Chapter 2, Problem 2.4P

CJ The numbers of homicides in five U.S. states and five Canadian provinces for the years 1997 and 2012 are presented in two accompanying tables.

a. Calculate the homicide rate per 100,000 populations for each state and each province for each year. Relatively speaking, which state and which province had the highest homicide rates in each year? Which society seems to have the higher homicide rate? Write a paragraph describing these results?

b. Using the rates you calculated in part a, calculate the percent change between 1997 and 2012 for each state and each province. Which states and provinces had the largest increase and decrease? Which society seems to have the largest change in homicide rates? Summarize your results in a paragraph.

State	1997		2012
	Homicides	Population	Homicides	Population
New Jersey	338	8,053,000	388	8,864,590
Iowa	52	2,852,000	45	3,074,186
Alabama	426	4,139,000	342	4,882,023
Texas	1327	19,439,000	1144	26,059,203
California	2579	32,268,000	1884	38,041,430

Source: Federal Bureau of Investigation. Uniform Crime Reports. Retrieved from http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2012/crime-in-the-u.s.-2012/tables/4tabledatadecoverviewpdf/table_4_crime_in_the_united_states_by_region_geographic_division_and_state_2011-2012.xls

Province	1997		2012
	Homicides	Population	Homicides	Population
Nova Scotia	24	936,100	17	945,100
Quebec	132	7,323,600	108	8,043,600
Ontario	178	11,387,400	162	13,490,500
Manitoba	31	1,137,900	52	1,274,100
British Columbia	116	3,997,100	71	4,678,100

Source: Statistics Canada. Retrieved from http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/legal12a-eng.htm

To determine

a)

To calculate:

The homicide rate per 100, 000 populations for each state and each province for each year.

Answer to Problem 2.4P

Solution:

The homicide rates per 100, 000 populations for each state and each province for each year are:

State	1997	2012
	Rate	Homicides
New Jersey	$\frac{338}{8,053,000}*100,000$= 4.20	$\frac{388}{8,864,590}*100,000$= 4.38
Iowa	$\frac{52}{2,852,000}*100,000$= 1.82	$\frac{45}{3,074,186}*100,000$= 1.46
Alabama	$\frac{426}{4,139,000}*100,000$= 10.29	$\frac{342}{4,882,023}*100,000$= 7.01
Texas	$\frac{1327}{19,439,000}*100,000$= 6.83	$\frac{1144}{26,059,203}*100,000$= 4.39
California	$\frac{2579}{32,268,000}*100,000$=7.99	$\frac{1884}{38,041,430}*100,000$= 4.95

In the year 1997, the state Alabama has the highest homicide rate of 10.29 compare to other states. In the year 2012, the state California has the highest homicide rate of 4.95 compare to other states.

Province	1997	2012
	Homicides	Homicides
Nova Scotia	$\frac{24}{936,100}*100,000$= 2.56	$\frac{17}{945,100}*100,000$= 1.80
Quebec	$\frac{132}{7,323,600}*100,000$= 1.80	$\frac{108}{8,043,600}*100,000$= 1.34
Ontario	$\frac{178}{11,387,400}*100,000$ = 1.56	$\frac{162}{13,490,500}*100,000$ = 1.20
Manitoba	$\frac{31}{1,137,900}*100,000$= 2.72	$\frac{52}{1,274,100}*100,000$ = 4.08
British Columbia	$\frac{116}{3,997,100}*100,000$= 2.90	$\frac{71}{4,678,100}*100,000$= 1.52

In the year 1997, the Province British Columbia has the highest homicide rate of 2.90 compare to other Provinces. In the year 2012, the Province Manitoba has the highest homicide rate of 4.08 compare to other provinces.

By comparing the homicide rates of the states and provinces of the year 1997, the homicide rate is higher for states; however, by comparing the homicide rates of the states and provinces of the year 2012, the homicide rate is higher for Provinces.

Explanation of Solution

Formula Used:

Rate = $\frac{\text{Actual Occurrence}}{\text{Total number of possible occurrence}}*\text{Some unit}$

For State:

For rate per 100, 000, substitute Actual occurrence = 338, and Total number of possible occurrence = 8, 053, 000, therefore, rate of Homicides in the state New Jersey is:

Rate = $\frac{338}{8,053,000}*100,000$= 4.20.

