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APA
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Mathematics & Economics
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English (U.S.)
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Calculating First and Third Quartiles Using the Mean and Standard Deviation

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Go to the table labeled SAT Participation and Performance: Score Distributions. What are the sample size, mean and standard deviation for the Math and EWR scores?

Assume the distribution of both Math and EWR test scores have a perfect normal distribution (bell-shaped curve). Calculate the first and third quartiles of a perfectly normally distributed variable using the mean and standard deviation as given in the report for each section?

Now go to the table labeled SAT Suite Performance: Interquartile Ranges. How do the observed first and third quartiles compare to the theoretical values from the perfectly normal distribution of scores. Is there any evidence that observed distribution of Math and EWR scores are skewed or not normally distributed?
If you used SPSS to find the theoretical first and third quartiles, attach the script (“.sps”) file and the data set (“.sav”) that you created to the post. If you did not use SPSS software, but a hand calculator instead, show your work: write out the equations, explain the solution.

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Reading Discussion
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What are the sample size, the mean, and the standard deviation for the ERW and Math scores?
The sample size of the students who complete the ERW and the Math tests was 1,737,678 students, with 51 percent of the participants being female and 48 percent of them being male. The mean ERW score for the students was 529, with a standard deviation of 108. On the other hand, the mean score for the Math test was 521, with a standard deviation of 120.
3. Assume the distributions of both ERW and Math test scores are perfectly normal. Calculate the first and third quartiles of a perfectly normal distribution using the mean and standard deviation as given in the report for each section.
The z-scores can be used to calculate the first and third quartiles of the data. In a perfect normal distribution, the z-score for the first quartile is -0.6745, with the corresponding z-score for the third quartile in a perfectly normal distribution being 0.6745 (Lecture slide 25).
Given that z= (desired value (x) – mean)...
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