Tutorial 2.1 Chapter 3Graphical descriptive methods - Nominal data MULTIPLE CHOICE QUESTIONS 1. Which of the following is a graphical technique used to present nominal (categorical) data? A. Bar chart. B. Pie chart. C. A bar chart and/or a pie chart. D. None of these choices are correct. 2. Which of the following best describes a bar chart? A. A chart in which vertical bars represent data in different categories. B. A circle subdivided into sectors representing data in different categories C. A chart in which vertical bars of unequal widths are usually used. D. A chart in which vertical bars usually have no gaps between them. 3. Which of the following best describes a component bar chart? A. A component bar chart represents all categories within a single bar. tioned B. The height of each component is proportional to the frequency of the category that it represents. When C. Component bar charts may be used as a comparison of two or more breakdowns as an alternative to using two pie charts. D. All of these choices are correct. 4. Which of the following statements about pie charts is false? A. Pie charts can only be used for nominal data. B. Pie charts are usually used to display the relative sizes of categories for qualitative data. C. Pie charts always have the shape of a circle. D. The area of each slice of a pie chart is proportional to the relative frequency of the corresponding category. 5. Which of the following applies to graphical techniques to describe ordinal data? A. We may use bar charts or pie charts. B. The bars in a bar chart should be arranged in ascending (or descending) ordinal values. C. In a pie chart, the wedges may be arranged clockwise in ascending (or descending) order. D. All of these choices are correct. 6. Which of the following statements is true? A. All calculations are permitted on nominal (categorical) data. B. A contingency table lists the counts of each combination of the values of the two variables. C. Bivariate refers to the distribution of one variable. D. A contingency table cannot be based on two nominal variables. 7.Which of the following statements is true? A. A contingency table may also be called a cross classification table B. A contingency table is used to describe two nominal variables. C. A bar chart may be used as a graphical display of a contingency table. D. All of these choices are correct. TRUE/FALSE 1. A bar chart is a graphical display of a nominal (categorical) variable. The reason for the gaps between the bars is to emphasise that the bars can be placed in any order as the variable is categorical. 2. A pie chart is always preferable to a bar chart, when describing a nominal variable. 3. When a comparison of two breakdowns is desired, component bar charts offer a good alternative to using two pie charts. Chapter 4 Graphical descriptive techniques - Numerical data MULTIPLE CHOICE QUESTIONS 1. Which of the following statements is true? A. A histogram is created by drawing rectangles whose bases correspond to the class intervals, and the area of each rectangle equals the total number of observations in the sample. B. A histogram can be used for only categorical variables. C. A histogram is created by drawing rectangles whose bases correspond to the number of observations in each class. D. A histogram is created by drawing rectangles whose bases correspond to the class intervals, and the area of each rectangle equals the number of observations in that class. 2. Which of the following statements about histograms is true? A. A histogram shows the cumulative relative frequency distribution. B. A histogram may be used as a graphical display of ordinal data. C. A histogram may be used as a graphical display of categorical data. D. A histogram generally has no gaps between rectangles, because it is a graphical display of a numerical variable and the horizontal axis follows a number scale. 3. Which of the following may be determined from the height of the bar in a relative frequency histogram? A. The sample size. B. The population size. C. The proportion of observations that fall into that class. D. The number of observations that fall into that class. 4. Which of the following statements is false? A. All calculations are permitted on numerical (quantitative) data. B. All calculations are permitted on nominal (categorical) data. C. The most important aspect of ordinal data is the order of the data values. D. The only permissible calculations on ordinal data are ones involving a ranking process. 5. Which of the following statements is false? A. A frequency distribution counts the number of observations that fall into each of a series of intervals, called classes that cover the complete range of observations. B. The intervals in a frequency distribution must not overlap to ensure that each observation is assigned to an interval. C. Although the frequency distribution provides information about how the numbers in the data set are distributed, the information is more easily understood and imparted by drawing a histogram. D. The number of class intervals in a frequency distribution must be the same as the number of observations. TRUE/FALSE 1. A relative frequency distribution describes the number of data values that fall within each class, and may be presented in histogram form. 2. A cumulative frequency distribution lists the proportion of observations that are within or below each of the classes. Tutorial 2.2 Chapter 5Numerical descriptive measures MULTIPLE CHOICE 1. A . B . C . D . 