Continuing in the similar way for other states, we have,

State	1997	2012
	Rate	Homicides
New Jersey	$\frac{338}{8,053,000}*100,000$= 4.20	$\frac{388}{8,864,590}*100,000$= 4.38
Iowa	$\frac{52}{2,852,000}*100,000$= 1.82	$\frac{45}{3,074,186}*100,000$= 1.46
Alabama	$\frac{426}{4,139,000}*100,000$= 10.29	$\frac{342}{4,882,023}*100,000$= 7.01
Texas	$\frac{1327}{19,439,000}*100,000$= 6.83	$\frac{1144}{26,059,203}*100,000$= 4.39
California	$\frac{2579}{32,268,000}*100,000$=7.99	$\frac{1884}{38,041,430}*100,000$= 4.95

For Province:

For rate per 100, 000, substitute Actual occurrence = 24, and Total number of possible occurrence = 936, 100, therefore, rate of Homicides in the Province Nova Scotia is:

Rate = $\frac{24}{936,100}*100,000$= 2.56

Continuing in the similar way for other Provinces, we have,

Province	1997	2012
	Homicides	Homicides
Nova Scotia	$\frac{24}{936,100}*100,000$= 2.56	$\frac{17}{945,100}*100,000$= 1.80
Quebec	$\frac{132}{7,323,600}*100,000$= 1.80	$\frac{108}{8,043,600}*100,000$= 1.34
Ontario	$\frac{178}{11,387,400}*100,000$ = 1.56	$\frac{162}{13,490,500}*100,000$ = 1.20
Manitoba	$\frac{31}{1,137,900}*100,000$= 2.72	$\frac{52}{1,274,100}*100,000$ = 4.08
British Columbia	$\frac{116}{3,997,100}*100,000$= 2.90	$\frac{71}{4,678,100}*100,000$= 1.52

In the year 1997, the state Alabama has the highest homicide rate of 10.29 compare to other states. In the year 2012, the state California has the highest homicide rate of 4.95 compare to other states.

In the year 1997, the Province British Columbia has the highest homicide rate of 2.90 compare to other Provinces. In the year 2012, the Province Manitoba has the highest homicide rate of 4.08 compare to other provinces.

By comparing the homicide rates of the states and provinces of the year 1997, the homicide rate is higher for states; however, by comparing the homicide rates of the states and provinces of the year 2012, the homicide rate is higher for Provinces.

To determine

b)

To calculate:

The percentage change between 1997 and 2012 for each state and province

Answer to Problem 2.4P

Solution:

State	Percent Change
New Jersey	$\frac{4.38-4.20}{4.20}*100$= 4.28
Iowa	$\frac{1.46-1.82}{1.82}*100$= -19.72
Alabama	$\frac{7.01-10.29}{10.29}*100$= -31.94
Texas	$\frac{4.39-6.83}{6.83}*100$= -35.69
California	$\frac{4.95-7.99}{7.99}*100$= -38.04

State	Percent Change
Nova Scotia	$\frac{1.80-2.56}{2.56}*100$= -29.84
Quebec	$\frac{1.34-1.80}{1.80}*100$= -25.51
Ontario	$\frac{1.20-1.56}{1.56}*100$= -23.18
Manitoba	$\frac{4.08-2.72}{2.72}*100$= 49.81
British Columbia	$\frac{1.52-2.90}{2.90}*100$= -47.70

The state New Jersey has the largest increase and the state California has the largest decrease in the rate. The province Manitoba has the largest increase and the province British Columbia has the largest decrease.

Explanation of Solution

Formula Used:

The formula of percent change is: $\frac{f_2-f_1}{f_1}*100$.

Here, $f_1$ is the value of the past year.

$f_2$ is the value of the current year.

Now, for the state New Jersey,

$f_1$ = 4.20.

$f_2$ = 4.38.

The percent change is $\frac{4.38-4.20}{4.20}*100$= 4.28.

Continuing in the same way for other states, we have,

State	Percent Change
New Jersey	$\frac{4.38-4.20}{4.20}*100$= 4.28
Iowa	$\frac{1.46-1.82}{1.82}*100$= -19.72
Alabama	$\frac{7.01-10.29}{10.29}*100$= -31.94
Texas	$\frac{4.39-6.83}{6.83}*100$= -35.69
California	$\frac{4.95-7.99}{7.99}*100$= -38.04

Now, for the province Nova Scotia,

$f_1$ = 2.56.

$f_2$ = 1.80.

The percent change is $\frac{1.80-2.56}{2.56}*100$= -29.84.

Continuing in the same way for other states, we have,

State	Percent Change
Nova Scotia	$\frac{1.80-2.56}{2.56}*100$= -29.84
Quebec	$\frac{1.34-1.80}{1.80}*100$= -25.51
Ontario	$\frac{1.20-1.56}{1.56}*100$= -23.18
Manitoba	$\frac{4.08-2.72}{2.72}*100$= 49.81
British Columbia	$\frac{1.52-2.90}{2.90}*100$= -47.70

The state New Jersey has the largest increase and the state California has the largest decrease in the rate. The province Manitoba has the largest increase and the province British Columbia has the largest decrease.