ID Salary 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 57.7 27.3 35.5 60.9 47 72.8 41.8 21.8 76.3 22.5 22.8 64.5 41.4 23.1 23.5 47.9 67 35.2 24.3 33.6 77.5 53.6 22.9 61.2 24.5 22.3 38.4 75.3 73.2 49.5 23.9 27.2 61.8 28.1 24.5 23 23.6 59.7 34.4 23.9 40.6 23.3 77.3 62.3 Compa Midpoint 1.013 0.880 1.146 1.068 0.979 1.086 1.046 0.947 1.139 0.978 0.991 1.132 1.035 1.003 1.021 1.198 1.175 1.134 1.058 1.085 1.156 1.116 0.996 1.276 1.066 0.970 0.961 1.124 1.092 1.031 1.040 0.877 1.084 0.905 1.066 0.998 1.026 1.047 1.111 1.040 1.016 1.011 1.154 1.093 57 31 31 57 48 67 40 23 67 23 23 57 40 23 23 40 57 31 23 31 67 48 23 48 23 23 40 67 67 48 23 31 57 31 23 23 23 57 31 23 40 23 67 57 Age 34 52 30 42 36 36 32 32 49 30 41 52 30 32 32 44 27 31 32 44 43 48 36 30 41 22 35 44 52 45 29 25 35 26 23 27 22 45 27 24 25 32 42 45 Performance Service Gender Rating 85 80 75 100 90 70 100 90 100 80 100 95 100 90 80 90 55 80 85 70 95 65 65 75 70 95 80 95 95 90 60 95 90 80 90 75 95 95 90 90 80 100 95 90 8 7 5 16 16 12 8 9 10 7 19 22 2 12 8 4 3 11 1 16 13 6 6 9 4 2 7 9 5 18 4 4 9 2 4 3 2 11 6 2 5 8 20 16 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 Raise Degree 5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 4 4.7 4.8 4.5 4.7 6 4.9 5.7 3 5.6 4.6 4.8 6.3 3.8 3.3 3.8 4 6.2 3.9 4.4 5.4 4.3 3.9 5.6 5.5 4.9 5.3 4.3 6.2 4.5 5.5 6.3 4.3 5.7 5.5 5.2 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 45 46 47 48 49 50 58 61.5 61.2 64.6 62.5 63.9 1.209 1.079 1.074 1.133 1.096 1.121 48 57 57 57 57 57 36 39 37 34 41 38 95 75 95 90 95 80 8 20 5 11 21 12 1 0 0 1 0 0 5.2 3.9 5.5 5.3 6.6 4.6 1 1 1 1 0 0 Gender 1 Gr M M F M M M F F M F F M F F F M F F M F M F F F M F M F M M F M M M F F F M F M M F F M E B B E D F C A F A A E C A A C E B A B F D A D A A C F F D A B E B A A A E B A C A F E Copy Employee Data set to this page. The ongoing question that the weekly assignments will focus on is: Are males and females p Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal wor The column labels in the table mean: ID - Employee sample number Salary - Salary in thousands Age - Age in years Performance Rating - Appraisal rating (Employee e SERvice - Years of service Gender: 0 = male, 1 = female Midpoint - salary grade midpointRaise - percent of last raise Grade - job/pay grade Degree (0= BS\\BA 1 = MS) Gender1 (Male or Female) Compa-ratio - salary divided by midpoint F M M F M M D E E E E E ge. Are males and females paid the same for equal work (under the Equal Pay Act)? grade comprise equal work. isal rating (Employee evaluation score) by midpoint This assignment covers the material presented in weeks 1 and 2. Before starting this assignment, make sure the the assignment data from the Employee Salary Data Set file is copi You can do this either by a copy and paste of all the columns or by opening the data file, right clicking on the Data (Weekly Assignment Sheet or whatever you are calling your master assignment file). It is highly recommended that you copy the data columns (with labels) and paste them to the right so that whateve To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks then the cells should have an "=XX" formula in them, where XX is the column and row number showing the valu value using fxfunctions, then each function should be located in the cell and the location of the data values should So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numer The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we ne In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences e 1 The first step in analyzing data sets is to find some summary descriptive statist focus mostly on the compa-ratios, we need to find the mean, standard deviatio Sorting the compa-ratios into male and females will require you copy and past The values for age, performance rating, and service are provided for you for fu (see if you can replicate the values). You can use either the Data Analysis Descriptive Statistics tool or the Fx =ave The range can be found using the difference between the =max and =min func Suggestion: Copy and paste the compa-ratio data to the right (Column T) and If you use Descriptive statistics, Place the output table in ro If you did not use Descriptive Statistics, make sure your cell Overall Female Male Mean Standard Deviation Range Mean Standard Deviation Range Mean Standard Deviation Range A key issue in comparing data sets is to see if they are distributed/shaped the same. At this point we can do this by looking at the probabilities that males and females are distributed in the same way for a grade levels. 