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Analysis of Crime Data Trends
- 1. Table of Contents Introduction 2 Descriptive statistics 3 Violent and property crimes 3 Categories of Violent and property crimes 5 Graphical Representation 9 Histogram 9 Boxplot 11 Scatterplot 12 Confidence interval 13 Murder 13 Non-negligent manslaughter rate 14 Paired t test 15 Ethical issues 17 Conclusion 18 Introduction I consider data sets namely number of violent crimes, number of property crimes, violent crime rates, and property crime rates for the years 1960 through 2012 for my analysis. Violent crime have has 4 categories Murder and non-negligent Manslaughter, Legacy rape /1, Robbery and Aggravated assault. Property crimes has 3 categories Burglary, Larceny-theft and Motor vehicle theft. Descriptive statisticsViolent and property crimes The table of descriptive statistics for total of violent crimes, total of property crimes, violent crime rates, and property crime rates along with population is given below. Population Violent crime total Property crime total Violent Crime rate Property crime rate
- 4. Sum 54465312 123613 2724954 11292.9 261855.8 Count 53 53 53 53 53 There are 53 observation for each year from 1960 to 2012. All the variables total of violent crimes, total of property crimes, violent crime rates, and property crime rates are observed to be skewed to the left. For a skewed data, median is considered as the best measure of central tendency. Median is the middle observation in a series of data when arranged in ascending order. The value of median for total of violent crimes, total of property crimes, violent crime rates, and property crime rates is 2744, 54573, 247.6, and 5143.3 respectively. Mean is defined as the sum of all observation divided by total number of observations. The mean value for total of violent crimes, total of property crimes, violent crime rates, and property crime rates is 2332.321, 51414.22, 213.07 and 4940.67 respectively. The value of standard deviation and variance is a measure of dispersion around mean. The value of standard deviation for total of violent crimes, total of property crimes, violent crime rates, and property crime rates is 1108.06, 17155.94, 82 and 1306.65. The low value of standard deviation of Violent Crime rate and Property crime rate implies that its mean is reliable. But high value of standard deviation of total of violent crimes and total of property crimes implies that mean is not reliable. Categories of Violent and property crimes
- 5. The descriptive statistics for 4 categories of violent crime namely Murder and non-negligent Manslaughter, Legacy rape /1, Robbery and Aggravated assault is given below. Murder and nonnegligent Manslaughter Legacy rape /1 Robbery Aggravated assault Mean 37.77358 266.7547 951.4906 1076.302 Standard Error 2.331186 18.67709 64.87113 89.56058 Median 35 333 1065 1095 Mode 44 18 1030 387 Standard Deviation 16.97129 135.9713
- 7. 57044 Count 53 53 53 53 Legacy rape /1 and Robbery are skewed to the left. Category Murder and non-negligent Manslaughter and Aggravated assault is skewed to the right. For a skewed data median is the best measure of central tendency. Median for Murder and non- negligent Manslaughter, Legacy rape /1, Robbery and Aggravated assault is 35, 333, 1065 and 1095 respectively. The descriptive statistics for 4 categories of violent crime rate namely Murder and non-negligent Manslaughter rate, Legacy rape /1 rate, Robbery rate and Aggravated assault rate is given below. Murder and nonnegligent manslaughter rate Legacy rape rate /1 Robbery rate Aggravated assault rate Mean 3.803774 24.29623 #NUM! 95.91698 Standard Error 0.258905 1.506837 6.100813
- 9. Minimum 1.5 0.8 10.7 5.2 Maximum 8.7 44.6 190.2 163.1 Sum 201.6 1287.7 4719.8 5083.6 Count 53 53 53 53 Legacy rape rate /1, Robbery rate and Aggravated assault rate are skewed to the left. Murder and non-negligent manslaughter rate is observed to be skewed to right. Median for Murder and non-negligent Manslaughter rate, Legacy rape /1 rate, Robbery rate and Aggravated assault rate is 3.4, 28.2, 91.4 and 112.7 respectively. The descriptive statistics for 3 categories of Property crime namely Burglary, Larceny-theft and Motor vehicle theft is given below. Burglary Larceny-theft Motor vehicle theft
- 10. Mean 11550.71698 35022.71698 4840.792453 Standard Error 491.1478169 1817.827423 270.3117473 Median 11409 38329 4469 Mode #N/A #N/A 3635 Standard Deviation 3575.610079 13233.9834 1967.899225 Sample Variance 12784987.44 175138316.6 3872627.36 Kurtosis -0.299426563 -0.645813313 0.43830898 Skewness -0.344400434 -0.478107721 0.754527051 Range 14494
- 11. 50538 8236 Minimum 3328 9369 1674 Maximum 17822 59907 9910 Sum 612188 1856204 256562 Count 53 53 53 Burglary, Larceny-theft and Motor vehicle theft is skewed to the right. For a skewed data, median is the best measure of central tendency. Median for Burglary, Larceny-theft and Motor vehicle theft is11409, 38329 and 4469. The descriptive statistics for Burglary rate, Larceny-theft rate and Motor vehicle theft rate is given below. Burglary rate Larceny-theft rate Motor vehicle theft rate Mean 1152.815 3324.311
