and are the recipients of more federal funds than may be deserved.
Achieving a large Enough Sample. A second important factor in data collection is whether the chosen sample is large enough. Are one thousand car owners a sufficient number of car owners from which to infer the opinion of all car owners? In order to answer this question, the margin of error needs to be calculated. The margin of error is a statistic that represents a range in which the surveyor feels confident that the population as a whole will fall. A sufficient sample size needs to have a small margin of error, usually around 5 percent. To determine the margin of error ( m divide one by the square root of the sample size (. Therefore, the sample of one thousand car owners gives us a margin of error of about 3 percent, an allowable margin of error. Asking the Proper questions.
Data presentation analysis, data Interpretation
Maybe car owners with business unlisted telephone numbers have very different car preferences than the broader population, but we will never know if they are not included in the sample. Biased sampling continues to challenge census takers. In 1990, nearly 35 percent of the households that were mailed census forms did not mail them back. If a form is not returned, the census Bureau must send someone to the person's house. Even with census takers visiting homes door to door, the census Bureau was still unable to contact one out of every five of the families who did not return their census form. Although hippie this may not sound like a lot, consider that in 1990 there were approximately 250 million people in the United States. If a household contains an average of four people, that means that there were.5 million forms mailed out.
For example, what if only ford owners were surveyed in the telephone survey? The survey would be quite likely to show that Fords were more popular. A biased sample is likely to skew the data, thus making data interpretation unreliable. If we want to know what sorts of cars are preferred. Car owners, we need to be sure that our sample of car owners is representative of the entire car owner population. One way of ensuring an unbiased sample is to choose memo randomly from the population. However, it is often difficult to design a study that will produce a truly unbiased sample. For example, suppose a surveyor decides to choose car owners at random to participate in a phone interview about car preferences. This may sound like a good plan, but car owners who do not have telephones or whose telephone numbers are unavailable will not have a chance to participate in the survey.
the popularity of various cars among all. The one thousand. Car owners who are surveyed are the sample and all car owners in the United States are the population. But there both an art and science to collecting high-quality data. Several key elements must be considered: bias, sample size, question design, margin of error, and interpretation. In order for data interpretation to be reliable, a number of factors must be in place. First and perhaps foremost, an unbiased sample must be used. In other words, every person (or item) in the population should have an equal chance of being in the sample.
The results are used to help determine the number of congressional seats that are assigned to each district; where new roads will be built; where new schools and libraries are needed; where new nursing homes, hospitals, and day care centers will be located; where new. In the past 30 years there has been a major shift in the. People have migrated from the northern states toward the southern states, and the result has been a major shift in congressional representation. With a net change of nearly 30 percent (a 17 percent drop plan in the northeast and Midwest coupled with a 12 percent gain in the south the south has gone from a position of less influence to one of greater influence in Congress. This is just one of many possible examples that reveal how data gathering and interpretation related to population can have a marked affect on the whole country. Gathering Reliable data, the process of data interpretation begins by gathering data. Because it is often difficult, or even impossible, to look at all the data (for example, to poll every high school student in the. United States data are generally obtained from a smaller unit, a subset of the population known as a sample.
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Mathematics, copyright 2002 The gale Group Inc. Data interpretation is part of daily life for most people. Interpretation is the process of making sense of numerical data that has been collected, analyzed, and presented. People interpret data when they turn on the television and hear the news anchor reporting on a poll, when they read advertisements claiming that one product is better than another, or when they choose grocery store items that claim they are more effective than other. A common method of assessing numerical data is known as statistical analysis, and the activity of analyzing and interpreting data in order to make predictions is known as inferential statistics. Informed consumers recognize the importance of judging the reasonableness of data interpretations and predictions by considering sources of bias such as sampling procedures or misleading questions, margins of error, confidence intervals, and incomplete interpretations. Why Is Accurate data collection Important? The repercussions of inaccurate or improperly interpreted data are wide-ranging. For example, every 10 years a major census is done in the.