2. A . B . C . D . Which of the following statements best describes the mean of a data set? The mean is a measure of spread. The mean is a measure of central location, defined as the middle value in a sorted set of data. The mean is a measure of central location, calculated by summing all observations in a data set divided by the number of observations in the data set. The mean is a measure of central location, defined as the observation in a data set with the highest frequency. Which of the following statements is true? When the distribution is skewed to the left, mean > median > mode. When the distribution is skewed to the right, mean < median < mode. When the distribution is symmetric and unimodal, mean = median = mode. When the distribution is symmetric and bimodal, mean = median = mode. 3. Which of the following statements describes when the median is a better measure of centre than the mean? A When the distribution is symmetric. . B When the distribution is positively skewed. . C When the distribution Is negatively skewed. . D When the distribution is positively skewed or negatively skewed. . 4. Which of the following is the proportion of the total area that must be to the left of the median, in a histogram? A 0.50. . B Less than 0.50 if the distribution is skewed to the left. . C More than 0.50 if the distribution is skewed to the right. . D Between 0.25 and 0.60 if the distribution is symmetric and unimodal. . 5. A . B . C . D . What measure of central location is best used with a categorical variable? The mean, median or the mode if the distribution is symmetric. 6. A . B . C . D . Which of the following statements is true? The population mean is always greater than the sample mean. 7. 4, A . B . C . D . Which of the following statements is true for the following data values: 7, 5, 6, 7, 8 and 12? The mean, median and mode are all equal. The median if the distribution is skewed. The range. The mode. The population mean is always smaller than the sample mean. The population mean must always equal the sample mean. The population mean may equal, be less than or greater than the population mean. Only the mean and median are equal. Only the mean and mode are equal. Only the median and mode are equal. 8. The average score for a class of 30 students was 75. The 20 male students in the class averaged 70. The female students in the class averaged: A 75. . B 85. . C 65. . D 70. . E 80. . 9. Which of the following is not a measure of variability? A . B . C . D . E . The range. The variance. The arithmetic mean. The standard deviation. The interquartile range. 10. Which of the following best describes the scenario when two data sets have the same range? A The distances from the smallest to the largest observations in both . data sets will be the same. B The smallest and largest observations are the same in both data sets. . C Both data sets will have the same mean. . D Both data sets will have the same interquartile range. . 11. Which of the following summary measures is affected by extreme values? A The median. . B The interquartile range. . C The range. . D The mode. . 12. Which measure of variability is appropriate when a sample is likely to contain one or several extreme values? A The variance. . B The standard deviation. . C The interquartile range. . D The range. . 13. Which of the following is the best measure of variability if the distribution of a set of data is skewed? A The standard deviation. . B The variance. . C The median. . D The interquartile range. . 14. Which of the following statements is true? A The standard deviation is always greater than the variance. . B The sum of the squared deviations from the mean is always zero. . C The standard deviation is in squared units. . D The sum of the deviations from each value in a data set to the mean, . is always zero. 15. According to Chebyshev's theorem, which of the following is the percentage of measurements in a data set that fall within three standard deviations of their mean? A 75%. . B At least 75%. . C 89%. . D At least 89%. . 16. According to the empirical rule, which of the following is the approximate percentage of measurements in a data set (provided that the data set has a bellshaped distribution) that fall within two standard deviations of their mean? A 68%. . B 75%. . C 95%. . D 99%. . SHORT ANSWER 1. Monthly rent data in dollars for a sample of 10 one-bedroom apartments in Perth are given below: 220 200 230 215 235 250 260 210 265 250 a. Compute the sample monthly average rent. b. Compute the sample median. c. What is the mode? 2. A sample of 25 families was asked how many pets they owned. Their responses are summarized in the following table. Number of pets Number of families 0 3 1 10 2 5 3 4 4 2 5 1 a. Determine the mean, the median and the mode of the number of pets owned per family. b. Describe briefly what each statistic in part (a) tells you about the data. 3. A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, 30. Compute the following measures of central location and variability: a. mean. b. median. c. standard deviation. d. coefficient of variation. Tutorial 3.1 Solution 1. Using percentiles, the difference between which of the following is the interquartile range? A 10% and 90% values. . B 25% and 75% values. . C 15% and 85% values. . D 30% and 70% values. . 2. Which of the following best describes the width of the box in the box-and-whisker plot? A The width of the box is the median. . B The width of the box is the range. . C The width of the box is the interquartile range. . D The width of the box is the standard deviation. . 3. Which of the following summary measures cannot be easily approximated from a box-and-whisker plot? A The range. . B The interquartile range. . C The second quartile. . D The standard deviation. . E All of these choices are correct. . 4. Which of the following statements is true? A The correlation coefficient is -1 if there is a perfect positive correlation between two . variables. B The correlation coefficient is 0 if there is a perfect positive correlation between two . variables. C The correlation coefficient is 0.5 if there is a perfect positive correlation between two . variables. D The correlation coefficient is 1 if there is a perfect positive correlation between two . variables. 5. Which of the following are measures of the linear relationship between two variables? A The covariance. . 