2 Empirical Probability: What is the probability for a: a. Randomly selected person being in grade E or above? b. Randomly selected person being a male in grade E or above? c. Randomly selected male being in grade E or above? d. 3 A Why are the results different? Normal Curve based probability: For each group (overall, females, males), wh Make sure your answer cells show the Excel function and cell location of the d The probability of being in the top 1/3 of the compa-ratio distribution. Note, we can find the cutoff value for the top 1/3 using the Value is the number that identifies the x-largest value. For the top 1/3 value w For the overall group, this would be the 50/3 or 17th (rounded), for the gender i. How nany salaries are in the top 1/3 (rounded to nearest whole number) for ea ii What Compa-ratio value starts the top 1/3 of the range for each group? iii What is the z-score for this value? iv. What is the normal curve probability of exceeding this score? B How do you interpret the relationship between the data sets? What does this s The data is very scewed. There is a obvious difference in pay according to gen 4 A Based on our sample data set, can the male and female compa-ratios in the pop First, we need to determine if these two groups have equal variances, in order What is the data input ranged us Ho: Ha: Step 1: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B77 in the output location box. 0.9137609129 F-Test Two-Sample for Variances Descriptive Statistics Sample size Mean Variance Standard Deviation Mean Standard Error Step 5: Conclusion and Interpretation Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? What is your decision: REJ or NOT reject the null? What does this result say about our question of variance equality? B Are male and female average compa-ratios equal? (Regardless of the outcome of the above F-test, assume equal variances for thi What is the data input ranged us Ho: Ha: Step 1: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B109 in the output location box 0.3943386356 Step 5: Conclusion and Interpretation Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? What is your decision: REJ or NOT reject the null? What does your decision on rejecting the null hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? What does the result of this test tell us about our question on salary equality? 5 Is the Female average compa-ratio equal to or less than the midpoint value of 1 This question is the same as: Does the company, pay its females - on average Suggestion: Use the data column T to the right for your null hypothesis value. What is the data input ranged used for this question: Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B162 in the output location box Step 5: Conclusion and Interpretation Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? What, besides the p-value, needs to be considered with a one tail test? Decision: Reject or do not reject Ho? What does your decision on rejecting the null hypothesis mean? What does your decision on rejecting the null hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? What does the result of this test tell us about our question on salary equality? 