Statistics for Business and Economics
What is a representative sample? What is its value?
The representative sample is a subset of a population of interest that is exhibiting the typical characteristics of the population. The most typical way to cover the up-mentioned criterion is the simple random sample which consist of a sample of units that is selected randomly, e. g. the sample is selected form the population on a way that every sample of the size is having the same or equal chance to be selected. The value of the representative sample is that it gives us the chance to observe and analyze different populations on a most economic and less time consuming way, because the observations made on the base of the representative sample could depicture on a reliable way the characteristics of the population that we are interested in without the need to observe all the samples in the population. That’s way the representative sample is the best way to analyze relatively big populations. 1.16
The experimental unit is the QB of the National Football League. In this case we have a sample of 331 QB drafted between 1970 and 2007. The type of the variables in this sample is as follows:
* Draft pick is a quantitative data (here I’ll would like to clarify that I have no idea what are the rules in the NFL and only trying to think logically I came to the conclusion that most probably this draft is composed according to some points that the QB won during the previous season. If the rules are not as described up and the draft is composed based on some personal characteristics of the QB, e.g. personal approach towards the game, reputation and so on the data would be qualitative, because such characteristics couldn’t be measured on a natural numerical scale.) * NFL wining ratio is a quantitative data
* QB production score is a quantitative data
Making estimates, decisions, predictions or generalizations based on sample data is the task of the interferential statistics. So in the NFL case the interferential statistics is the area of the statistical science that could be used. The task of the descriptive statistic is not to predict or make generalizations, but to explore the data, to summarize the information that the data are revealing and to present them in a convenient form.
The analysis of the graphs shows that there is no clear dependence between the different parameters observed. Nevertheless the graphical presentation of the data shows clearly the economic status of every single team. The Dallas cowboys are with any doubt the most stable team nevertheless that some of other teams show bigger positive change during the 1-Year period. 2.32
The data shows that the companies having a joint or a prepack plans are solving more easily their economical problems. Also this observation is applicable to the time needed for a company’s recovery and getting out of bankruptcy.
The mean of this particular set of data is 67.755. We could agree with the statement, quoted in the text of the exercise, because the figures support it. The median is 68.000 Representing the middle figure of the presented data we could judge that the statement is true. The mode is 64. The statement that “Most of 992 senior managers reported a level of support below 64” is false. Given the fact that under the term “mode” we understand the measurement that occurs most frequently in the data set it is possible that relatively big number of managers could report a support lower than 64 but in this case we will be supposed to observe a skewed data set. Based on the facts we are disposing in this case we can’t judge that the data set is skewed, so we can’t agree with the statement for the level of support. Analyzing the data we could consider that more or less the distribution could be represented more or less by a bell-diagram (with some higher values of a right site of the...
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