homework set #2/97-98 - mitweb.mit.edu/11.220/€¦ · web view... percent nonwhite percent...

Department of Urban Studies and PlanningMassachusetts Institute of Technology

11.220 Quantitative Reasoning and Statistical Methods for PlanningSpring 1998

Homework Set #2 Solutions

[Total = 100 points]

Measures of Central Tendency, Measures of Dispersion, Crosstabulations, Scattergrams, Regression Lines, Indices, and Measures of Inequality

Question 1Kirk McClure, a former MCP student in our department wrote a Masters thesis on rent control in Cambridge.1 In the course of his study he collected data on mean values of nine variables characterizing the neighborhoods of Cambridge. His table, also available from the course home page, is reproduced below as Table 1.

Table 1: NEIGHBORHOOD CHARACTERISTICS—CAMBRIDGE, MASSACHUSETTS

Neighborhood Household Income (mean)

Rent Per Apartment

(mean)

Rent Per Room(mean)

Rooms Per Apartment

(mean)

Persons Per Room

(mean)

Length of Residence

(mean)

Percent Nonwhite

Percent Student

Percent Age 65+

1 11481 152.98 35.35 4.49 0.681 3.68 18.5 22.3 5.23 9392 197.42 57.99 4.11 0.679 3.34 10.7 21.7 9.04 8074 154.70 36.64 4.29 0.640 2.64 25.2 34.2 5.55 8353 231.64 66.02 3.54 0.723 3.40 10.0 33.8 21.76 11658 220.74 61.30 4.06 0.539 2.54 17.2 43.2 4.27 9295 202.47 46.34 4.68 0.504 2.91 27.3 45.6 4.38 10798 248.69 56.89 4.57 0.490 3.09 15.3 47.6 9.69 7730 231.37 63.07 4.03 0.538 2.97 26.5 42.2 9.2

10 10989 256.56 51.04 5.09 0.439 3.06 26.7 34.4 8.911 8135 190.93 46.55 4.57 0.635 2.41 43.3 42.3 4.112 na 195.00 33.50 6.00 0.542 4.30 na na na13 8622 168.26 33.33 5.00 0.662 2.71 28.0 30.6 7.6

Notes: na = not availableNeighborhood 2 is the M.I.T. campus. Because it included no market housing it was not included in the analysis.

[3] (a) At the time of McClure’s study did Cambridge neighborhoods show greater relative diversity in percentage nonwhite or in percentage student? Explain your reasoning.

1 Kirk McClure, An Evaluation of the Rent Control Policy of Cambridge, Massachusetts MCP Thesis, Department of Urban Studies and Planning, Massachusetts Institute of Technology, 1978.

11.220: Quantitative Reasoning and Statistical Methods for Planning Homework Set #2

To compare the relative diversity between two different variables we must use the coefficient of variation (i.e., the standard deviation divided by the mean). This statistic measures relative dispersion of a variable.

There is greater relative diversity in percent non-white. Although the absolute values of the standard deviations for each variable are similar (% non-white: s = 9.58%; % students: s = 8.88%), consider the coefficients of variation: CV = s * 100

x

CV (% non-white) = 9.50 * 100 = 42% 22.61

CV (% student) = 8.80 * 100 = 24%36.17

The larger CV for % non-white indicates greater relative diversity (or variability).

Note: This problem was treated as if the data represented a sample of neighborhoods (data for neighborhood 2 is missing); for this reason S was used as the numerator for the CV. Had the data been treated as representative of all the neighborhoods in the universe (i.e., population) then would have been used as the numerator yielding: CV = * 100

µ

CV (% non-white) = 9.14 * 100 = 40% 22.61

CV (% student) = 8.47 * 100 = 23%36.17

[3] (b) Neighborhood 6 had a relatively high mean rent per room and a relatively low mean length of residence. Which of these two values was more extreme when taking into account the distribution of the values of these two variables across all the neighborhoods? Explain your reasoning.