6 Considering both the salary information in the lectures and your compa-ratio in Why - what statistical results support this conclusion? Six Questions the Employee Salary Data Set file is copied over to this Assignment file. ing the data file, right clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file gnment file). nd paste them to the right so that whatever you do will not disrupt the original data values and relationships. our results. For example, Question 1 asks for several data values. If you obtain them using descriptive statistics, column and row number showing the value in the descriptive statistics table. If you choose to generate each and the location of the data values should be shown. =average(T2:T26)". Having only a numerical value will not earn full credit. tools if the answers are not correct - we need to see how the results were obtained. riptive statistics and seeing if differences exist. Probing into reasons and mitigating factors is a follow-up activity. s to find some summary descriptive statistics for key variables. Since the assignment problems will e need to find the mean, standard deviations, and range for our groups: Males, Females, and Overall. nd females will require you copy and paste the Compa-ratio and Gender1 columns, and then sort on Gender1. ng, and service are provided for you for future use, and - if desired - to test your approach to the compa-ratio answers s Descriptive Statistics tool or the Fx =average and =stdev functions. fference between the =max and =min functions with Fx functions or from Descriptive Statistics. pa-ratio data to the right (Column T) and gender data in column U. ptive statistics, Place the output table in row 1 of a column to the right. Descriptive Statistics, make sure your cells show the location of the data (Example: =average(T2:T51) Compa-ratio Age Perf. Rat. Service 1.0616 35.7 85.9 9.0 0.0820501986715500 8.2513 11.4147 5.7177 0.399 30 45 21 1.1163 32.5 84.2 7.9 0.0831834719 6.9 13.6 4.9 0.329 26.0 45.0 18.0 1.0516 38.9 87.6 10.0 0.0813459075 8.4 8.7 6.4 0.321 28.0 30.0 21.0 d the same. At this point we can do this the same way for a grade levels. robability for a: ng in grade E or above? ng a male in grade E or above? in grade E or above? r each group (overall, females, males), what are the values for each question below?: he Excel function and cell location of the data used. /3 of the compa-ratio distribution. or the top 1/3 using the fx Large function: =large(range, value). he x-largest value. For the top 1/3 value would be the value that starts the top 1/3 of the range, the 50/3 or 17th (rounded), for the gender groups, it would be the 25/3 = 8th (rounded) value. (rounded to nearest whole number) for each group? op 1/3 of the range for each group? y of exceeding this score? p between the data sets? What does this suggest about our equal pay for equal work question? obvious difference in pay according to gender for equal work. e male and female compa-ratios in the population be equal to each other? wo groups have equal variances, in order to decide which t-test to use. What is the data input ranged used for this question: male mean salary = female mean salary male mean salary not equal to female mean salary Reject Ho if p -value is less than Alpha = 0.025 for one tail F-test F-test is for variance. Since we are testing for equality, there are 2 sample test and rejection region is in both tails place cell B77 in the output location box. ple for Variances Ratio of variances Var[0.947]/Var[0.877] 0.947 terpretation What is 0.877 24 1.07683 0.00652 0.08073 F 24 F Critical value (5%) 1.05892 F Critical value (5%) 2-tailed 0.00552 p-level 2-tailed (H1: F 1) 0.07432 p-level 1-tailed (H1: F > 1) 1.17981 2.01442 2.31164 0.69506 0.34753 0.01648 0.01517 p-level 1-tailed (H1: F < 1) 0.65247 p-level 2-tailed (H1: F 1) the p-value: p-level 1-tailed (H1: F > 1) 0.69506 0.34753 H1 rejected H1 rejected p-level 1-tailed (H1: F < 1) 0.65247 H1 rejected il test) or 0.025 (for a two tail test)? neither ecision: REJ or NOT reject the null? rejected ut our question of variance equality? male mean salary not equal to female mean salary -ratios equal? bove F-test, assume equal variances for this test.) What is the data input ranged used for this question: male mean salary = female mean salary male mean salary not equal to female mean salary Reject