IB math studies Internal Assessment.Is there a relation or a correlation between unemployment rate and crime rate in the US?Can unemployment be a danger?Word count: 1569Candidate number:School: Introduction:As a young adult who is new in the real world, you start learning about things that you do not think of as teenager. Photosynthesis, asyndeton, the cold war, inflation. One of the things that you learn in economics is unemployment and how it sounds harmless if you live in a country with a good unemployment benefit. But is it harmless or can too much free time cause harm? Since in every article that you read about unemployment, it is almost always mentioned that the crime rates will be increasing with the unemployment rates, but is that true?It would be very interesting to investigate whether there is a mathematical correlation between the crime rates in a country and the unemployment rate.Unemployment occurs when there are people actively looking for employment but are unable to find it, economists divide unemployment into different categorize. One of the categories is hidden unemployment which is when a person is either working a part time job while looking for a full-time job or a person who is over qualified for hisher job and a person who have given up on finding one.The unemployment rate can be measured in two ways: Claimant count: the number of people eligible for unemployment benefits. Labour force survey: A survey based on International labour organization (ILO) which is asking people whether they are out of work and actively seeking work.Crime rates is said to be noticeably increased in a country where unemployment rate is at dangerous levels, crime rate in a country is measured by National Crime Victimisation Survey (NCVS). Recently, it has become clear that only a proportion of crimes are reported to the police and that if we wanted a more accurate count of the crimes, we would have to conduct scientific surveys of the population and ask people if they had been victims of crime. This is what the National Crime Victimization Survey (NCVS) does.In this essay, it will be interesting to see if there is a relation between the two variables, hint the statement: is there a relation or a correlation between unemployment rate and crime rate in a country?To answer this question mathematically, I plan to use the correlation coefficient by using the Pearson equation of calculating r, r stands for the strength of the relationship between the two variables, there will be information and data and statistics collected from different sites with a scatter plot to show the relationship of the two variables. Then the result will be presented with a discussion and conclusion.1.2- Information/measurement:Unemployment is a serious issue that faces every country, as goes for crime rates.To answer the statement and to find if there is a mathematical correlation between unemployment rate and crime rate. A country and its data is needed, in this investigation the country chosen is the united states of America.The united states of America is a country of 50 states covering a vast swath of North America, with Alaska in the northwest and Hawaii extending the nation’s presence into the Pacific Ocean.1.3- Information on unemployment data:”US unemployment rate fell to 4.4 percent in April 2017 from 4.5 percent in the previous month, better than market expectations of 4.6 percent. It was the lowest jobless rate since May 2007, as the number of unemployed persons declined by 146 thousand to 7.1 million and the labour force participation rate edged down to 62.9 percent from an 11-month high of 63 percent in March. Unemployment Rate in the United States averaged 5.80 percent from 1948 until 2017, reaching an all-time high of 10.80 percent in November of 1982 and a record low of 2.50 percent in May of 1953″ (“United States Unemployment Rate | 1948-2017 | Data | Chart | Calendar”) Mathematical investigation2.1- Data:The data that will be used in the correlation is less specific