In order to determine how extreme the value is for neighborhood 6 as compared to the average for all neighborhoods 6 one can use the z score. This is defined as: Z = x6 - x , where x6 is the value for neighborhood 6. s

Z (rent/room) = 61.3 - 49.00 = 1.0212.1

Z (length) = 2.54 - 3.09 = -1.040.53

Mean length of residence is slightly more extreme than mean rent per room. The observation for neighborhood 6 lies 1.04 standard deviations below the mean for length of residence, and 1.02 standard deviations above the mean for rent per room.


Had these data been treated as representing a population, the Z-scores would have been:For the population, Z = x6 - µ

Z (rent/room) = 61.3 - 49.00 = 1.0611.63

Z (length) = 2.54 - 3.09 = -1.080.51

Note: Since the data on percent non-white and percent student for neighborhood 12 are not available, one should technically consider the 11 neighborhoods as a sample for part (a.). On the other hand, since we are considering all 12 relevant neighborhoods of Cambridge, the calculations for part (b.) should be those for a population. For purposes of this problem set, however, either calculation we have accepted.

[5] (c) What would you expect the relationship to be between mean rent per apartment and mean household income? Construct a scattergram to see if the actual observations by neighborhood agree with what you expected. Write a sentence or two summarizing what the scattergram actually shows.

It would be reasonable to expect that neighborhoods with higher household income levels would also be neighborhoods with higher mean rents. Higher income households would be more likely to be able to and want to move into these neighborhoods.

The scattergram indicates no obvious systematic relationship between mean reant and mean household income across the neighborhoods. Neighborhood 1, which has a relatively low rent and a relatively high mean household income, might be an outlier, though these values are well within the values for each of the variables.


[5] (d) What would you expect the relationship to be between mean rent per apartment and percent student? Construct a scattergram to see if the actual observations by neighborhood agree with what you expected. Write a sentence or two summarizing what the scattergram actually shows.

It would be reasonable to expect that neighborhoods with higher percentages of students would be neighborhoods with lower mean rents because students would be attracted to these neighborhoods. (This theory, however, does not account for the fact that students are more likely than other individuals to double up and together may be able to pay higher rents.)

The scattergram indicates the opposite effect: the higher the percentage of students the higher the mean rent for the neighborhood.

[5] (e) What would you expect the relationship to be between mean rent per apartment and percent age 65+? Construct a scattergram to see if the actual observations by neighborhood agree with what you expected. Write a sentence or two summarizing what the scattergram actually shows.

It would be reasonable to expect that neighborhoods with higher percentages of elderly individuals would be neighborhoods with lower mean rents because the elderly would be attracted to more affordable neighborhoods. (Also, if age is correlated with length of residence, landlords may have kept rents lower for tenants with long residency than for tenants with high turnover.)


This scattergram indicates to opposite effect: the higher the percentage of elderly individuals the higher the mean rent for the neighborhood. Neighborhood 5, with a very high percentage of elderly residents, is a possible outlier.

[6] (f) Write the formula for the regression line for each scattergram and write a simple sentence interpreting the slope in each case.

Mean Rent = 156.05 + 0.005 Income The mean rent increases by $0.005 for every $1 increase in income

Mean Rent = 129.84 + 2.08 Percentage StudentsThe mean rent increases by $2.08 for every 1% increase in Percentage Students

Mean Rent = 179.32 + 3.17 Percentage over age 65 The mean rent increases by $3.17 for every 1% increase in Percentage residents over the age of 65

[3] (b) What is the value of R2 for each regression line? From the information contained in the R2 statistics alone, which of the three independent variables is the better one to use in predicting mean rent per apartment (if you were only going to use one independent variable)?

Income R2 = 0.04

Percentage students R2 = 0.26

Percentage over the age of 65 R2 = 0.19


Percentage of students seems to be the best one to use in predicting the mean rent per apartment if we are allowed to use only one independent variable.

[3] (h) Use the regression lines to predict the missing values of the three independent variables for neighborhood 12.