the null hypothesis is less than Alpha = 0.05 2 sample unequal variance T-Test p-value greater than rejection alpha place cell B109 in the output location box. terpretation What is the p-value: il test) or 0.025 (for a two tail test)? ecision: REJ or NOT reject the null? rejecting the null hypothesis mean? ected, calculate the effect size value: hy the null hypothesis was rejected? hy the null hypothesis was rejected? tell us about our question on salary equality? qual to or less than the midpoint value of 1.00? he company, pay its females - on average - at or below the grade midpoint (which is considered the market rate)? o the right for your null hypothesis value. or this question: place cell B162 in the output location box. terpretation What is the p-value: il test) or 0.025 (for a two tail test)? o be considered with a one tail test? ecision: Reject or do not reject Ho? rejecting the null hypothesis mean? rejecting the null hypothesis mean? ected, calculate the effect size value: hy the null hypothesis was rejected? tell us about our question on salary equality? tion in the lectures and your compa-ratio information, what conclusions can you reach about equal pay for equal work? t this conclusion? sheet to this file relationships. scriptive statistics, generate each follow-up activity. ort on Gender1. he compa-ratio answers Note - remember the data is a sample from the larger company population Probability 18/50 13/50 13/25 the sample size increased Overall 61 Female Male All of the functions below are in the 61 #VALUE! Use the "=ROUND" function (found 1.086 Use the "=LARGE" function 1.093 1.116 0.382205 -0.003506 0.422394 Use Excel's STANDARDIZE functio 0.6488454 0.498601 0.663631 Use "=1-NORM.S.DIST" function ejection region is in both tails and makes each tail 0.25 F [larger/smaller] H1 rejected H1 rejected H1 rejected F 1.17981 F Critical value (5%) 2.01442 F Critical value (5%) 2-tailed 2.31164 H0 F=1 (5%)? accepted the market rate)? ual pay for equal work? overall F M Compa Gender 1 Total ^2 Variance 1.1270794896 1.06164 0.947 F 53.082 ### 1.07164 0.970 F 26.791 1.1059466896 1.05164 0.978 F 26.291 0.991 F 0.996 F 0.998 F 1.003 F 1.011 F 1.021 F 1.026 F 1.035 F 1.040 F 1.046 F 1.066 F 1.085 F 1.111 F 1.116 F 1.124 F 1.133 F 1.134 F 1.146 F 1.154 F 1.175 F 1.209 F 1.276 F 0.877 M 0.880 M 0.905 M 0.961 M 0.979 M 1.013 M 1.016 M 1.031 M 1.040 M 1.047 M 1.058 M 1.066 M 1.068 M 1.074 M 1.079 M 1.084 M 1.086 M 1.092 M Gender1 1.093 M F 1.096 M F 1.121 M F functions below are in the fx statistical list. =ROUND" function (found in Math or All list) =LARGE" function l's STANDARDIZE function NORM.S.DIST" function 1.132 1.139 1.156 1.198 M M M M F F F F F F F F F F F F F F F F F F F F F F M M M M M M M M M M M M M M M M M M M M M M M M M Gr B C A Salary 35.5 41.8 21.8 A A C A A E B B D A D A F A A A A B A F D E E B E D 22.5 22.8 41.4 23.1 23.5 67 35.2 33.6 53.6 22.9 61.2 22.3 75.3 23.9 24.5 23 23.6 34.4 23.3 77.3 58 64.6 57.7 27.3 60.9 47 F F E C A F A C F D B E B E A C E E E E 72.8 76.3 64.5 47.9 24.3 77.5 24.5 38.4 73.2 49.5 27.2 61.8 28.1 59.7 23.9 40.6 62.3 61.5 61.2 62.5 E 63.9 Week 3 ANOVA Three Questions Remember to show how you got your results in the appropriate cells. For questions using functions, show the inp 1 One interesting question is are the average compa-ratios equal across salary ranges of 10K each. While compa-ratios remove the impact of grade on salaries, are they different for different pay levels, that is are people at different levels paid differently relative to the midpoint? (Put data values at right.) What is the data input ranged used for this question: Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell b16 in the output location box. Step 5: Conclusions and Interpretation What is the p-value? Is P-value < 0.05? What is your decision: REJ or NOT reject the null? If the null hypothesis was rejected, what is the effect size value (eta squared)? If calculated, what does the effect size value tell us about why the null hypothesis was rejected? What does that decision mean in terms of our equal pay question? 