and shows only the rate of unemployment over the years, that is to have an answer that shows the correlation between the rate of unemployment and the rate of crime in general rather than have characteristics like age and ethnicity and education. (“Databases, Tables & Calculators By Subject”)NATIONAL UNEMPLOYMENT RATES | 2008 – 2017 Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec.2017 4.8 4.7 4.5 4.4 4.3 4.4 4.3 2016 4.9 4.9 5.0 5.0 4.7 4.9 4.9 4.9 5.0 4.9 4.6 4.72015 5.7 5.5 5.5 5.4 5.5 5.3 5.3 5.1 5.1 5.0 5.0 5.02014 6.6 6.7 6.7 6.3 6.3 6.1 6.2 6.1 5.9 5.8 5.8 5.62013 7.9 7.7 7.5 7.5 7.5 7.5 7.3 7.2 7.2 7.2 7.0 6.72012 8.3 8.3 8.2 8.1 8.2 8.2 8.2 8.1 7.8 7.9 7.8 7.82011 9.0 8.9 8.8 9.0 9.1 9.2 9.1 9.1 9.1 9.0 8.6 8.52010 9.7 9.7 9.7 9.9 9.7 9.5 9.5 9.6 9.6 9.6 9.8 9.42009 7.6 8.1 8.5 8.9 9.4 9.5 9.4 9.7 9.8 10.2 10.0 10.02008 4.9 4.8 5.1 5.0 5.5 5.6 5.8 6.2 6.2 6.6 6.8 7.2An average rate will be calculated for each year, the year 2017 will not be used since the data in this year is yet to be completed. The reason an average rate for the unemployment is calculated is that in order to calculate correlation you need similar data between the two variables and the data used in crime rates are percentages per year.In order to calculate the average unemployment rate of every year, addition will be used to add the unemployment rate of every month followed by dividing the number by the number of months in every year.2008: (4.9 + 4.8 + 5.1 + 5.0 + 5.5 + 5.6 + 5.8 + 6.2 + 6.6 + 6.8 + 7.2) ÷ 12 = 5.22009: (7.6 + 8.1 + 8.5 + 8.9 + 9.4 + 9.5 + 9.4 + 9.7 +9.8 + 10.2 + 10.0 + 10.0) ÷ 12 = 9.22010: (9.7 + 9.7 + 9.7 + 9.9 + 9.7 + 9.5 + 9.5 + 9.6 + 9.6 + 9.6 + 9.8 + 9.4) ÷ 12 = 9.62011: (9.0 + 8.9 + 8.8 + 9.0 + 9.1 +9.2 + 9.1 + 9.1 + 9.1 + 9.0 + 8.6 + 8.5) ÷ 12 = 8.92012: (8.3 + 8.3 + 8.2 + 8.1 + 8.2 + 8.2 + 8.2 + 8.1 + 7.8 + 7.9 + 7.8 + 7.8) ÷ 12 = 8.02013: (7.9 + 7.7 + 7.5 + 7.5 + 7.5 + 7.5 + 7.3 + 7.2 + 7.2 + 7.2 + 7.0 + 6.7) ÷ 12 = 7.32014: (6.6 + 6.7 + 6.7 + 6.3 + 6.3 + 6.1 + 6.2 + 6.1 + 5.9 + 5.8 + 5.8 + 5.6) ÷ 12 = 6.12015: (5.7 + 5.5 + 5.5 + 5.4 + 5.5 + 5.3 + 5.3 + 5.1 + 5.1 + 5.0 + 5.0 + 5.0) ÷ 12 = 5.2Table 1:Year crime rate unemployment rate2008 3.6 5.22009 3.4 9.22010 3.3 9.62011 3.2 8.92012 3.2 82013 3.1 7.32014 2.9 6.12015 2.8 5.22.2- mathematical processes: Graph 1graph 1 shows the percentage of crime rates while the y axis shows the percentage of unemployment rates, by looking at the scatter plot it appears to show no correlation between the two variables, Further calculation can be more specific in giving a more accurate answer to this investigation’s statement.Calculating the correlation coefficient is the way to get a better understanding on how much of a relation the two variables share. Correlation coefficient is calculated with the formula below: (“Mark Gardener: Statistics For Ecologists Using R And Excel (Edition 2): Support: Exercises: Use Excel For Spearman Rank Correlation”)When r is equal to 1 or -1 it means that the two variables share a correlation and if r is equal to 0 it means little correlation or no correlation at all.To start solving the formula we find the mean of the sit x and the sit y by adding all the sits and dividing them with the number of sits. (X is unemployment rates and Y is crime rates)x? = 5.2 + 9.2 + 9.6 + 8.9 + 8 + 7.3 + 6.1 + 5.2 = 59.559.5 ÷ 8 = 7.43? = 3.6 + 3.4 + 3.3 + 3.2 + 3.2 + 3.1 + 2.9 + 2.8 = 25.525.5 ÷ 8 = 3.18After finding the mean for each sit, a table is made to calculate each value that the formula needs in order to find r.Table 2: the values used in calculation the correlation.X Y (x- x?) (y- ?) (x- x?)*(y- ?) (x- x?) 2 (y- ?) 25.2 3.6 -2.23 0.42 -.9366 4.972 .17649.2 3.4 1.77 0.22 .3894 3.132 .04849.6 3.3 2.17 .12 .2604 4.708 .01448.9 3.2 1.47 .02 .0294 2.160 0.00048.0 3.2 .57 .02 .0114 0.324 0.00047.3 3.1 -.13 -0.08 -0.0104 0.0169 0.00646.1 2.9 -1.33 -.28 .3724 1.768 0.07845.2 2.8 -2.23 -.38 .8474 4.972 .1444x? = 7.43 ? = 3.18 ?=.9634 ?=22.0529 ?