Neighborhood 12 Variable Value from regression equationIncome $7550Percentage student 31.3%Percentage age 65+ 4.9%


REGRESSION RESULTS

SUMMARY OUTPUT (Income)Regression Statistics

Multiple R 0.2099745R Square 0.044089291Adjusted R Square -0.06212301Standard Error 37.25539494Observations 11

Coefficients Standard Error t StatIntercept 156.052239 76.90404465 2.029181166Income 0.005158336 0.008006274 0.644286672

SUMMARY OUTPUT (Percentage students)

Regression StatisticsMultiple R 0.510791071R Square 0.260907519Adjusted R Square 0.178786132Standard Error 32.7589445Observations 11

Coefficients Standard Error t Stat P-valueIntercept 129.842907 43.34441923 2.995608414 0.01506326Percentage students 2.079638 116.6736053 1.782440985 0.108357665

SUMMARY OUTPUT Percentage over age 65

Regression StatisticsMultiple R 0.439446775R Square 0.193113468Adjusted R Square 0.103459409Standard Error 34.22841125Observations 11

Coefficients Standard Error t Stat P-valueIntercept 179.3245579 20.35209084 8.811112297 1.01524E-05Percentage over age 65 3.1712197 216.0752087 1.46764596 0.176257621


Question 2

In 1994 I was asked by the Supreme Judicial Court of Massachusetts to do a study for its Commission to Study Racial and Ethnic Bias in the Courts. This study entailed analyzing survey results from two surveys—one of attorneys and the other of judges—that looked at a number of ways that racial and ethnic bias might be experienced in the Massachusetts courts.2

Though they were not included in the final report in this form, the two tables that follow (Table 2 and Table 3) are part of the analysis that I did of the results from the survey of attorneys. These data are also available in spreadsheet form from the course home page.

Table 2: Massachusetts Attorneys by Age and Race

White

Black/ African-

AmericanHispanic/

Latino

Asian/ Pacific Islander

Native American Other

All Attorneys

30 years or younger 244 23 22 19 0 7 315

31-40 years 760 83 37 36 0 12 928

41-50 years 672 63 18 17 0 10 780

51-60 years 226 15 0 3 2 6 252

61-70 years 146 8 00 0 3 1 158

71 years or older 95 1 0 0 4 0 100

2143 193 77 75 9 36 2533

Note: Out of a total sample of 2541 attorneys, 2533 answered both the question concerning race and the question concerning age.

[5] (a) Transform this table into a contingency table that treats age as the dependent variable by calculating the appropriate row or column percentages. Then write several sentences summarizing what this contingency table allows you to say about the relationship between these two variables among Massachusetts attorneys.

Table 2a. Massachusetts Attorneys by Age and Race

2 J. Mark Schuster with Lijian Chen, Eyes on the Courts: Attorneys and Judges Voice Their Opinions on Racial and Ethnic Bias in the Courts (Supreme Judicial Court, Commonwealth of Massachusetts, Commission to Study Racial and Ethnic Bias in the Courts, June 1994).


White Black/ African-American

Hispanic/ Latino


Native American

Other

30 years or younger 11.4% 11.9% 28.6% 25.3% 0.0% 19.4%31-40 years 35.5% 43.0% 48.1% 48.0% 0.0% 33.3%41-50 years 31.4% 32.6% 23.4% 22.7% 0.0% 27.8%51-60 years 10.5% 7.8% 0.0% 4.0% 22.2% 16.7%61-70 years 6.8% 4.1% 0.0% 0.0% 33.3% 2.8%71 years or older 4.4% 0.5% 0.0% 0.0% 44.4% 0.0%

100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

White attorneys tend to be older, and the few Native American attorneys quite a bit older, than attorneys in other racial and ethnic groups.

[5] (b) Transform this table into a contingency table that treats race as the dependent variable by calculating the appropriate row or column percentages. Then write several sentences summarizing what this contingency table allows you to say about the relationship between these two variables among Massachusetts attorneys.