1 B The coefficient of correlation. . C The coefficient of determination. . D All of these choices are correct. . 6. Which of the following would be the value of the correlation coefficient of two variables which are not linearly related. A 1 . B -1 . C 0.5 . D 0 . 7. Which of the following may be answered by knowing the shape of the distribution? A What is the best measure of central location to use. . B What is the best measure of variability to use. . C What the best measure of central location and variability to use. . D None of these choices are correct. . ANS: D True/False 1.Quartiles divide the values in a data set into four parts of equal size. 2.The interquartile range is found by taking the difference between the 1st and 3rd quartiles and dividing that value by 2. 3. The boxplot may be used for ordinal data or numerical data. 4. The left side of the box in a boxplot is the first quartile and the right side of the box in a boxplot is the third quartile, so the width of the box is the interquartile range. 5. The width of the box in a boxplot is the mean of the data set. 2 6. The coefficient of correlation indicates the direction and the strength of the linear relationship between two variables. 7. If the coefficient of correlation r = 0, then there is no linear relationship between the dependent variable y and the independent variable x. 8. The coefficient of correlation is the covariance divided by the standard deviation 9. Generally speaking, if two variables have a strong positive linear relationship, the covariance between them is equal to one. 10. The correlation coefficient only measures the direction and strength of a linear relationship between two numerical variables. 3 4 5 6 Tutorial 3.2 True/ False 1. According to least square method single linear regression line shows the relationship of a dependent variable and an independent variable. 2. Dependent variable and independent variables are denoted by y and x, respectively. 3. Suppose, y = 0 + 1x is a linear regression model, where, y = total mixed cost, 0 = fixed cost and 1 = variable cost, and x is the number of units. 4. Suppose, y = 0 + 1x is a linear regression model, where, 0 = intercept and 1 = slope. 5. Assume, y = total electricity cost of tools production and x = number of tools production in the following regression line. The regression model shows that 1-unit increase in the number of tools, the marginal increase in the electricity cost 2.245. Thus, the estimated variable cost is $2.25 per tool. Is this interpretation correct for the regression model? 6. The coefficient of determination is calculated by squaring the coefficient of correlation. 7. The coefficient of determination is denoted by R2. 8. The coefficient of determination is R2 = 0.758 that means that 75.8% of the variation in dependent variable is explained by the independent variable and the remaining 24.2% is unexplained. 9. There are two types of mathematical model one is called deterministic model and another is probabilistic model. 10. Random term (also known as error variable) in a probabilistic model is denoted by . Problem Compute the covariance, the coefficient of correlation between advertising expenditure and sales level and regression coefficient by using Microsoft Excel based on the following data in Table 1. Also discuss the strength and direction of the relationship between them and interpret the results of regression coefficient. Table1 Sales 30 40 40 50 35 50 35 25 Advertisement 1 3 5 4 2 5 3 2 Tutorial 4.1 Chapter 19 Index Numbers 1. Index numbers allow the statistician to summarise a large body of data with A. A single number. B. More than a number. C. A couple of numbers. D. None of the above. 2. The 'base' group is used as a basis for comparison with a A. Given group. B. Not given group. C. Unknown group. D. None of the above. 3. The consumer price index (CPI) measures what has happened to the prices of A. Hundreds of consumer goods and services. B. Hundreds of consumer and producer good and services. C. One particular consumer good and service. D. None of the above. 4. In Australia, the quarterly CPI figures for the eight capital cities are compiled and published by A. Australian Bureau of Statistics (ABS). B. Commonwealth Bank. C. Reserve Bank of Australia (RBA). D. None of the above. 5. CPI for the 'all consumer goods basket' and the 'all consumer goods basket excluding A. Housing. B. Electricity. C. Mobile phones. D. Transportation. 6. The current CPI population group represents A. About 60% of all Australian private households. B. About 75% of all Australian private households. C. About 64% of all Australian private households. D. None of the Above. 7. The CPI has been used for a variety of purposes: A. in the development and analysis of government economic policy. B. to determine the size and nature of wage adjustments by the Arbitration Commission. C. for the indexation of income ranges for income tax purposes by the taxation department. D. All of the above. 8. The CPI basket consists of all the important kinds of consumer purchase items to reflect price changes for a wide range of consumer goods and services. A. A wide range of consumer goods and services. B. A wide range of producer goods and services. C. A wide range of wholesaler goods and services. D. A wide range of retailer goods and services. 9. The CPI basket is divided into a number of expenditure classes that is called A. Groups. B. Teams. C. Units. D. None of the above. 10. To construct the CPI, the ABS collects prices for most commodities every quarter from A. Retail outlets. B. Farm gate. C. Wholesaler. D. None of the Above. 11. The price of petrol in Australia was 50.7 cents per litre in 1985 and the price of petrol in Australia was 60.6 cents per litre in 1998. Assume 1985 as a base year and calculate the simple price index for petrol in 1998. A. 118.5 B. 119.5 C. 120.5 D. None of the above