=.4692To find the (x- x?) values in column 3, all the x values need to be subtracted from the mean of x that was calculated earlier. The same operation goes for finding the results of (y- ?).After calculating, all the values are added together to find (x- x?)*(y- ?). next the values calculated for column 3 and 4 are used to in the values for column 6 and 7, using the same result to the power of 2.After finding all the sums and results, next step would be to fill in the formula and solve the equation:r= .9634/?(22.0529×.4692) = .9634/?10.34722068= .9634/3.216709605 = .30Since the value of r is 0.30 it is considered a positive correlation even though the relationship between the two variable is weak. The closer the r value is to 0 the weaker the correlation is. Discussion and validity:In calculating correlation, any value that is close to 1 mean that the correlation is positive and the value of r which is close to -1 means the correlation is negative. The result of calculating the correlation of unemployment and crime rates was 0,30 which is considered to be a weak uphill positive linear relationship, since the value is not 0 it is still considered to have a correlation. Since this is real life data expecting the r value to be 1 or 0.99 would be unrealistic because data is simply not perfect. The investigation can be continued or repeated using a wider range of years or taking the rates of robbery crimes only since it is the most related to unemployment.The validity of this investigation does not depend on how this investigation was carried rather on how and what the results mean.Throughout the investigation some limitations may have affected the outcome. The number showed no relationship at all. But after the mathematical analysis the outcome clearly showed a weak correlation.One of the limitation is the crime rate data, the data was describing all types of crime rather than showing theft and robbery for example which can be traced back to recent unemployment. Since the data includes murder and rape which are usually not directly related to unemployment it can be argued that it did influence the outcome of the result.Another limitation is the fact that not all crimes are reported, some supermarkets may choose to not report theft every time it happens. Studies clearly show that there is a significant percentage of crime that goes by unreported which can influence the correlation between the crime rates and the unemployment rate. To continue, there could be a limitation to the data due to culture and race. The data did not mention any information regarding race. Taking into consideration that the data was collected from America.Adding to that is the limitation of the range of the data collected, the data only covered the last 8 years which might not provide enough data to reflect on the correlation of the two variables. This limitation showed when making the scatter plot, the lack of data made the graph difficult to read and reach a result without doing the mathematical part. Lastly, a limitation worth mentioning is the reason of which a person will commit a crime, not everyone will have unemployment as a reason for what they have committed. Conclusion:Despite having limitation throughout the investigation, the result showed r to be 0.30 which concludes the correlation between the unemployment rate and the crime rate to be weak but positive. Crime rates are associated with unemployment rates even if the cause of the crime is unclear if the unemployment rate is rising there will be a slight increase in crimes. The investigation clearly showed the dependency that the two variables have on each other, when one rises the other follows. Work cited:”Databases, Tables & Calculators By Subject.” U.S. Bureau Of Labor Statistics, 2017, https://data.bls.gov/timeseries/LNS14000000.”Mark Gardener: Statistics For Ecologists Using R And Excel (Edition 2): Support: Exercises: Use Excel For Spearman Rank Correlation.” Dataanalytics.Org.Uk, 2017, http://www.dataanalytics.org.uk/Publications/S4E2e%20Support/exercises/spearman.htm.