Table 2b. Massachusetts Attorneys by Age and Race

30 years or younger

31-40 years

41-50 years

51-60 years 61-70 years

71 years or older

White 77.5% 81.9% 86.2% 89.7% 92.4% 95.0%Black/ African-American 7.3% 8.9% 8.1% 6.0% 5.1% 1.0%Hispanic/ Latino 7.0% 4.0% 2.3% 0.0% 0.0% 0.0%Asian/ Pacific Islander 6.0% 3.9% 2.2% 1.2% 0.0% 0.0%Native American 0.0% 0.0% 0.0% 0.8% 1.9% 4.0%Other 2.2% 1.3% 1.3% 2.4% 0.6% 0.0%

100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

The older an attorney is, the more likely he or she is to be white. This percentage increases from 77.5% of lawyers who are 30 or younger to 95.0% of attorneys who are older than 70.


Table 3: Massachusetts Attorneys by Number of Years of Practice as a Lawyer in Massachusetts and Race

White

Black/ African-

AmericanHispanic/

Latino


Native American Other

All Attorneys

5 years or fewer 517 64 42 28 0 16 667

6-10 years 457 58 25 22 0 5 567

11-15 years 399 31 7 17 0 5 459

16-20 years 272 17 2 7 2 6 306

21-30 years 259 17 1 0 1 3 281

31 years or more 235 5 0 1 6 1 248

2139 192 77 75 9 36 2528

Note: Out of a total sample of 2541 attorneys, 2528 answered both the question concerning race and the question concerning number of years of practice in Massachusetts.

[5] (c) Transform this table into a contingency table that treats years of practice as the dependent variable by calculating the appropriate row or column percentages. Then write several sentences summarizing what this contingency table allows you to say about the relationship between these two variables among Massachusetts attorneys.

Table 3a: Massachusetts Attorneys by Number of Years of Practice as a Lawyer in Massachusetts and Race

White Black/ African-American

Hispanic/ Latino


Native American

Other

5 years or fewer 24.2% 33.3% 54.5% 37.3% 0.0% 44.4%6-10 years 21.4% 30.2% 32.5% 29.3% 0.0% 13.9%11-15 years 18.7% 16.1% 9.1% 22.7% 0.0% 13.9%16-20 years 12.7% 8.9% 2.6% 9.3% 22.2% 16.7%21-30 years 12.1% 8.9% 1.3% 0.0% 11.1% 8.3%31 years or more 11.0% 2.6% 0.0% 1.3% 66.7% 2.8%

100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

Minority attorneys are much more likely than white attorneys to have 5 or fewer years of experience. Over half of Hispanic attorneys have 5 or fewer years of experience. The very few Native American attorneys all seem to be very experienced.

[5] (d) Transform this table into a contingency table that treats race as the dependent variable by calculating the appropriate row or column percentages. Then write several sentences summarizing what this contingency table allows you to say


about the relationship between these two variables among Massachusetts attorneys.

Table 3b: Massachusetts Attorneys by Number of Years of Practice as a Lawyer in Massachusetts and Race

5 years or fewer

6-10 years 11-15 years

16-20 years

21-30 years

31 years or more

White 77.5% 80.6% 86.9% 88.9% 92.2% 94.8%Black/ African-American 9.6% 10.2% 6.8% 5.6% 6.0% 2.0%Hispanic/ Latino 6.3% 4.4% 1.5% 0.7% 0.4% 0.0%Asian/ Pacific Islander 4.2% 3.9% 3.7% 2.3% 0.0% 0.4%Native American 0.0% 0.0% 0.0% 0.7% 0.4% 2.4%Other 2.4% 0.9% 1.1% 2.0% 1.1% 0.4%

100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

The more experience an attorney has had, the more likely he or she is to be white. This percentage increases from 77.5% of lawyers who are 30 or younger to 94.8% of attorneys who are older than 70.


