You are part of a school and have to report the results of standardized test sco
ID: 3485618 • Letter: Y
Question
You are part of a school and have to report the results of standardized test scores. Which measure of central tendency would you use? Assume that you don't know how your students will perform; consider the general effects of outliers on the three measures of central tendency. Research and summarize the general effects that outliers have on each of the measures of central tendency. Then, using some real values, provide an example of how the three measures of central tendency vary due to outlier effects. Recently, two new transfer students joined your school, and both have received extremely high scores on the test. Which measure of central tendency would you use, and why? Explain which measure you would use in this situation by using actual numbers to illustrate your point. Calculate all three measures of central tendency and depict what happens before and after the addition of the two transfer students. Justify your answers with appropriate reasoning and research from your textbook and course readings. Start reviewing and responding to at least two of your classmates as early in the week as possible. You can ask technical questions or respond generally to the overall experience. Be honest, clear, and concise. Always use constructive language, even in criticism, to work toward the goal of positive progress. Using questions and seeking clarifications are good ways to make your reviews substantive!
Explanation / Answer
The ideal measures of central tendency to be used in the case are mean (the average scores of all the students, median (the middle score when arranged in a sequence), mode (most frequently occurring value). The same can be measured in order to evaluate the results. Outlier effects can impact the results while evaluating the data sets, merely because of their atypical nature. For instance, a number has an atypical value when compared to others in a data set, it may lead to distortion of the final outcome while taking out the measure of central tendency. For instance, in the following data set:
(54+54+54+55+56+57+57+58+58+60+81 = 644), divided by 11 = 58.5 years
In this distribution the outlier value has increased the mean value.
In case two additional high scores are added to the distribution, median would be the appropriate measure of central tendency. This is because the mean may provide an extremely skewed result thereafter since the outlier impact would change the outcome to a great extent, further reducing the authenticity of the result (since only two tend to have the high score). For instance
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If 97 and 98 are added to these values, the mean may be changed to a great deal from 53.9 to 60.6 as the mean average score. The difference between the two measures is great and to avoid the same, median would be an appropriate measure of central tendency. The median before would be 56 and after the addition it would remain the same.
The mean score however would be changed as stated above. The mode earlier was 56 and remains the same after the addition of the two numbers in the data set.
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56
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87
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92
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