- 12. 463.5264 Standard Error 54.71263 132.7419 19.0792 Median 1152.4 3544.3 430.1 Mode #N/A #N/A #N/A Standard Deviation 398.314 966.3753 138.8987 Sample Variance 158654 933881.2 19292.84 Kurtosis -0.72562 -0.86604 -0.38551 Skewness 0.374369 -0.39523 0.553889 Range 1411.8 3566.3 557.6 Minimum 525.9 1480.6
- 13. 241.2 Maximum 1937.7 5046.9 798.8 Sum 61099.2 176188.5 24566.9 Count 53 53 53 Burglary rate and Motor vehicle theft rate is skewed to the right. Larceny-theft rate is skewed to the left. For a skewed data, median is the best measure of central tendency. Median for Burglary rate, Larceny-theft rate and Motor vehicle theft rate is 1152.4, 3544.3 and 430.1 respectively. Graphical Representation Histogram The histogram violent crime rates (as well as its categories) for the years 1960 through 2012 is given below. Legacy rape rate /1, Robbery rate and Aggravated assault rate are skewed to the left. Murder and non-negligent manslaughter rate is observed to be skewed to right. This implies there are very few years with low Legacy rape rate /1, Robbery rate and Aggravated assault rate. Also, there are very few years with high Murder and non-negligent manslaughter rate. The histogram property crime rates (as well as its categories) for the years 1960 through 2012 is given below. Burglary rate and Motor vehicle theft rate is skewed to the
- 14. right. Larceny-theft rate is skewed to the left. This implies there are very few years with high Burglary rate and Motor vehicle theft rate. Also, there are very few years with low Larceny-theft rate. Boxplot The boxplot for total property crimes (as well as its categories) for the years 1960 through 2012 is given below. I observe that there are no outliers in the data. The boxplot for total violent crimes (as well as its categories) for the years 1960 through 2012 is given below. I observe that there are no outliers in the data. Scatterplot The scatterplot for namely number of violent crimes, number of property crimes, violent crime rates, and property crime rates for the years 1960 through 2012 is given below. There is strong positive linear relationship observed between violent crime total and year as well as violent crime rate and year. That with every year, the value of total violent crime increases. With increase in every year, the value of violent crime rate also increases. There is a moderate positive linear relationship observed between property crime total and year as well as property crime rate and year. That with every year, the value of total property crime increases. With increase in every year, the value of property crime rate also increases. Confidence interval The 95% confidence interval for the mean murder and non- negligent manslaughter rate is calculated with the help of
- 15. following formula. Murder The 95% confidence interval for the mean murder is (33.2, 42.34). Calculations are shown below. Confidence Interval Estimate for the Mean Data Population Standard Deviation 16.971 Sample Mean 37.77358491 Sample Size 53 Confidence Level 95% Intermediate Calculations Standard Error of the Mean 2.3311 Z Value -1.9600 Interval Half Width 4.5690 Confidence Interval Interval Lower Limit 33.20 Interval Upper Limit 42.34 I am 95% confident that estimated population mean for mean
- 16. murder lies in the interval (33.2, 42.34). Non-negligent manslaughter rate The 95% confidence interval for the mean non-negligent manslaughter rate is (3.30, 4.31). Calculations are shown below. Confidence Interval Estimate for the Mean Data Population Standard Deviation 1.884 Sample Mean 3.803773585 Sample Size 53 Confidence Level 95% Intermediate Calculations Standard Error of the Mean 0.2588 Z Value -1.9600 Interval Half Width 0.5072 Confidence Interval Interval Lower Limit 3.30 Interval Upper Limit 4.31 I am 95% confident that estimated population mean for mean
- 17. non-negligent manslaughter rate lies in the interval (3.30, 4.31). Paired t test I want to test if mean property crime rates for 1960 through 1981 (collectively) are different from the mean property crime rates from 1982 through 2012. The two variables for years 1960 through 1981 and 1982 through 2012 are dependent on each other. Hence I apply paired t test. Paired t Test Data Hypothesized Mean Difference 0 Level of significance 0.05 Intermediate Calculations Sample Size 22 DBar -25768.3182 Degrees of Freedom 21 SD 16572.0207 Standard Error 3533.1667 t Test Statistic -7.2933 Two-Tail Test Lower Critical Value -2.0796