Question 3

Below is a table of annual percent changes in consumer prices for the United States and the member countries of the Organization for Economic Cooperation and Development :3

Table 4. Annual Percent Changes in Consumer Prices, United States and OECD Countries: 1975 to 1992

Country 1975 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

United States 9.1 13.5 10.3 6.1 3.2 4.3 3.5 1.9 3.7 4.1 4.8 5.4 4.2 3.0

OECD 11.7 13.5 10.8 8.0 5.6 5.6 4.9 3.0 3.6 4.3 5.4 5.8 5.2 4.0

Australia 15.1 9.8 10.1 11.2 10.1 3.9 6.7 9.1 8.5 7.3 7.5 7.3 3.2 1.0Canada 10.7 10.2 12.4 10.8 5.8 4.3 4.0 4.2 4.4 4 5 4.8 5.6 1.5Japan 11.8 7.8 4.9 2.7 1.9 2.2 2.0 0.6 0.1 0.7 2.3 3.1 3.3 1.7New Zealand 14.7 17.2 15.4 16.2 7.3 6.2 15.4 13.2 15.8 6.4 5.7 6.1 2.6 1.0Austria 8.4 6.3 6.8 5.4 3.3 5.7 3.2 1.7 1.4 1.9 2.6 3.3 3.3 4.0Belgium 12.8 6.7 7.1 8.7 7.7 6.3 4.9 1.3 1.6 1.2 3.1 3.4 3.2 2.4Denmark 9.6 12.3 11.7 10.1 6.9 6.3 4.7 3.6 4.0 4.6 4.8 2.7 2.4 2.1Finland 17.9 11.6 12 9.6 8.3 7.1 5.9 2.9 4.1 5.1 6.6 6.1 4.3 2.9France 11.8 13.6 13.4 11.8 9.6 7.4 5.8 2.7 3.1 2.7 3.6 3.4 3.2 2.4Greece 13.6 24.7 24.5 21.0 20.2 18.5 19.3 23.0 16.4 13.5 13.7 20.4 19.5 15.9Ireland 20.9 18.3 20.4 17.1 10.5 8.6 5.5 3.8 3.1 2.1 4.1 3.3 3.2 3.1Italy 1 17.2 21.1 18.7 16.3 15.0 10.6 8.6 6.1 4.6 5.0 6.6 6.1 6.5 5.3Luxembourg 10.7 6.3 8.1 9.4 8.7 5.6 4.1 0.3 -0.1 1.4 3.4 3.7 3.1 3.2Netherlands 10.2 6.5 6.7 5.9 2.7 3.3 2.3 0.1 -0.7 0.7 1.1 2.5 3.9 3.7Norway 11.7 10.9 13.7 11.3 8.4 6.3 5.7 7.2 8.7 6.7 4.6 4.1 3.4 2.3Portugal 2 20.4 16.6 20.0 22.4 25.5 28.8 19.6 11.8 9.4 9.7 12.6 13.4 11.4 8.9Spain 17.0 15.6 14.5 14.4 12.2 11.3 8.8 8.8 5.2 4.8 6.8 6.7 5.9 5.9Sweden 9.8 13.7 12.1 8.6 8.9 8.0 7.4 4.2 4.2 5.8 6.4 10.5 9.3 2.3Switzerland 6.7 4.0 6.5 5.6 3.0 2.9 3.4 0.8 1.4 1.9 3.2 5.4 5.8 4.0Turkey 19.5 110.2 36.6 29.7 31.4 48.4 45.0 34.6 38.9 75.4 63.3 60.3 66.0 70.1United Kingdom 24.2 18.0 11.9 8.6 4.6 5.0 6.1 3.4 4.1 4.9 7.8 9.5 5.9 3.7Germany 5.9 5.5 6.3 5.3 3.3 2.4 2.2 -0.1 0.2 1.3 2.8 2.7 3.5 4.0

Notes: 1 Households of wage and salary earners.2 Excludes rent.

Source: Organization for Economic Cooperation and Development, Paris, France, Main Economic Indicators, monthly.

[8] (a) With the information given here construct Consumer Price Indices for 1979 to 1992 for the Netherlands, Ireland, and the OECD. Set each index at 1985 = 100. Present all three of these indices in graphical form on one clearly labeled graph. Then write a sentence or two describing how the Dutch and Irish experiences with consumer prices compared to the overall OECD experience during that period.

3 U.S. Bureau of the Census, Statistical Abstract of the United States: 1984 (114th edition), Washington, DC, 1994, p. 492.


