14. The ogive shows the percentage of divorced persons who are younger than the age specified on the x axis, for 1997 an

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14 The Ogive Shows The Percentage Of Divorced Persons Who Are Younger Than The Age Specified On The X Axis For 1997 An 1 (46.22 KiB) Viewed 56 times

14 The Ogive Shows The Percentage Of Divorced Persons Who Are Younger Than The Age Specified On The X Axis For 1997 An 2 (46.22 KiB) Viewed 56 times

14 The Ogive Shows The Percentage Of Divorced Persons Who Are Younger Than The Age Specified On The X Axis For 1997 An 3 (77.31 KiB) Viewed 56 times

14 The Ogive Shows The Percentage Of Divorced Persons Who Are Younger Than The Age Specified On The X Axis For 1997 An 4 (35.65 KiB) Viewed 56 times

14 The Ogive Shows The Percentage Of Divorced Persons Who Are Younger Than The Age Specified On The X Axis For 1997 An 5 (47.67 KiB) Viewed 56 times

14. The ogive shows the percentage of divorced persons who are younger than the age specified on the x axis, for 1997 and 2001. Note: the interval boundaries are 14, 24, 34 etc. The last interval might have a double interval width or the cumulative frequency mark is missing for age 84. % Ogive of age distribution of divorced people in Australia, 1997 and 2001 100 150 0 0 20 24 34 60 Age in years 100 (a) Interpret the fact that the 2001 ogive is to the right of the 1997 ogive. (b) Based on the ogive, determine the modal class for the 2001 distribution. (c) (i) Cell F9 (1,562) (ii) Cell H3 (0.00) (iii) Cell J17 (59.82) 1997 2001 For each of 1997 and 2001, use the ogive to estimate the median and the interquartile range of the age of divorced persons. (d) Interpret IQR calculated in part (c). 15. The following analysis relates to the Taxation Department's assessments of last year's gross annual incomes (GAI) for all taxpayers in the towns of Aville and of Betown. Incomes were assessed to the nearest thousand dollars. Exhibit 1 shows frequency distributions, percentage frequency distributions and cumulative frequency distributions. Refer to Exhibit 1. Why is it not necessary to introduce frequency density in this table? Briefly explain what information is conveyed by the value in each of the following cells.

Exhibit 1 (a) (b) 1 2 3 (d) 10 11 12 13 A 14 15 16 17 18 19 20 21 22 23 24 25 4 5 6 7 8 50 9 Income ($'000s) 0 2829882888222 20 30 up to up to up to up to up to up to up to up to up to up to 140 up to 60 70 80 90 100 110 120 130 up to up to up to up to 298228 150 up to 160 up to 170 up to 180 up to 190 up to с 200 up to 210 up to 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 D Class Midpoint 5 15 25 35 45 A3AA82429592* 55 75 105 65 6,990 6,953 6,618 6,287 4,897 4,367 115 155 165 175 E Frequency 185 195 205 215 Aville 4 6,458 6,477 6,634 6,717 7,569 3.749 3,670 3.118 2.085 1,502 704 225 12 F Betown Aville 0,00 7.59 114 7.62 387 7.80 1 7 G 772 7.90 8.90 8.22 1,280 1.562 2.039 8.18 2.192 7.78 2.344 7.39 2.596 5.76 3,034 5.14 3.560 4.41 3,866 4.32 4.173 3.67 4.003 2.45 3.698 1.77 3.517 0.83 3,186 0.26 2,402 0,01 1,950 0 0 0 85,036 46,683 0 0 100 H Freq Betown 0,00 0.01 0.24 I % Cum Freq Betown Aville 0.00 7.60 15.22 0.83 23.02 1.65 30.92 2.74 39.82 3.35 48.04 4.37 56.21 4.70 64.00 5.02 71.39 5.56 77.15 6.50 82.28 7.63 86,69 8.28 91.01 7.53 6.82 5.15 4.18 0 100 8.94 94.68 8.57 97.13 7.92 98.89 99,72 99.99 100 100 100 0.00 0.02 0.26 1.09 2.74 5.49 8.83 13.20 17.90 22.92 28.48 34.98 42.60 50.88 59.82 68.40 76.32 16. In 1998, and again in 2008, the same sample of 102 households in the city of Lyon were surveyed and asked for their net household income (in thousands of dollars) for each year. Note that the incomes for 2008 are expressed in terms of 1998 dollars, so data for the two years are comparable. Note also that, because 'net' household income was used, some of these income values were negative. Table 1 gives a set of summary measures of the data. Assume that the sampled families are representative of families living in Lyon. 83.85 90.68 95.82 100 100 The mayor of Lyon claims that households in the city are on average better off in 2008 than they were in 1998. Do you agree? Discuss, basing your discussion on the information given in Table 1. The deputy mayor of Lyon claims that richer households in the city have become richer over the decade, and the poorer households have become poorer. Do you agree? Base your argument on the information given in Table 1 and quote suitable figures to justify your answer. Calculate the interquartile range and the coefficient of variation for each of the two distributions. Briefly compare the two distributions in terms of their variability. A journalist in the local newspaper reported this study. She wrote, "... in both 1998 and 2008, most households had much lower net incomes than a few households which had higher net incomes". Briefly comment on the correctness or otherwise of this observation. Use suitable figures to justify your answer.

