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Owner: leiolak
Created: Oct 2, 2019
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Chapter 3 Project Leiola Esau
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This is my Chapter 3 Project for Prof. Sanford's Stat 300 T/Th 5:30pm-7:35pm.

1. Below are my stats for each test, which consists of their mean, median, and standard deviation.

 

Result 1: Summary Stats : mean, med, and std. dev   [Info]

Summary statistics:


ColumnMeanMedianStd. dev.
version 179.2777788211.262101
version 284.121951859.399987

2. Below is a histogram for the set of test 1 scores.

Result 2: Histogram test 1   [Info]
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Below is a histogram for the set of test 2 scores.

 

Result 3: Histogram of both Tests   [Info]
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3. Below is a pie chart showing the letter grade breakdown for test 1.

 

Result 4: Pie Chart, Version 1 grades   [Info]
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Below is a pie chart showing the letter grade breakdown for test 2.

 

Result 5: Pie Chart, version 2 grades   [Info]
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4. Below is a pie chart showing the pass/fail breakdown for test 1.

Result 6: Pie Chart, Pass/Fail v1   [Info]
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Below is a pie chart showing the pass/fail breakdown for test 2.

 

Result 7: Pie Chart, pass/fail v2   [Info]
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5.  Suppose I scored an 82 on the first test; and a friend of mine also scored an 82, but on the second test. Who scored relatively better? To determine this, I'd have to calculate the z-scores and compare. The formula: z= x - population mean all divided by the standard deviation. To calculate my z score : 82 - 79.28 = 2.72, then divided by the standard deviation, I get z = 0.24. To calculate my friend's z-score : same formula, but this time subtracting the population mean of the second test which will look like : z = 82 - 84.12 = -2.12, then divided by it's population standard deviation of 9.4 , I get z = -0.23 for my friends test score. I can conclude that I did relatively better because I scored 0.24 higher than the average test scores of my class, and my friend scores 0.23 below her class average. 

6. Below is a 5-number summary for each set of scores.

 

Result 8: 5-number Summary   [Info]

Summary statistics:


ColumnMinQ1MedianQ3Max
test 15373.5828898
test 26477859498

7. Below is a box plot for test 1.

 

Result 9: Boxplot v1   [Info]
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Below is a box plot for test 2.

 

Result 10: Boxplot test 2   [Info]
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8. Below are the descriptive statistics for both tests. I do not think the tests were created of equal difficulty. As shown below, the standard deviation which is how spread out the data are, in other words, how far a data value is from normal, the numerical summaries of test 2 are a bit higher than those of test 1. Along with the minimum, median, quartiles, etc., the students who took test 2 scored higher than the students who took test 1. The minimum score in test 1 is a score of 53 and the minimum of test 2 is a score of 64. That is a difference of 11 points, which is significant in terms of a test. Also the first quartiles show that 25% of students who took the first test scored 73.5 or lower, whereas 25% of students who took test 2 scored 77 or lower. Taking a look at the third quartile, it shows that 75% of students who took test 1 scored 88 or lower, which means the other 25% scored higher than 88. As for those students who took test 2, 75% of the students scored 94 or lower, which means the other 25% scored higher than 94.  As we can see in the pie chart that shows the breakdown of letter grades for test 2, more than about 68% of the students scored a B or higher. The letter grade breakdown for students who took test 1 shows that barely over 54% of the class scored a B or higher. Also the pass/fail pie charts show that of the students who took test 1, 22.22% failed, whereas of those who took test 2, only 9.76% failed. Therefore, I am convinced that the tests were not created of equal difficulty and test 2 was a bit easier than test 1.

 

Result 11: Descriptive Stats for both tests   [Info]

Summary statistics:


ColumnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3IQRUnadj. varianceUnadj. std. dev.Coef. of var.SkewnessKurtosisMode
test 179.277778126.8349211.2621011.87701688245539873.58814.5123.3117311.10458114.205874-0.64400153-0.3013712582
test 284.12195188.3597569.3999871.46803138534649877941786.204649.284645411.174238-0.37510054-0.9489327Multiple modes

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=91414">Chapter 3 Project Leiola Esau</A>

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