Assume 1985 is the base year (CPI index at the end of 1985 = 100), CPI index for Netherlands can be calculated as:

1979 79.09 / (1+0.065) = 76.571980 84.24 / (1+0.067) = 81.541981 89.88 / (1+ 0.059) = 87.011982 95.18 / (1+0.027) = 92.141983 97.75 / (1+0.033) = 94.631984 100 / (1+0.023) = 97.751985 1001986 100 x (1+0.01) = 100.11987 100.1 x (1-.007) = 99.41988 99.4 x (1+0.007) = 100.11989 100.1 x (1+0.011) = 101.21990 101.2 x (1+0.025) = 103.731991 103.73 x (1+0.039) = 107.771992 107.77 x (1+0.037) = 111.76

Based on the above calculation, a table (Table 4a) and a figure of CPI on Netherlands, Ireland, and all OECD countries are constructed.

Table 4a. Consumer Price Index for Netherlands, Ireland, and OECD countries--1979-921979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

Netherlands 76.57 81.54 87.01 92.14 94.63 97.75 100.00 100.10 99.40 100.10 101.20 103.73 107.77 111.76Ireland 47.36 56.02 67.45 78.99 87.28 94.79 100.00 103.80 107.02 109.27 113.75 117.50 121.26 125.02OECD 62.94 71.44 79.15 85.49 90.27 95.33 100.00 103.00 106.71 111.30 117.31 124.11 130.56 135.79

Source: Organization for Economic Cooperation and Development, Paris, France, Main Economic Indicators, monthly.


Compared with overall OECD CPI, the Dutch CPI increased relatively slower as compared to the Irish CPI. Between 1979 and 1992, the Netherlands consistently experienced less inflation in consumer prices than Ireland and less inflation than the OECD countries overall. Between 1979 and 1985 Ireland experienced more inflation than the OECD countries overall, but after 1985 it experienced less inflation.

[4] (b) In which country was inflation the biggest problem between 1979 and 1992? In which country was inflation the least problematic during that period? How do you know?

Between 1979 and 1992, Japan has the least inflation problem shown by a CPI increase of only 38.61% in these 13 years, whereas Turkey has the biggest inflation problem shown by a CPI increase of 25422.88%


ALL RESULTS

Country

1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 Percent change

United States

67.6 76.7 84.6 89.8 92.6 96.6 100.0 101.9 105.7 110.0 115.3 121.5 126.6 130.4 93.0%

OECD 62.9 71.4 79.2 85.5 90.3 95.3 100.0 103.0 106.7 111.3 117.3 124.1 130.6 135.8 115.7%Australia

60.9 66.9 73.7 81.9 90.2 93.7 100.0 109.1 118.4 127.0 136.5 146.5 151.2 152.7 150.6%

Canada

63.5 70.0 78.6 87.1 92.2 96.2 100.0 104.2 108.8 113.1 118.8 124.5 131.5 133.4 110.2%

Japan 81.1 87.4 91.7 94.1 95.9 98.0 100.0 100.6 100.7 101.4 103.7 107.0 110.5 112.4 38.6%New Zealand

48.4 56.7 65.4 76.0 81.6 86.7 100.0 113.2 131.1 139.5 147.4 156.4 160.5 162.1 235.0%

Austria 74.2 78.8 84.2 88.7 91.7 96.9 100.0 101.7 103.1 105.1 107.8 111.4 115.0 119.7 61.3%Belgium

67.0 71.5 76.6 83.3 89.7 95.3 100.0 101.3 102.9 104.2 107.4 111.0 114.6 117.3 75.0%

Denmark

60.9 68.3 76.3 84.1 89.9 95.5 100.0 103.6 107.7 112.7 118.1 121.3 124.2 126.8 108.4%

Finland 59.4 66.3 74.3 81.4 88.2 94.4 100.0 102.9 107.1 112.6 120.0 127.3 132.8 136.7 130.0%France 55.8 63.3 71.8 80.3 88.0 94.5 100.0 102.7 105.9 108.7 112.7 116.5 120.2 123.1 120.8%Greece

