ETF1100 Business Statistics Semester Two 2020
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Semester Two 2020
Exam - Alternative Assessment Task - Main
ETF1100
Business Statistics
Question 1
(a) Let us begin by looking at some statistics on covid-19 for Australia and the United States
shown in Exhibit 1. This data is for 2 October 2020.
Exhibit 1
|
Country |
Population |
Total Cases |
Total Deaths |
Total Cases per Million |
Total Deaths per Million |
|
Australia |
25,499,881 |
27,136 |
894 |
1,064.162 |
35.059 |
|
United States |
331,002,647 |
7,417,845 |
209,794 |
22,410.229 |
633.814 |
(i). Is it useful to compare total cases in Australia with those in the United States? Explain your answer and how the countries could be better compared.
|
No, not particularly useful. The United States has a much larger population than Australia so the total number of cases will naturally be higher. A better comparison is on a per million (persons) basis. |
(ii). With reference to Exhibit 1, outline how “Total Cases per Million” is calculated for
Australia from the other data in the table.
|
Total cases per million for Australia = 27,136 / ( 25,499,881/1,000,000 ) = 1,064.162 |
(iii). Explain what “Total Deaths per Million” measures and compare this statistic for
Australia and the United States.
|
Total deaths per million is the number of persons who have died of covid-19 per million persons in the population. There have been 633.814 deaths per million persons in the United States. This is much larger than the 35.059 deaths per million in Australia |
(iv). A further important statistic, which is not shown in Exhibit 1, is the death rate per
covid-19 case. Using the numbers in Exhibit 1 calculate this figure for Australia and the United States and compare the numbers.
|
Australia: 894 / 27,136 = 0.032945 (3.3%) United States: 209,794 / 7,417,845 = 0.028282 (2.8%) Interestingly, Australia has had a higher death rate than the United States. |
(b) In Exhibit 2 we outline some summary statistics across all countries, for a single day (2
October 2020), on total deaths and total deaths per million persons.
Exhibit 2
|
total_deaths total_deaths_per_million |
|
|
Mean |
4899.516746 Mean 126.5259139 |
|
Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count |
1399.483337 138 0 20232.0959 409337704.6 61.68438692 7.319112388 207808 0 207808 1023999 209 |
Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count |
13.90254442 37.485 0 200.9867531 40395.67491 7.071985387 2.496156331 1237.551 0 1237.551 26443.916 209 |
(i). How many countries are included in the data?
|
There are 209 observations/countries in the data. This is reflected in the value of “Count” . |
(ii). Are the two variables skewed and if so in what direction? Provide reasons for your answers.
|
Both variables appear to be highly positively skewed. In both cases the mean is much larger than the median. For total deaths the mean is 4,900 while the median is 138. For total deaths per million the mean is 127 compared with a median of 37. |
What is the mode for total deaths? Interpret what this value means in the context of the data and whether you think it is informative.
|
The mode is 0. The most common value for a country is no deaths from covid-19. Generally, the mode is not so useful when there are many values that a variable can take. In our case it seems unlikely that two countries would have exactly the same number of deaths from covid-19. So, it seems unlikely that the mode will be particularly useful here. Nevertheless, there do seem to be a number of countries with zero covid-19 deaths. |
In Exhibit 3 we provide descriptive statistics across countries on 2 October 2020 for the variables; population and GDP per capita.
|
population |
Exhibit 3 gdp_per_capita |
|
|
|
Mean |
37083651.23 |
Mean |
19284.98379 |
|
Standard Error |
9880221.384 |
Standard Error |
1459.349887 |
|
Median |
6871287 |
Median |
13031.5265 |
|
Mode |
#N/A |
Mode |
#N/A |
|
Standard Deviation |
142836703.6 |
Standard Deviation |
19687.70634 |
|
Sample Variance |
2.04023E+16 |
Sample Variance |
387605781.1 |
|
Kurtosis |
81.75228927 |
Kurtosis |
4.107205715 |
|
|
(i). What is the mean population and GDP per capita of the countries in our data? Also report the units of measurement for each of these values.
|
Mean population = 37,083,651 persons Mean GDP per capita = $19,284.98 (i.e. dollars) |
(ii). The standard error for the population variable is 9880221.384 while the standard
deviation is 142836703.6. Write a formula which shows the relationship between these two values?
|
9880221.384 = 142836703.6 / sqrt(209) |
(iii). The value of the mode for GDP per capita is “#NA” . Explain what this means and why
you think this has occurred.
|
It seems that the mode cannot be meaningfully defined for GDP per capita. This is most likely to be because every country has a unique value for GDP per capita. So, there is no ‘most common’ value. |
(2 marks)
2022-08-10