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Statistics Applied With Excel Data Analysis Is An Art 1st Edition Franz Kronthaler - Solutions
7. The deviations are normally distributed.
1.1 First, with statistics knowledge is generated and we can generate knowledge ourselves. Second, statistics enables us to make informed decisions. Third, with knowledge of statistics, we can better evaluate studies and statements based on data and recognize attempts of manipulation.
1.2 In a data set, the following three main pieces of information are contained: for what objects or people do we have information; what information do we have; the information itself.
1.3 Nominal, ordinal and metric: a nominal scale allows us to distinguish people or objects; an ordinal scale gives information about the rank order in addition to the distinction; a metric scale allows to distinguish people or objects, rank them, and provides information about the difference
1.4 The variable sector is nominal, the variable self-assessment is ordinal and the variable turnover is metric.
1.5 The variable education with the characteristics secondary school, A-level, bachelor, master is ordinal, a ranking is possible.
1.6 One possibility is to measure the number of years spent in an educational institution.An objection could be that the number of years spent in educational institutions has little to do with the level of education. The objection is a good one, but it can be raised in the same way if we measure
1.7 The solution is the created data set in the task.
1.8 The scale of a variable determines, in addition to the question, which statistical procedure can be used.
1.9 A legend is necessary because the data are usually coded. With the help of the legend we understand the meaning of the data, even at a later point in time.
1.10 The data set contains 100 observations. It contains three nominal, two ordinal and five metric variables (the running index was not counted).
1.11 The trustworthiness of the source is decided by the seriousness of the source and our level of knowledge about it. data_growth.xlsx is not a real data set, but a simulated one for teaching purpose?
Knowledge is based on experience, theories, and data, but most of our knowledge is based on data.
Data is sometimes used to manipulate.
Sound data analysis helps to make good decisions.
A data set is organized into columns and rows. The rows contain the objects of the study, and the columns contain the variables.
A data set is usually organized using numbers. It is easier to calculate this way.
The legend of the data set should contain the variable name, the variable description, the definition of the values, the information about missing values and the scale.
Knowledge is based on experience, theories, and data, but most of our knowledge is based on data.
Data is sometimes used to manipulate.
Sound data analysis helps to make good decisions.
Nominal variables allow for a distinction between the objects of study.
Ordinal variables include a ranking in addition to the distinction.
Metric variables allow in addition to distinction and ranking a precise distance measurement.
Ordinal data can be treated like metric data, if enough characteristics are possible and the data is normally distributed. More elegant is the creation of a quasi-metric variable.
The scale level plays a decisive role in determining which statistical methods can be used.
1.1 Give three reasons why statistics is useful.
1.2 What information does a data set contain?
1.3 What scales are important for statistical data analysis and what properties do they have?
1.4 What are the scales of the variables sector (industry, service), self-assessment (very experienced, experienced, less experienced, not experienced), and turnover (in Swiss francs)?
1.5 What is the scale of the variable education (secondary school, A-level, bachelor, master)?
1.6 Variables can sometimes be measured using different scales. Consider how the educational level of individuals can be measured in a metric way.
1.7 The hotel satisfaction of guests should be measured in a quasi-metric way. For this purpose, create eight lines with a length of 10 cm, measure a hypothetical value for each guest and create a small data set with the variables guest, age, gender and hotel satisfaction.
1.8 Why are scales important for data analysis?
1.9 Why do we need a legend for a data set?
1.10 Open our data set data_growth.xlsx with Excel and learn about it. Answer the following questions: What is the number of observations? How many metric, ordinal, and nominal variables are in the data set? How are the metric, ordinal, and nominal data measured?
1.11 How trustworthy is our data set data_growth.xlsx?
1.12 Name one trustworthy data source each for your country, continent and the world?
1.13 Think of three questions that are likely to be analyzed with data. Find the appropriate data sources.
The mode is used for nominal variables.
For ordinal variables, we can calculate both the mode and the median.
For metric variables, we have the mode, the median, and the arithmetic mean.
The arithmetic mean is often simply called mean.
The arithmetic mean is sensitive to outliers, while the mode and median are not sensitive to extreme values.
The geometric mean is used to calculate average growth rates over time.
Serious people specify which average value they used.
3.1 Which average value should be applied at which scale?
3.2 Calculate by hand for the first six companies of the data set data_growth.xlsx the arithmetic mean for the variables innovation and marketing and interpret the results.
3.3 Calculate by hand for the first six companies of the data set data_growth.xlsx the median for the variables self-assessment and education and interpret the results.
3.4 Calculate by hand for the first six companies of the data set data_growth.xlsx the mode for the variables gender and expectation and interpret the results.
3.5 Is it possible to calculate the median meaningfully for the variable motive?
3.6 For the data set data_growth.xlsx, calculate the average values for all variables using Excel, when meaningful.
3.7 Our third company in the data set grew at 16% in the first year, 11% in the second year, 28% in the third year, 13% in the fourth year, and 23% in the fifth year. What is the average growth rate?
3.8 The turnover of our fourth company is said to have been 120’000 Fr in 2007, 136’800 Fr in 2008, 151’848 Fr in 2009, 176’144 Fr in 2010, 202’566 Fr in 2011 and 193’451 Fr in 2012. Calculate the average growth rate over the years and make a forecast for 2016.