2 If the null hypothesis in question 1 was rejected, which pairs of means differ? Groups Compared G1 G2 G1 G3 G1 G4 G1 G5 G1 G6 Diff T +/- Term Low to G2 G3 G2 G4 G2 G5 G2 G6 G3 G4 G3 G5 G3 G6 G4 G5 G4 G6 G5 G6 3 Since compa is already a measure of pay for equal work, do these results impact your conclusion on equal pay for equal work? Why or why not? High ng functions, show the input range when asked. anges of 10K each. for different pay levels, (Put data values at right.) Group name: Salary Intervals: Compa-ratio values: G1 22-29 G2 30-39 G3 40-49 G4 50-59 G5 60-69 Why? Difference Significant? Why? G6 70-79 Regression and Corellation Five Questions Remember to show how you got your results in the appropriate cells. For questions using functions, show the inp 1 Create a correlation table using Compa-ratio and the other interval level variables, except for Suggestion, place data in columns T - Y. What range was placed in the Correlation input range box: Place C9 in output box. b What are the statistically significant correlations related to Compa-ratio? c Are there any surprises - correlations you though would be significant and are not, or non sign d Why does or does not this information help answer our equal pay question? 2 Perform a regression analysis using compa as the dependent variable and the variables used in including the dummy variables. Show the result, and interpret your findings by answering the Suggestion: Place the dummy variables values to the right of column Y. What range was placed in the Regression input range box: Note: be sure to include the appropriate hypothesis statements. Regression hypotheses Ho: Ha: Coefficient hyhpotheses (one to stand for all the separate variables) Ho: Ha: Place B36 in output box. Interpretation: For the Regression as a whole: What is the value of the F statistic: What is the p-value associated with this value: Is the p-value < 0.05? What is your decision: REJ or NOT reject the null? What does this decision mean? For each of the coefficients: What is the coefficient's p-value for each of the variables: Is the p-value < 0.05? Do you reject or not reject each null hypothesis: Midpoint Age Perf. Rat. What are the coefficients for the significant variables? Using the intercept coefficient and only the significant variables, what is the equation? Compa-ratio = Is gender a significant factor in compa-ratio? Regardless of statistical significance, who gets paid more with all other things being equal? How do we know? 3 What does regression analysis show us about analyzing complex measures? 4 Between the lecture results and your results, what else would you like to know before answering our question on equal pay? Why? 5 Between the lecture results and your results, what is your answer to the question of equal pay for equal work for males and females? Why? g functions, show the input range when asked. vel variables, except for Salary. T= Significant r = nt and are not, or non significant correlations you thought would be? and the variables used in Q1 along with indings by answering the following questions. he question Service Gender Degree Compa- Midpoint ratio Age Performa Service nce Rating Raise Degree Gender Salary Gender 1 21.8 F 22.5 F 22.8 F 23.1 F 23.5 F 24.3 M 22.9 F 24.5 M 22.3 F 23.9 F 24.5 F 23 F 23.6 F 23.9 M 23.3 F 27.3 M 35.5 F 35.2 F 33.6 F 27.2 M 28.1 M 34.4 F 41.8 F 41.4 F 47.9 M 38.4 M 40.6 M 47 M 53.6 F 61.2 F 49.5 M 58 F 57.7 M 60.9 M 64.5 M 67 F 61.8 M 59.7 M 62.3 M 61.5 M 61.2 M 64.6 F 62.5 M 63.9 M Gr A A A A A A A A A A A A A A A B B B B B B B C C C C C D D D D D E E E E E E E E E E E E A B C D E 21.8 22.5 22.8 23.1 23.5 24.3 22.9 24.5 22.3 23.9 24.5 23 23.6 23.9 23.3 27.3 35.5 35.2 33.6 27.2 28.1 34.4 41.8 41.4 47.9 38.4 40.6 47 53.6 61.2 49.5 58 57.7 60.9 64.5 67 61.8 59.7 62.3 61.5 61.2 64.6 62.5 63.9 72.8 76.3 77.5 75.3 73.2 77.3 M M M F M F F F F F F F F 72.8 76.3 77.5 75.3 73.2 77.3 Alpha (significance level) 5.