Dispersion of a dataset with the variance

by | May 29, 2023 | Statistics

 

What is the biggest disadvantage of summarizing the dispersion of a dataset with the variance?

Question 1 options:

 

The variance is sometimes twice the range.

 

 

The variance is always twice the range.

 

 

The units are in the original form.

 

 

The units are squared.

 

 

The value cannot be negative.

 

 

The value always contains outliers.

 

None of these

 

 

Under which of the following circumstances would a sample variance be zero?

 

Question 2 options:

 

If the mean was zero

 

Question 3
If the mean, median and mode were the same number
Variance can never be zero
None of these
If exactly half of the values were above the mean and half below the mean
If all the values in the sample were the same
If the variance of a dataset is correctly computed with the formula using (n – 1) in the denominator, which of the following is true?
Question 3 options:
The degrees of freedom will be twice the standard error.
None of these
The variance will be negative.
The dataset is a sample.
The variance will be zero.
The variance is a population parameter.

Question 4
Which of the following measures of central tendency will always change if a single value in the data changes?
Question 4 options:
None of these
Mode

 

 

Mean

 

 

Midrange

 

 

Variance

 

 

Standard deviation

 

 

Median

If a positively skewed distribution (right skewed) has a median of 50, which of the following statement is true?

 

 

Question 5 options:

 

None of these

 

 

The mean and median are the same

 

 

The mode and the median are the same

 

 

The variance is negative

 

 

The mean is less than 50

 

 

The mode is greater than 50

 

Which of the following variables are not of the ratio level of measurement?

 

 

Question 6 options:

 

Length

 

 

None of these

 

 

Loudness

 

 

Luminosity

 

 

Temperature (in Celsius)

 

 

Time (in seconds)

 

 

Velocity

 

A grocery store is interested in knowing how many times a typical customer visits in a week. They decide to randomly pick a customer passing through the front door and ask every tenth customer on a specified day to complete a short survey including information about how many times they have visited the store in the past week. What kind of a sampling design is this?

 

 

Question 7 options:

 

None of these

 

 

Stratified

 

 

Convenience

 

 

Multistage

 

 

Simple random

 

 

Cluster

 

Suppose that the following tree diagram depicted the results of a survey about the choice of condiment sauces. Based on this diagram, is the probability that a respondent would choose a particular sauce independent of the type of meat? Why or why not?

 

Tree Diagram

 

 

Question 8 options:

 

They are not independent, because the same sauce is used regardless of the type of meat.

 

 

They are independent, because the same sauce is used regardless of the type of meat.

 

 

They are not independent, because the sauces have the same probability of being chosen.

 

 

They are not independent, because the probability of a sauce is related to the type of meat.

 

 

They are independent, because the probabilities are the same regardless of the type of meat.

 

 

They are independent, because the sauces have the same probability of being chosen.

 

Suppose a school sports team has 12 players, of which 10 are taking at least one foreign language class. The school offers only Spanish and French classes. If 8 of the players are taking Spanish and 5 of the players are taking both languages, what is the probability that a random chosen

 

player from this team is taking French?

 

 

Question 9 options:

 

3/12

 

 

10/24

 

 

10/12
None of these
7/24
3/10
7/12
Question 10
What is the probability that, of three randomly selected people, none were born on Monday?
Question 10 options:
1/343
1400/2401
342/343
1/2401
None of these
2400/2401
240/343
Consider the following contingency table for a drug test.
Question 11
What is the sensitivity of this test?
Question 11 options:
1/5a
2a
75%
3a
None of these
60%
67%
40%
Consider the following contingency table for a drug test.
Question 12
Which of the following has the highest value?
Question 12 options:
Sensitivity and specificity
Positive predictive value
Negative predictive value and specificity
Positive predictive value and sensitivity
Specificity
Sensitivity
Negative predictive value
None of these
Positive predictive value and specificity
Question 13
Bag A contains 5 blue marbles and 3 red marbles. Bag 2 contains 4 blue marbles and 6 red marbles. If a bag is selected at random and a ball is drawn from it, what is the probability that the marble is not blue?
Question 13 options:
3/16
6/20
39/40
9/40
124/320
None of these
156/320
Question 14
Consider the following set of numbers a population.
3 3 5 6 7 12
What is the variance?
Question 14 options:
56/6
56/5
65/6
38/5
None of these
56/5
38/6
Question 15
For the data depicted in the boxplot below, what is the upper bound for check for outliers?
Question 15 options:
105
97
90
110
None of these
100
95
Question 16
In the data set below, which of the values are outliers using the Quartile Method?
4, 13, 27, -10, 6, 5, 8, -15, 8, 15, 28, 2
Question 16 options:
-15 and -10
-15, -10 and 28
-15
28
There are no outliers in this data set.
-15 and 28
-15, 27 and 28
27 and 28

Question 17
Suppose a lie detector machine has an 8% False Negative rate. A group of 100 subjects are asked a sensitive question and one quarter of the subjects decide to lie. From this group, the machine has 75 positive results. What is the specificity of this test?
Question 17 options:
None of these
58.25%
30.67%
45.05%
85.25%
25.25%
39.98%

 

 

 

 

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.


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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.

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