Dm Report

MDM4U – Mathematics in Data Management: As unemployment rate rises the rate of crime will increase. Stephanie Lui and Jennifer Yeung May 2008

INTRODUCTION CRIME RATE IN CANADA

According to recent statistics from StatCan, Canada’s crime rate has been at its lowest point in 25 years for the year of 2006. From 2005, the crime rate has dropped 3 percent in total. In all provinces, homicide rates have been on the decline since the early 90s. Although the general crime rate in Canada has increased, there have been more cases of youth coming in contact with the police for offenses. However, the number of charges is still lower in 2006 compared to the year before. In the above map, you can see the distribution of the crime rates through the 10 provinces and 3 territories of Canada. The territories all have darker shades of red, meaning that crime rates in those areas are much higher than the ones with lighter shades like Ontario or Quebec. The province of Ontario sees the lowest crime rate – consecutively topping the list for the 3rd year UNEMPLOYMENT RATE IN CANADA In 1993, the unemployment rate in Canada reached its peak of 10.8% and then declined to 6.1% in 2001. However, in 2003, it increased again. Over the past 12 months, employment has increased steadily. However, as more and more people entered the labour market, the number of people who are unemployed has increased. Ken Georgetti, president of the Canadian Labour Congress says, “Over and above the self-employment figures, the continuous bleeding of the manufacturing sector and the steep rise in youth unemployment further raise the spectre of a looming economic slowdown. More than ever, the government should consider the labour movement’s practical proposals to address sustained creation of good jobs.” It seems that in the recent increase of jobs, they were not paid employment but self-employment that are most often insecure and low-paying, Unemployment rate among youth is also increasing where young adults who joined the labour market could not find any jobs. In addition, an interesting point is that the crime rate varies from coast to coast. From history, the East has had lower crime rates than the West.

THESIS BACKGROUND We began this year by exploring what interested us. From chapter 2.1 in the textbook, we compiled a personal interest inventory and compared our results with other classmates. After choosing our favourite academic and non-academic subjects from a list, we ranked them in order and finally, used an index to measure the similarity between ourselves. Eventually, both of us ended up together since our interests were fairly similar. Here are our mind maps:

For this project, we wanted to do something about teenagers and their lifestyle. We first thought of doing a project on Facebook and Myspace. We began to go on the Internet to see what we could find. However, after conducting some research, we concluded that these websites were still relatively new and it would be difficult for us to find more in-depth statistics on them. Eventually we moved on to research about food, especially the significance of fast food in our lives. We

decided that since we are in Hong Kong, we will include both Western and Chinese food specifically McDonalds and Hong Kong styled cafes. We believe that the two represents an average teenager’s eating habits in Hong Kong. Over the course of researching for our project, we found a lot of information on the calories of different foods from Western and Chinese styled fast food stores. Even though the topic was very interesting, we thought that just focusing our project on the food we eat did not give us enough opportunities to use what we have learned in Data Management. Hence, after some more research and some more discussion, we decided that we would like to know more about a teenager’s daily habits and how breakfast may influence their health overall. We went on the Statistics Canada website and began to search for information that would help us with our topic. We found only a few pieces of information that would be helpful to us.

Again, we thought that the topic did not allow us to fully use the knowledge we have gained in the Data Management course. We went back to understanding what topics would satisfy our interests. We discussed for a while and found out that both of us were concerned about crime rates in Canada. The topic is pretty important to us because after this year, our senior year in CDNIS, we will be going off to universities in Canada by ourselves. A lot of parents feel uncomfortable to let their children go away to study independently. Particularly when we are walking to school, anything could happen. Therefore, we figured we would do something about the crime rate in Canada. It seems that Hong Kong is one of the safest cities where not much would happen on the streets at midnight and it is relatively safer than other places. Of course, Canada is not the same as Hong Kong. So we wanted to know about crime rates and what affects it. Eventually, we thought that the unemployment rate and income level could influence the crime rate of a place. Finally, we came to a conclusion that we would like to know if there is a direct correlation between crime rate and the unemployment rate in Canada.