Table -1 17. 25.0% 20.0% 15.0% 10.0% 5.0% 0.0% 40.0% 30.0% As part of an Australian Household Expenditure Survey (1988-89), the following data was collected for 1000 households: 20.0% Summary Measures ($,000) INCOME Weekly household income (in dollars) CONSUME = Consume alcohol (1=yes, 0 =no) The variable income was studied for the two groups: "Consume alcohol", and "Do not consume alcohol", and the following graphs and summary statistics were obtained. Notice that values 250, 500, 750 etc. refer to Weekly income (S) upper class limit and not to the interval midpoint. 10.0% Mean Standard Deviation Maximum 0.0% 95th percentile Third quartile Median First quartile 5th percentile Weekly income (5) 50.0% Percentage frequency for income of households that do not consume alcohol 0001 Minimum Count 1998 2008 46.667 48.382 38.179 46.113 165.000 190.000 120.850 145.850 70.750 68.750 34.000 32.500 17.750 16.250 2050 -0.950 1.000 -3.000 102 102 Percentage frequency for income of households that consume alcohol 1250 05/2 000€ Weekly income (5) 3250 3500 OSZE 4000 33

Mean Median Modal class Standard deviation Coefficient of variation Minimum Maximum Lower quartile Upper quartile Interquartile range Count No alcohol 456.9 353 $0-$250 (a) (b) (c) 403.0 Age of Employee At least 20 but not yet 30 At least 30 but not yet 40 At least 40 but not yet 50 At least 50 but not yet 60 At least 60 but not yet 70 88.2% 12 3846 173.75 632.25 458.5 234 Consume alcohol $500-$750 708.4 638.5 Amount of Insurance 461.3 Using the above results, compare the distribution of the variable "Income" for the two groups, discussing typical values (i.e. "central tendency"), how spread out the values are, and the shape of the distributions. Comment on what this tells us about the association between income and the consumption of alcohol. 18.Term life insurance provides a fixed amount of insurance on a person's life for a specified period of time. In most cases, the face value of a term life insurance policy is reduced incrementally as the insured increases in age. The accompanying data represent the term life insurance provided through a corporate insurance plan for the 100 employees of a manufacturing firm. $70,000 60,000 40,000 25,000 10,000 65.1% 12 3696 356.75 936 579.25 766 Frequency 26 33 21 6 100 From the above grouped data, calculate the mean age of employees covered by the insurance policy. Is the value found in part (a) an approximation? Explain. Find the mean amount of insurance carried by the 100 employees. Is this value an approximation? Explain. (d) What percentage of the insured employees are 50 years of age or older? (e) What percentage of the term policies carries a face value of $40,000 or less? Recommendation: Before Tutorial 4, complete question 19 for homework. Textbook questions for further practice: Numerical descriptive measures (Chapter 3) p. 78: 3.1 (omit interquartile range calculation), 3.6 p. 84: 3.23 and p. 86: 3,25 34