31.3 39.1 48.6 58.8 70.7 83.8 100.0 123.0 143.2 162.5 184.8 222.5 265.8 308.1 883.5%

Ireland 47.4 56.0 67.5 79.0 87.3 94.8 100.0 103.8 107.0 109.3 113.7 117.5 121.3 125.0 164.0%Italy 43.3 52.4 62.2 72.4 83.3 92.1 100.0 106.1 111.0 116.5 124.2 131.8 140.4 147.8 241.3%Luxembourg

66.6 70.8 76.5 83.7 91.0 96.1 100.0 100.3 100.2 101.6 105.1 108.9 112.3 115.9 74.1%

Netherlands

76.6 81.5 87.0 92.1 94.6 97.8 100.0 100.1 99.4 100.1 101.2 103.7 107.8 111.8 46.0%

Norway

58.5 64.9 73.8 82.1 89.0 94.6 100.0 107.2 116.5 124.3 130.1 135.4 140.0 143.2 144.8%

Portugal

30.2 35.2 42.3 51.7 64.9 83.6 100.0 111.8 122.3 134.2 151.1 171.3 190.9 207.8 588.1%

Spain 48.6 56.2 64.3 73.6 82.6 91.9 100.0 108.8 114.5 120.0 128.1 136.7 144.8 153.3 215.4%Sweden

57.2 65.0 72.9 79.2 86.2 93.1 100.0 104.2 108.6 114.9 122.2 135.1 147.6 151.0 164.0%

Switzerland

78.0 81.1 86.4 91.2 94.0 96.7 100.0 100.8 102.2 104.2 107.5 113.3 119.9 124.7 59.8%

Turkey 9.5 20.0 27.3 35.4 46.5 69.0 100.0 134.6 187.0 327.9 535.5 858.4 1425.0 2423.9 25422.9%

United Kingdom

59.8 70.6 79.0 85.8 89.8 94.3 100.0 103.4 107.6 112.9 121.7 133.3 141.1 146.4 144.6%

Germany

78.3 82.6 87.8 92.5 95.6 97.8 100.0 99.9 100.1 101.4 104.2 107.1 110.8 115.2 47.1%


A good way to test your comprehension of the concepts we have been studying is to read through the articles in just about any issue of The Economist, paying particular attention to the graphics that are used to illustrate the articles. Questions 4, 5, and 6 are all based on information or graphs taken from the pages of The Economist.

Question 4

This graph is reproduced from an article entitled “Drowning their sorrows in fizz,” which was published in the 11 January 1997 issue (p. 47).

[6] (a) Write several sentences summarizing what this graph tells us about the French consumption of champagne as compared to the consumption of wine.

This graph compares the champagne and wine consumption in France to the base levels of wine and champagne consumption in 1965. Thus the base levels of 1965 consumption of wine and champagne are set at an index of 100. The graph indicates that champagne consumption has increased to a level that is a bit more than 2.5 times higher than it was in 1965 (an index of > 250 as compared to 100), while wine consumption has decreased to approximately 75% of what it was in 1965 (an index of 75 as compared to 100).

[4] (b) Which is higher wine consumption or champagne consumption? How can you tell from this graph?

Neither the black line nor the white line can be used to track actual level of consumption. The actual consumption levels of wine and champagne are simply superimposed on the chart: wine 17.1 million hectolitres, champagne 1.2 million hectolitres.

Question 5

An article on income levels for blacks in South Africa was published in the 25 October 1997 issue of The Economist. The following pieces of quantitative information appeared in the article:

• For blacks in South Africa the Gini coefficient was 0.35 in 1990 and 0.51 in 1995.

• For the entire South African population the Gini coefficient was 0.63 in 1990 and 0.55 in 1995.

• Rich industrialized countries tend to have Gini coefficients of approximately 0.4.

[10] (a) Write several sentences explaining to a layperson what these pieces of information indicate about income levels in South Africa, particularly for blacks.