THESIS QUESTION: How does the unemployment rate and income level affect the crime rate in Canada? We think that the unemployment rate does affect the crime rate in Canada because when people do not have enough money to sustain their daily lifestyle they tend to seek other ways to earn money, sometimes involving illegal activity or methods. Also, with an unstable unemployment rate in Canada at the moment, it is possible that people will go against the law to support themselves and possibly their family.

FINAL THESIS : VARIABLES: Crime Rate: (measured by the number of Criminal Code incidents reported to the police) Unemployment Rate: Property Crime: Crimes of Violence: Criminal Code offenses:

DATA RAW DATA + ANALYSIS OF DATA Unemployment/Income To look for information on our topic, Statistics Canada became the website we frequented the most. On this website were numerous pieces of information that became helpful to us. We especially used the statistics on the labour force in Canada and the employment/unemployment rates that were collected over certain periods of time. We first decided to find out more about the employment rates in Canada to further understand the labour force of the country. From Statistics Canada, we obtained monthly statistics on the unemployment rate.

Unemployment Rate Unemployment rate (%)

8 7 6 5

y = -0.0383x + 7.081 R² = 0.34507

4 3 2 1

2005/01 2005/02 2005/03 2005/04 2005/05 2005/06 2005/07 2005/08 2005/09 2005/10 2005/11 2005/12 2006/01 2006/02 2006/03 2006/04 2006/05 2006/06 2006/07 2006/08 2006/09 2006/10 2006/11 2006/12 2007/01 2007/02 2007/03 2007/04 2007/05

0

Time (Year/Month) We graphed the statistics using Excel and created a trend line with the equation. As the equation suggests: y = -0.0383x + 7.081 The trend is a negative correlation meaning that the unemployment rate has gone through a decline. However, the R2 value shows that this trend line cannot properly fit to the points, as the ideal value should be closer to 1. But overall, this shows us that the unemployment rate in Canada is decreasing. Since the r-value was so low, we decided to analyze the data by the distance between the data points and the line of best fit. This is called the residual value and is calculated by subtracting the calculated value from the actual value R 1 = y 1 – [ a(x 1 ) + b ] where a and b are the slope and the intercept of the line. We graphed another set of statistics: unemployment rate over a longer period of time (1990-2005) and made a residual plot.

Scatter Plot

Unemployment Rate from 1990-2005 12 11 10 9 8 7 6 1990

1992

1994

1996

2000

2002

2004

2006

1990

1992

1994

1996

1998 2000 year unemployment_rate = -0.25794year + 523.9; r2 = 0.62

2002

2004

2006

2

1998 year

0 -2

From the residual plot above, we can see that the points are fairly close to the line of best fit with the point from 1990 being a bit further away than the other ones. Overall, the two graphs shows that less and less people are getting unemployed.

Labour force (Employment)

# of people employed (in thousands)

2500 2000 1500 1000 500 0 2000 15 to 19 years 45 to 49 years

2001 20 to 24 years 50 to 54 years

2002 25 to 29 years 55 to 59 years

2003

2004

Year 30 to 34 years 60 to 64 years

2005

35 to 39 years 65 to 69 years

2006 40 to 44 years

# of people unemployed (in thousands)

Next, we moved on to look at the labour force in Canada to see which age group accounts for the most part of the labour force. From Statistics Canada, we found a survey conducted about the labour force in Canada. It included both unemployment and employment. So, we graphed the variable of employment first, to see which age group is the biggest. From the above histogram, we can see that the orange bars reach the highest and therefore, we can conclude that the largest age group in the labour force is from 40 to 44 years old. Following closely is the age group of 45 to 49 and then 35 to 39. Basically, the labour force is mostly made up of people from ages 40 to around 50.

