In course text: Moore,D.S.,Notz,W.I.,&Fligner). M.(2021). Basic Practice of Statistics (9th ed). Macmillan Learning ISBN 9781319244
Please read:
Chapter 1 Picturing Distributions with Graphs
Chapter 2 Describing Distributions with Numbers
Chapter 3 The Normal Distributions
Please answer the following questions
D1. Define these descriptive statistics: mean, proportion, percentage, variance, standard deviation, minimum (Min), maximum (Max), range, first quartile (Q1), third quartile (Q3), interquartile range (IQR), and standard error.
D2. Describe/explain the 68–95–99.7 rule (BPS9e, Ch. 3, section 3.4).
D3. Briefly describe and display the following graphs: Bar, Histogram, Box Plot, Line Graph, and Scatterplot.
In your replies to classmates, what way of looking at these statistical concepts was most helpful? Are you nervous about any aspect of this course or content? Do you have experience and examples you can share with your classmates?
Sample solution
Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell.
In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.
God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.
Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.
To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.
References
Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.
Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.
Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.
Sample Answer
Sample Answer
Understanding Descriptive Statistics and Graphs in Statistics
D1. Definitions of Descriptive Statistics:
– Mean: The average value of a dataset calculated by summing all values and dividing by the total number of observations.
– Proportion: A part or share of a whole expressed as a fraction of 1.
– Percentage: A proportion multiplied by 100, representing the share of a whole in terms of parts per hundred.
– Variance: A measure of how spread out the values in a dataset are from the mean.
– Standard Deviation: The square root of the variance, indicating the average distance between each data point and the mean.
– Minimum (Min): The smallest value in a dataset.
– Maximum (Max): The largest value in a dataset.
– Range: The difference between the maximum and minimum values, representing the spread of data.
– First Quartile (Q1): The value below which 25% of the data falls.
– Third Quartile (Q3): The value below which 75% of the data falls.
– Interquartile Range (IQR): The range between the first and third quartiles, indicating the middle 50% of data values.
– Standard Error: An estimate of how far the sample mean is likely to be from the population mean.
D2. The 68–95–99.7 Rule:
The 68–95–99.7 rule, also known as the Empirical Rule, states that in a normal distribution:
– Approximately 68% of data falls within one standard deviation of the mean.
– Around 95% falls within two standard deviations.
– Roughly 99.7% falls within three standard deviations.
This rule provides a quick way to understand the distribution of data in a normal curve and identify percentages of values within specific ranges.
D3. Description of Graphs:
– Bar Graph: A graph that represents categorical data with bars whose lengths correspond to the frequency or proportion of each category.
– Histogram: A graphical representation of numerical data where bars represent intervals or ranges of values, showing the frequency or density distribution.
– Box Plot (Box-and-Whisker Plot): A visual display showing the median, quartiles, and outliers in a dataset using a box and whiskers diagram.
– Line Graph: A graph that connects data points with straight lines, often used to show trends or changes over time.
– Scatterplot: A plot that displays individual data points on a two-dimensional graph to show the relationship between two variables.
Reflection on Statistical Concepts:
Understanding descriptive statistics and various graphs is crucial for interpreting and communicating data effectively. Personally, I found visualizing distributions through histograms and box plots particularly helpful in grasping the spread and central tendency of data. While statistical concepts can be intimidating at first, practice and real-world examples can aid in comprehension.
Nervousness and Experience:
I believe that consistent practice and seeking clarification on challenging topics can alleviate nervousness about statistics. Sharing experiences and examples with classmates can enhance understanding and provide different perspectives on statistical concepts. Drawing connections between theoretical concepts and practical applications can also make statistics more relatable and engaging for learners.