Here is how The Economist wove this information into its article:


“...new figures from South Africa’s statistical service confirm what many already suspected: since 1990, the gap between rich and poor blacks has widened dramatically. The Gini coefficient measures this: it varies from zero, where income is evenly spread across a population, to one, where it is entirely skewed. For blacks, the Gini coefficient shot up from 0.35 in 1990, to 0.51 in 1995...

South Africa is one of the world’s most unequal countries thanks, in part, to apartheid. In 1990, the Gini coefficient was 0.63, a figure matched only by a few, such as Brazil. Rich industrialized countries, where wealth is more evenly spread, tend to rate about 0.4Despite the widening wealth gap among blacks, South Africa as a whole is becoming less unequal. By 1995, a year after the first non-racial general election, the Gini coefficient for the whole population had dropped to 0.55.”

Of course, this is more detailed than I am looking for in an answer of several sentences. What I am looking for is a sense of what is being measured (e.g. what a higher value means and what a lower value means) and a sense of comparisons among the various populations and subpopulations mentioned. Something along the following lines would be fine.

“The Gini coefficient is a measure of how equally or unequally incomes are distributed among a population. It ranges from 0 for a population in which all individuals have exactly the same income (perfect equality) to 1 in a population in which one individual has all the income (perfect inequality). Between 1990 and 1995 income inequality rose among blacks in South Africa. Income inequality among the entire population, on the other hand, was considerably higher than for blacks alone in 1990, but by 1995 it had fallen to nearly the same level as that for blacks. Income inequality among South African blacks was lower than the average for the general population of rich industrialized nations in 1990, but by 1995 had become higher than the average among the populations of these countries.”

Question 6

The 29 July 1989 Economist included an article looking at regional variations in unemployment rates for a variety of countries. It was entitled “Regional Mismatch” (p. 55). The graphic that was used to illustrate this article was a particularly complicated one. It is reproduced on the next page.

[9] (a) First focus on the top half of this graphic.

• Explain in your own words how the numbers corresponding to the white dots for each country were calculated.

• Explain how the numbers corresponding to the black dots for each country were calculated.

• Write several sentences summarizing what this graph shows about regional variation in unemployment rates across these countries. (Be sure to take into account where along the horizontal axis the dots fall as well as how close the white dots are to the black dots.)


The first step in creating the top diagram was to calculate the unemployment rate for each of the regions of each country. The regions in each country were then ordered from lowest to highest regional unemployment rate. The white dots represent the mean unemployment rate for the twenty five percent of the regions of each country with the lowest regional unemployment rates. The black dots represent the mean unemployment rate for the twenty five percent of the regions of each country with the highest regional unemployment rates. (It is unclear whether this mean was simply calculated as the unweighted mean of the corresponding regions or as a weighted mean dividing total unemployed by total labor force in the corresponding regions.)

This graph shows that the discrepancy in unemployment rates across regions is highest in Spain and Italy, while it is lowest Holland and Japan. Overall, unemployment rates are lowest in Japan, the United States, and West Germany, while they are highest in Italy and Spain.

[6] (b) Now focus on the bottom half of this graphic.

• Explain how the correlation coefficient was calculated for each country.

• Write several sentences summarizing what this graph shows about regional variation in unemployment rates across these countries.

The lower graph analyzes changes in umemployment rates by region over time. The first step was to calculate the correlation coefficient for each country: the regional unemployment rates for the country’s regions in 1975 were correlated with the corresponding regional unemployment rates for 1987. A high value of this correlation coefficient (i.e. close to +1.0) for a country indicates that regions with relatively high unemployment rates in 1975 still had relatively high unemployment rates in 1987 and regions with relatively low unemployment rates in 1987 still had relatively low unemployment rates in 1987. In other words, regions did not change relative position.

This graph indicates that in Britain, Japan, Italy, and Canada, regions have tended to maintain their relative unemployment rates. Low unemployment rate regions have remained that way and high unemployment regions have remained that way. In Australia there was a more random pattern between these two years. And, finally, in the United States there was a slight trend toward regions changing their relative positions with high unemployment regions realizing relatively lower unemployment rates and low unemployment regions realizing relatively higher unemployment rates.

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