- 18. Upper Critical Value 2.0796 p-Value 0.0000 Reject the null hypothesis Consider null hypothesis, ho: there is no significant difference in the mean property crime rates for 1960 through 1981 and 1982 through 2012. This is tested against the alternative hypothesis, h1; there is significant difference in the mean property crime rates for 1960 through 1981 and 1982 through 2012. With t = -7.29 and p-value < 0.05 (alpha), I reject null hypothesis and conclude that there is significant difference in the mean property crime rates for 1960 through 1981 and 1982 through 2012. Ethical issues It is important to check for assumption of normality for application of parametric test. Shapiro-Wilk test and Kolmogorov-Smirnov (K-S) are few test to check the assumption of normality. A bell shaped histogram is said to have normal distribution. A PP plot with S shape is also said to follow normal distribution. It is also required to check that all units are measured in same units. If it is not true then raw data should be converted into z scores. Conclusion · The variables total of violent crimes, total of property crimes, violent crime rates, and property crime rates are observed to be skewed to the left. · The value of median for total of violent crimes, total of property crimes, violent crime rates, and property crime rates is 2744, 54573, 247.6, and 5143.3 respectively. · Legacy rape /1 and Robbery are skewed to the left. Category Murder and non-negligent Manslaughter and Aggravated assault
- 19. is skewed to the right. · Legacy rape rate /1, Robbery rate and Aggravated assault rate are skewed to the left. Murder and non-negligent manslaughter rate is observed to be skewed to right. · Burglary, Larceny-theft and Motor vehicle theft is skewed to the right. · Burglary rate and Motor vehicle theft rate is skewed to the right. Larceny-theft rate is skewed to the left. · There are no outliers in the data. · There is strong positive linear relationship observed between violent crime total and year. · There is a moderate positive linear relationship observed between property crime total and year · I am 95% confident that estimated population mean for mean murder lies in the interval (33.2, 42.34). · I am 95% confident that estimated population mean for mean non-negligent manslaughter rate lies in the interval (3.30, 4.31). · There is significant difference in the mean property crime rates for 1960 through 1981 and 1982 through 2012. 4000 3000 2000 1000 0 200019801960 80000 60000 40000 20000 200019801960 300 200 100 0 6000
- 20. 4000 2000 Violent crime total Year_1 Property crime total Violent Crime rateProperty crime rate Scatterplot of Violent crim, Property cri, Violent Crim, ... vs Year_1 1 4 0 0 0 0 0 1 2 0 0 0 0 0 1 0 0 0 0 0 0 8 0 0 0 0 0 6
- 23. 0 4 0 16 12 8 4 0 1 6 0 1 2 0 8 0 4 00 12 9 6 3 0 Population F r e q u e n c y Violent Crime rateMurder and nonnegligent manslau Legacy rape rate /1Robbery rateAggravated assault rate Histogram of Population, Violent Crim, Murder and n, Legacy
- 28. 4 0 0 3 0 0 10.0 7.5 5.0 2.5 0.0 Population F r e q u e n c y Property crime rateBurglary rate Larceny-theft rateMotor vehicle theft rate Histogram of Population, Property cri, Burglary rat, Larceny- thef, ... 1400000 1200000 1000000 800000 600000 80000 60000 40000 20000 15000 10000
- 29. 5000 60000 40000 20000 10000 8000 6000 4000 2000 PopulationProperty crime totalBurglary Larceny-theftMotor vehicle theft Boxplot of Population, Property cri, Burglary, Larceny-thef, ... 1400000 1200000 1000000 800000 600000 4000 3000 2000 1000 0 80 60 40 20 480 360 240 120 0 2000 1500 1000 500 0
- 30. 2000 1500 1000 500 0 PopulationViolent crime totalMurder and nonnegligent Manslau Legacy rape /1RobberyAggravated assault Boxplot of Population, Violent crim, Murder and n, Legacy rape , ... Instructions: Access the Uniform Crime Reporting Statistics Web site, linked in Resources. Select the state in which you were born or one in which you live now. If you are an international student, choose a state which interests you. Download all available data for the number of violent crimes, number of property crimes, violent crime rates, and property crime rates for the years 1960 through 2012. Using the data, provide an analysis of the data set to include the following: 1.Provide overall descriptive statistics including measures of center (mean, median, and mode where appropriate) and dispersion (standard deviation, variance, and range). Provide one example of each of the following graphs: histogram and boxplot. Provide a scatterplot of violent crimes by year as well as property crimes by year. Interpret all statistics and graphs.. 2.Build a 95 percent confidence interval for the mean murder and non-negligent manslaughter rate. Interpret it.. 3.Conduct a hypothesis test to see if the mean property crime rates for 1960 through 1981 (collectively) are different from the mean property crime rates from 1982 through 2012 (collectively).. 4.What, if any, ethical issues should concern you in conducting your research?.
- 31. Complete your report in a Word document (submitted as a .docx file), including relevant tables and graphics you need to support your findings. Place your tables and graphics within the text and be sure to clearly title them. Your tables and graphics must be legible and suitable for inclusion in a management report. Before you submit your assignment to your instructor for grading, submit a final version of your paper to Turnitin. Assignments must be submitted to the assignments area for grading. Work e-mailed or otherwise presented cannot be graded in accordance with Capella grading standards. Refer to the scoring guide to ensure that you meet the grading criteria for this assessment. The link to Access the Uniform Crime Reporting Statistics Web site https://www.ucrdatatool.gov/Search/Crime/State/StatebyState.cf m