3.9 We are interested in population growth in India and want to compare it with population growth in China. We do some research on the internet and find data for this at the World Bank (https://data.worldbank.org/indicator):
3.10 Which average value is sensitive to outliers, which two are not, and why?
Measures of variation complement our information on the average; the smaller the variation, the more meaningful the average value is.
The range is the difference between maximum and minimum of a variable, it is very sensitive to outliers.
The standard deviation can be interpreted as the average deviation of all values from the mean. The variance is the squared standard deviation. For metric variables, both values can be calculated in a meaningful way.
The interquartile range gives information about the area in which the middle 50% of the values are located. It can be used with both metric and ordinal data.
The coefficient of variation is applied to analyze in which variable people or objects are more consistent, it is applied with metric data.
The boxplot is a popular graphical tool to analyze variation.
4.1 Which measure of variation is useful at which scale?
4.2 For nominal data, is there a measure of variation, why or why not?
4.3 For the first eight companies in our data set data_growth.xlsx, calculate by hand the range, the standard deviation, the variance, the interquartile range, and the coefficient of variation for the variable age and interpret the result.
4.4 For the first eight companies in our data set data_growth.xlsx, calculate by hand the range, the standard deviation, the variance, the interquartile range, and the coefficient of variation for the variable marketing and interpret the result.
4.5 For the first eight companies in our data set data_growth.xlsx, calculate by hand the range, the standard deviation, the variance, the interquartile range, and the coefficient of variation for the variable innovation and interpret the result.
4.6 In which variable are the enterprises less consistent, marketing or innovation(applications 4.4 and 4.5)? What measure of variation do you use to answer the question?
4.7 We are interested in the volatility of two shares, that is, how much the share prices fluctuate over time. We look for a financial platform on the Internet that provides the data and look at the daily closing prices for one week (e.g. https://www.finanzen.ch).For the first share (Novartis) we
4.8 We have the following values for the variable growth from our data set: minimum−9, maximum 22, first quartile 4, median 8, third quartile 11. Draw the boxplot by hand. What is the range of the middle 50% of the observations?
4.9 Using Excel, draw the boxplot for the variable growth of the data set data_growth.xlsx.
4.10 We have the following values for the variable growth, grouped by motive for starting a business, from our data set: unemployment: minimum −3, maximum 22, first quartile 2, median 7, third quartile 10; implement idea: minimum −7, maximum 20, first quartile 4.25, median 8, third quartile 11;
4.11 Use Excel, draw the boxplots for the variable growth by motive for starting an enterprise.
4.12 For our data set data_growth.xlsx, calculate the range, the interquartile range, the standard deviation, and the variance for all variables using Excel (if possible). Also, draw the associated boxplots.
Graphical presentation of data helps to explain facts.
Graphical presentations of data often give hints about the behavior of people or objects, as well as patterns in the data.
We use frequency charts to display how often certain values occur.
The frequency table shows how often certain values occur in absolute and relative terms.
Graphically, we can represent the frequency distribution absolutely, relatively, or with the histogram.
If we have equal class widths, the absolute or relative frequency plot is preferable; if we have different class widths, the histogram is preferable.
A good chart is as simple as possible and presents information clearly.
5.1 Calculate the average growth rate of the enterprises in Fig. 5.6. To do this, read the numbers from the figure. Compare the calculated growth rates with the respective growth rates from our data set data_growth.xlsx.
5.2 Give two reasons why charts are helpful.
5.3 For what purpose do we need frequency charts?
5.4 For different class widths, is the absolute frequency chart, the relative frequency chart, or the histogram preferable? Why?
5.5 For the variable expectation for the first six companies in our data set data_growth.xlsx, create the frequency table, absolute and relative frequency chart by hand and interpret the result.
5.6 For our data set data_growth.xlsx, create the frequency table and the relative frequency chart for the variables marketing and innovation using Excel and interpret the result.
5.7 Is the marketing variable more symmetric or the innovation variable more symmetric? Why?
5.8 Create the relative frequency chart and the histogram for the variable growth using the following class widths: −10 to −5, −5 to 0, 0 to 5, and 5 to 25. Draw the charts by hand, it is very tedious with Excel. What do you notice? Which presentation is preferable and why?
5.9 Create a pie chart for the variable education and interpret the result.
5.10 Create a bar chart for our variable motive, distinguish between service and industrial companies and interpret the result.
5.11 The second enterprise in our data set had a turnover of CHF 120,000 in 2007. In the first year it grew by 9%, in the second year by 15%, in the third year by 11%, in the fourth year by 9% and in the fifth year by −3%. Using this information, prepare a line graph showing the turnover
5.12 Search the Internet for the number of overnight stays for the Swiss holiday destinations Grison, Lucerne/Lake Lucerne, Berne upper country and Valais for the years 2005 to 2019 at the Swiss Federal Statistical Office. Plot the development of overnight stays using a line chart. We go into more
5.13 We are interested in the population density in South America and want to visualize it using a map chart. We go to the World Bank on the Internet and find the data for 2018. Then we prepare the data and map it using Excel.
Correlations provide information about whether there is a relationship between two variables, they do not say anything about causality.
It is often the case that correlations are due to the influence of third variables.Correlations must always be theoretically justified.
The Bravais–Pearson correlation coefficient is suitable for metric variables, when a linear relationship exists.
Before calculating the Bravais–Pearson correlation coefficient, the scatterplot should be drawn.
The correlation coefficient of Bravais–Pearson is sensitive to unusual observations or outliers.
The Spearman correlation coefficient is used to calculate the correlation between two ordinal variables.
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