Labour Force (Unemployed)

250 200 150 100 50 0 2000 15 to 19 years 45 to 49 years

2001 20 to 24 years 50 to 54 years

2002 25 to 29 years 55 to 59 years

2003

2004

Year 30 to 34 years 60 to 64 years

2005 35 to 39 years 65 to 69 years

2006 40 to 44 years

Next, we looked at the unemployed people in the labour force. Unemployment is the: “number of persons who, during the reference week, were without work, had actively looked for work in the past four weeks, and were available for work. Those persons on layoff or who had a new job to start in four weeks or less are considered unemployed.” (Statistics Canada) From the above, it shows that the age group represented by the dark blue colour is the most unemployed. Looking at the legend, this turns out to the 15 to 19 year olds. Next are the 20 to 24 year olds, and then 40 to 44 year olds. In general, the histogram shows us that people aged 15 to 24 make up a large portion of the unemployed population. This could be explained because of the continuation of education or the level of education needed for regular office jobs.

Distribution of total income of individuals (2005) Under $5,000 $5,000 to $9,999 $10,000 to $14,999 $15,000 to $19,999 $20,000 to $24,999 $25,000 to $29,999 $30,000 to $34,999 $35,000 to $39,999 $40,000 to $44,999 $45,000 to $49,999 $50,000 to $54,999 $55,000 to $59,999 $60,000 to $64,999 $65,000 to $69,999 $70,000 to $74,999 $75,000 to $79,999 $80,000 to $84,999 $85,000 to $89,999 $90,000 to $99,999 $100,000 to $124,999 $125,000 to $149,999 $150,000 and over After obtaining the distribution of the total income of individuals in Canada in the year 2005 from Statistics Canada, we put it into a pie graph to visually show the percentages of each income group. Obviously, the dark blue colour takes up the most area, meaning that there are more people who have an income under $5000 than any other levels of income. From the graph, we see that around half of the population earns less than around $25,000. We also did some calculations on weight mean. We realized that after $89,999, the income levels were not equally split, so we used the statistics up to $89,999. Income Frequency (f) Midpoint (m) fxm Under $4,999 12.4 2499.5 30993.8 $5,000 to $9,999 10.3 7499.5 77244.85 $10,000 to $14,999 10.8 12499.5 134994.6 $15,000 to $19,999 9.8 17499.5 171495.1 $20,000 to $24,999 8 22499.5 179996 $25,000 to $29,999 7.1 27499.5 195246.45 $30,000 to $34,999 6.8 32499.5 220996.6 $35,000 to $39,999 6 37499.5 224997 $40,000 to $44,999 4.9 42499.5 208247.55 $45,000 to $49,999 4 47499.5 189998 $50,000 to $54,999 3.3 52499.5 173248.35 $55,000 to $59,999 3 57499.5 172498.5 $60,000 to $64,999 2.3 62499.5 143748.85 $65,000 to $69,999 1.8 67499.5 121499.1 $70,000 to $74,999 1.8 72499.5 130499.1 $75,000 to $79,999 1.3 77499.5 100749.35 $80,000 to $84,999 1.1 82499.5 90749.45 $85,000 to $89,999 0.9 87499.5 78749.55

We calculated the weighted mean according to what we have been taught. Sum of all f x m 2645952.2 Sum of all f 95.6 Weighted Mean 27677.32427 We took the sum of (f x m) and divided it by the sum of all the frequencies to get the weighted mean. The final answer $27,677.32, represents the mean (or average) income. So, we can say that the average income an individual earns is approx. $27,677. However, we did not consider the higher income groups, so we cannot take this answer as the definite average income.

