Given the following data, develop a frequency distribution:
5, 3, 2, 6, 6, 7, 3, 3, 6, 7, 7, 9, 7, 5, 3, 12, 6, 10, 7, 2, 12, 6, 10, 7, 2, 6, 8, 0, 7, 4
You are given the following data:
6 10 6 4 9 5
5 5 5 7 6 2
5 5 5 4 5 7
6 7 8 6 8 4
7 5 5 5 5 7
8 7 6 7 5 4
6 4 4 7 4 6
6 7 8 6 7 6
7 8 5 6 5 7
3 6 4 7 4 4
Construct frequency distribution for these data.
Based on the frequency distribution, develop a histogram.
Construct a relative frequency distribution.
Develop a relative frequency histogram_______________________________________________________________________
Please answer the following questions and submit your answers below.
Given the following data, develop a frequency distribution:
5 3 2 6 6
7 3 3 6 7
7 9 7 5 3
12 6 10 7 2
6 8 0 7 4
Assuming you have data for electronic sales for 120 months, using the 2k>n guideline, what is the smallest number of groups that should be used in developing a grouped data frequency distribution?__________________________________________________________________________________
Discuss the advantages of constructing a relative frequency distribution as opposed to a frequency distribution.
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
Frequency Distribution and Histogram Development
The following analysis will develop a frequency distribution based on the provided dataset, create a histogram, construct a relative frequency distribution, and develop a relative frequency histogram.
Given Data
The provided data points are:
5, 3, 2, 6, 6,
7, 3, 3, 6, 7,
7, 9, 7, 5, 3,
12, 6, 10, 7, 2,
6, 8, 0, 7, 4
Step 1: Frequency Distribution
First, we will tally the occurrences of each value in the dataset.
| Value | Frequency |
|---|---|
| 0 | 1 |
| 1 | 0 |
| 2 | 3 |
| 3 | 6 |
| 4 | 4 |
| 5 | 7 |
| 6 | 7 |
| 7 | 8 |
| 8 | 3 |
| 9 | 1 |
| 10 | 2 |
| 11 | 0 |
| 12 | 2 |
Step 2: Histogram
To visualize the frequency distribution, we can create a histogram. Each bar will represent the frequency of each value.
Frequency Histogram:
Value
|
|
| ████████
| ████████
| ████████ ████████
| ████████ ████████
| ████████ ████████
| ████████ ████████
| ████████ ████████
| ████████ ████████
|_______|____|_____|____|_____|____|_____|____
0 2 4 6 8 10 12
Step 3: Relative Frequency Distribution
To create a relative frequency distribution, we calculate the relative frequency for each value by dividing its frequency by the total number of observations.
Total number of observations = 30 (counting all values)
| Value | Frequency | Relative Frequency |
|---|---|---|
| 0 | 1 | 1/30 = 0.033 |
| 2 | 3 | 3/30 = 0.100 |
| 3 | 6 | 6/30 = 0.200 |
| 4 | 4 | 4/30 = 0.133 |
| 5 | 7 | 7/30 = 0.233 |
| 6 | 7 | 7/30 = 0.233 |
| 7 | 8 | 8/30 = 0.267 |
| 8 | 3 | 3/30 = 0.100 |
| 9 | 1 | 1/30 = 0.033 |
| 10 | 2 | 2/30 = 0.067 |
| 12 | 2 | 2/30 = 0.067 |
Step 4: Relative Frequency Histogram
A relative frequency histogram can be visualized similarly to the frequency histogram, but with the height of each bar representing the relative frequency:
Relative Frequency Histogram:
Value
|
|
| ███████
| ███████
| ███████ ███████
| ███████ ███████
| ███████ ███████
| ███████ ███████
| ███████ ███████
|_______|_____|_____|_____|_____|_____|_____|
0 .1 .2 .3 .4 .5
Grouped Data Frequency Distribution
Assuming you have data for electronic sales for 120 months, using the 2k > n guideline, we can determine the smallest number of groups (k) to use for constructing a grouped frequency distribution.
Using the formula k=log2(n)k = \log_2(n):
- Here n=120n = 120
- k≈log2(120)≈log10(120)log10(2)≈2.0790.301≈6.9k \approx \log_2(120) \approx \frac{\log_{10}(120)}{\log_{10}(2)} \approx \frac{2.079}{0.301} \approx 6.9
Since k must be a whole number, we round up to 7. Thus, the smallest number of groups is 7.
Advantages of Relative Frequency Distribution
- Standardization: Relative frequencies allow for comparison across different datasets or distributions regardless of sample size, as they express frequencies as proportions of the total.
- Interpretability: Understanding relative frequencies can be more intuitive for interpreting how significant each category is in relation to the whole dataset.
- Normalization: It helps in normalizing data and understanding patterns when working with different scales and units.
- Data Visualization: When creating visual representations like pie charts or relative frequency histograms, it becomes easier to comprehend the distribution of data.
Overall, the construction of a relative frequency distribution offers valuable insights that can enhance data interpretation and analysis in various fields.
