CRJ 511 HW3

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Arizona State University *

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511

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Statistics

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Feb 20, 2024

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CRJ 511 Homework Assignment #3 1. Use the Recidivism.xls data , generate the range, variance, and standard deviation for the variable AGE in Excel . Copy and paste the Excel output here. Then report the results. Can you get the range, variance, and standard deviation for SEX, RACE, and CUSTODY? Why? REPORT OF RESULTS : The age range is 57 with the highest value being 75 and the lowest value being 21. As for the age variance, it is 266.06437. The standard deviation is 16.31148. EXCEL OUTPUTS: person sex race age crime recidivis m custody 1 1 1 52 2 1 Minimu m 2 1 1 43 3 0 Close 3 1 2 22 1 0 Close 4 1 2 47 1 0 Close 5 1 2 63 2 0 Minimu m 6 1 2 31 3 1 Medium 7 1 2 76 2 1 Medium 8 1 1 70 1 0 Close 9 1 1 37 2 1 Medium 10 1 2 49 2 1 Medium 11 1 2 54 2 0 Minimu m 12 1 2 68 2 0 Minimu m 13 1 2 23 1 1 Medium 14 1 2 47 3 0 Close 15 1 2 61 2 0 Medium 16 1 1 33 2 0 Close 17 1 2 45 3 0 Minimu m 18 1 1 34 1 0 Minimu m 19 1 2 54 2 1 Minimu m 20 1 2 29 2 0 Medium 21 1 2 56 2 0 Medium 22 1 2 29 3 1 Medium 23 1 2 30 1 1 Minimu

m 24 1 2 21 1 0 Medium 25 1 1 51 1 0 Medium 26 1 1 55 2 1 Medium 27 1 1 78 2 1 Medium 28 1 2 72 3 0 Medium 29 1 2 46 2 0 Medium 30 1 2 42 2 0 Medium AGE Max 78 Min 21 Range 57 SD 16.31148 Variance 266.06437 Mean 47.266667 Coefficient of Variance 0.3450948 AGE Mean 47.26666 7 Standard Error 2.978055 1 Median 47 Mode 47 Standard Deviation 16.31148 Sample Variance 266.0643 7 Kurtosis - 0.816067 6 Skewness 0.171850 7 Range 57 Minimum 21 Maximum 78 Sum 1418 Count 30 Largest(2) 76

Smallest(2) 22 SEX Mean 1 Standard Error 0 Median 1 Mode 1 Standard Deviation 0 Sample Variance 0 Kurtosis #DIV/ 0! Skewness #DIV/ 0! Range 0 Minimum 1 Maximum 1 Sum 30 Count 30 Largest(2) 1 Smallest(2) 1 RACE Mean 1.7 Standard Error 0.08509 6 Median 2 Mode 2 Standard Deviation 0.46609 2 Sample Variance 0.21724 1 Kurtosis -1.24213 Skewness -0.9195 Range 1 Minimum 1 Maximum 2 Sum 51 Count 30 Largest(2) 2 Smallest(2) 1

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2. Years of education each ex-offender received are shown below. Enter the education data in the Recidivism.xls data (you can copy and paste the years of education column below into the excel spreadsheet). Generate the range, variance, and standard deviation on Years of Education in Excel . Copy and paste the Excel output here. Report the results. REPORT THE RESULTS : Based on the data of YEARS OF EDUCATION, the generated range is 6. The max is 12, and the min is 6, so the difference of 6 is what is the range. Person Years of Education 1 10 2 11 3 12 4 8 5 12 6 11 7 9 8 10 9 9 10 12 11 8 12 9 13 10 14 11 15 9 16 12 17 10 18 6 19 9 20 8 21 8 22 10 23 11 24 12 25 11 26 7 27 6 28 12 29 11 30 10 EXCEL OUTPUT:

person sex race age crime recidivis m custody Years of Educatio n 1 1 1 52 2 1 Minimu m 10 2 1 1 43 3 0 Close 11 3 1 2 22 1 0 Close 12 4 1 2 47 1 0 Close 8 5 1 2 63 2 0 Minimu m 12 6 1 2 31 3 1 Medium 11 7 1 2 76 2 1 Medium 9 8 1 1 70 1 0 Close 10 9 1 1 37 2 1 Medium 9 10 1 2 49 2 1 Medium 12 11 1 2 54 2 0 Minimu m 8 12 1 2 68 2 0 Minimu m 9 13 1 2 23 1 1 Medium 10 14 1 2 47 3 0 Close 11 15 1 2 61 2 0 Medium 9 16 1 1 33 2 0 Close 12 17 1 2 45 3 0 Minimu m 10 18 1 1 34 1 0 Minimu m 6 19 1 2 54 2 1 Minimu m 9 20 1 2 29 2 0 Medium 8 21 1 2 56 2 0 Medium 8 22 1 2 29 3 1 Medium 10 23 1 2 30 1 1 Minimu m 11 24 1 2 21 1 0 Medium 12 25 1 1 51 1 0 Medium 11 26 1 1 55 2 1 Medium 7 27 1 1 78 2 1 Medium 6 28 1 2 72 3 0 Medium 12 29 1 2 46 2 0 Medium 11 30 1 2 42 2 0 Medium 10

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Years of Education Max 12 Min 6 Range 6 Standard Deviation 1.7694 7 Mean 9.8 Coefficent of Variable 0.1805 6 Count 30 Count - 1 29 Variance 3.1310 Years of Education Mean 9.8 Standard Error 0.32306008 1 Median 10 Mode 10 Standard Deviation 1.76947293 9 Sample Variance 3.13103448 3 Kurtosis - 0.41425355 5 Skewness -0.55535945 Range 6 Minimum 6 Maximum 12 Sum 294 Count 30 Largest(2) 12 Smallest(2) 6 3. Assume that you have a normal distribution of prior arrests with a mean of 6 and a standard deviation of 2.5. a. What is the z score for 10? Z = 1.6

b. What is the z score for 4? Z = -0.80 c. What is the z score for 9? Z = 1.2 d. What is the z score for 2? Z = - 1.6 4. Student A has taken a number of tests. The table below presents his score on each test. Note that scores on each of these tests are normally distributed, and the mean and standard deviation for each test are also presented in the table below. Please calculate z scores to assess which test Student A did the best and which test he did the worst. Test Student A’s score Mean sd I.Q. 100 120 15 Reading ach. 11.4 12.6 1.8 Math ach. 10.0 10.8 1.8 High school math grade 76 90 11 GRE 1000 1100 100 Test Studen t A’s score Mean sd Z-Score I.Q. 100 120 15 (100-120 = -20) /15 = -

1.33333 Readin g ach. 11.4 12.6 1.8 (11.4-12.6= -1.2) /1.8 = - 0.66667 Math ach. 10 10.8 1.8 (10 - 10.8 = -0.8) / 1.8 = - 0.44444 High school math grade 76 90 11 (76 - 90 = -14) / 11 = -1.27272 GRE 1000 110 0 10 0 (1000-1100 = -100) / 100 = -1 **Z-Score = Raw Score – Mean / Standard Deviation REPORT THE RESULTS: The best test score was math and the worst was the IQ test.

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