Distribution of income 14

Frequency

12 10 8 6 4 2 $150,000 and over

$125,000 to $149,999

$100,000 to $124,999

$90,000 to $99,999

$85,000 to $89,999

$80,000 to $84,999

$75,000 to $79,999

$70,000 to $74,999

$65,000 to $69,999

$60,000 to $64,999

$55,000 to $59,999

$50,000 to $54,999

$45,000 to $49,999

$40,000 to $44,999

$35,000 to $39,999

$30,000 to $34,999

$25,000 to $29,999

$20,000 to $24,999

$15,000 to $19,999

$10,000 to $14,999

$5,000 to $9,999

$0 to $5,000

0

Income Another way to analyze the piece of information was to put it in a histogram. When we created a frequency distribution in which the frequency is the percentage of the people who earn a specific income, the histogram showed a right-skewed distribution. This meant that there are more people who fall in the lower half of the incomes.

Total income of individuals 35000 30000

Income ($)

25000 20000

Average income

15000

Median income

10000 5000 0 2000

2001

2002

Year

2003

2004

2005

Scatter Plot

Average Income in Individuals 33200 33000 32800 32600 32400 32200 32000 31800 31600 2000

2001

2002

2003 2004 Year Average_Income = 248.57Year - 4.6548e+05; r2 = 0.88

2005

2006

Distribution of income 14

Frequency

12 10 8 6 4 2 $150,000 and over

$125,000 to $149,999

$100,000 to $124,999

$90,000 to $99,999

$85,000 to $89,999

$80,000 to $84,999

$75,000 to $79,999

$70,000 to $74,999

$65,000 to $69,999

$60,000 to $64,999

$55,000 to $59,999

$50,000 to $54,999

$45,000 to $49,999

$40,000 to $44,999

$35,000 to $39,999

$30,000 to $34,999

$25,000 to $29,999

$20,000 to $24,999

$15,000 to $19,999

$10,000 to $14,999

$5,000 to $9,999

$0 to $5,000

0

Income When we created a frequency distribution in which the frequency is the percentage of the people who earn a specific income, the histogram showed a right-skewed distribution. This meant that there are more people who fall in the lower half of the incomes.

Scatter Plot

Unemployment Rate vs Crime Rate from 1990-2005 11

10

9

8

7

0.080

0.095 0.100 crime_rate unemployment_rate = 128crime_rate - 3.5; r2 = 0.72 u

0.085

0.090

0.105

0.110

0.115

Rates of Criminal Code in Canada

12000

Rate per 100,000 population

10000 8000 6000 4000 2000

1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

0

Year Total, Criminal Code, excluding traffic

Total, crimes of violence

Total, property crimes

Total, other Criminal Code

Total Criminal Incidents

700000

Number of Incidents

600000 500000 400000 Youths charged

300000

Adults charged

200000 100000 0 2000

2001

2002

2003 Year

2004

2005

4500

Youth Crime 1990-2005

Rate per 100,000 population

4000 3500 3000 2500

Violence

2000

Robbery

1500

Property

1000

Drugs

500 0 Year

Youth Unemployment Rate vs Youth Crime rate (2000-2005)

Scatter Plot

13.5

13.0 12.5

12.0

11.5 3200

3400

3600

3800 4000 4200 4400 Crime_rate Unemployment_rate = 0.000977Crime_rate + 8.97; r2 = 0.56

4600

4800

Unemployment rate vs Property Crime rate (1990-2005)

Scatter Plot

6500 6000 5500 5000 4500 4000 7

8

7

8

1200 800 400 0 -400

9 10 Unemployment_rate

11

9 10 11 Unemployment_rate Property_Crime_rate_per_100000 = 448Unemployment_rate + 9.1e+02; r2 = 0.77

Unemployment rate vs Crimes of Violence (1990-2005) 1100 1080 1060 1040 1020 1000 980 960 940 7

8

40 20 0 -20 7

8

9 10 Unemployment_Rate

Scatter Plot

11

9 10 11 Unemployment_Rate Crimes_of_Violence = 27.5Unemployment_Rate + 7.6e+02; r2 = 0.87