% Variable #1 (A) Count Mean Mean LCL Mean UCL Variance Standard Deviation Mean Standard Error Coefficient of Variation Minimum Maximum Range Median Median Error Percentile 25% (Q1) Percentile 75% (Q3) IQR MAD (Median Absolute Deviation) Coefficient of Dispersion (COD) 15 Mean Deviation 23.32667 Second Moment 22.87899 Third Moment 23.77435 Fourth Moment 0.65352 0.80841 Sum 0.20873 Sum Standard Error 0.03466 Total Sum Squares Adjusted Sum Squares 21.8 24.5 Geometric Mean 2.7 Harmonic Mean Mode 23.3 0.06755 Skewness 22.85 Skewness Standard Error 23.9 Kurtosis 1.05 Kurtosis Standard Error 1.2 Skewness (Fisher's) 0.02804 Kurtosis (Fisher's) Variable #2 (B) Count Mean Mean LCL Mean UCL Variance Standard Deviation Mean Standard Error Coefficient of Variation Minimum Maximum Range Median Median Error Percentile 25% (Q1) Percentile 75% (Q3) IQR MAD (Median Absolute Deviation) Coefficient of Dispersion (COD) 7 Mean Deviation 31.61429 Second Moment 28.03021 Third Moment 35.19836 Fourth Moment 15.0181 3.87532 Sum 1.46473 Sum Standard Error 0.12258 Total Sum Squares Adjusted Sum Squares 27.2 35.5 Geometric Mean 8.3 Harmonic Mean Mode 33.6 0.69386 Skewness 27.7 Skewness Standard Error 34.8 Kurtosis 7.1 Kurtosis Standard Error 0 Skewness (Fisher's) 0.09566 Kurtosis (Fisher's) Variable #3 (C) Count 5 Mean Deviation Mean Mean LCL Mean UCL Variance Standard Deviation Mean Standard Error Coefficient of Variation Minimum Maximum Range Median Median Error Percentile 25% (Q1) Percentile 75% (Q3) IQR MAD (Median Absolute Deviation) Coefficient of Dispersion (COD) 42.02 Second Moment 37.62444 Third Moment 46.41556 Fourth Moment 12.532 3.54006 Sum 1.58316 Sum Standard Error 0.08425 Total Sum Squares Adjusted Sum Squares 38.4 47.9 Geometric Mean 9.5 Harmonic Mean Mode 41.4 0.88736 Skewness 40.6 Skewness Standard Error 41.8 Kurtosis 1.2 Kurtosis Standard Error 6.5 Skewness (Fisher's) 0.05169 Kurtosis (Fisher's) Variable #4 (D) Count Mean Mean LCL Mean UCL Variance Standard Deviation Mean Standard Error Coefficient of Variation Minimum Maximum Range Median Median Error Percentile 25% (Q1) Percentile 75% (Q3) IQR MAD (Median Absolute Deviation) Coefficient of Dispersion (COD) 5 Mean Deviation 53.86 Second Moment 46.58932 Third Moment 61.13068 Fourth Moment 34.288 5.8556 Sum 2.6187 Sum Standard Error 0.10872 Total Sum Squares Adjusted Sum Squares 47 61.2 Geometric Mean 14.2 Harmonic Mean Mode 53.6 1.46778 Skewness 49.5 Skewness Standard Error 58 Kurtosis 8.5 Kurtosis Standard Error 7.6 Skewness (Fisher's) 0.0847 Kurtosis (Fisher's) Variable #5 (E) Count Mean Mean LCL Mean UCL Variance 12 Mean Deviation 62.3 Second Moment 60.73426 Third Moment 63.86574 Fourth Moment 6.07273 Standard Deviation Mean Standard Error Coefficient of Variation Minimum Maximum Range Median Median Error Percentile 25% (Q1) Percentile 75% (Q3) IQR MAD (Median Absolute Deviation) Coefficient of Dispersion (COD) 2.46429 Sum 0.71138 Sum Standard Error 0.03956 Total Sum Squares Adjusted Sum Squares 57.7 67 Geometric Mean 9.3 Harmonic Mean Mode 62.05 0.25738 Skewness 61.125 Skewness Standard Error 64.05 Kurtosis 2.925 Kurtosis Standard Error 1.3 Skewness (Fisher's) 0.02955 Kurtosis (Fisher's) Variable #6 (F) Count Mean Mean LCL Mean UCL Variance Standard Deviation Mean Standard Error Coefficient of Variation Minimum Maximum Range Median Median Error Percentile 25% (Q1) Percentile 75% (Q3) IQR MAD (Median Absolute Deviation) Coefficient of Dispersion (COD) 6 Mean Deviation 75.4 Second Moment 73.27817 Third Moment 77.52183 Fourth Moment 4.088 2.02188 Sum 0.82543 Sum Standard Error 0.02682 Total Sum Squares Adjusted Sum Squares 72.8 77.5 Geometric Mean 4.7 Harmonic Mean Mode 75.8 0.42234 Skewness 73.725 Skewness Standard Error 77.05 Kurtosis 3.325 Kurtosis Standard Error 1.1 Skewness (Fisher's) 0.02155 Kurtosis (Fisher's) 0.65511 0.60996 -0.06135 0.80301 349.9 3.13095 8,171.15 9.14933 23.31354 23.30037 #N/A -0.12878 0.54006 2.15836 0.89214 -0.14356 -0.67005 3.49796 12.87265 -10.78583 192.5325 221.3 10.25313 7,086.35 90.10857 31.40619 31.19545 #N/A -0.23353 0.67082 1.1619 0.88192 -0.3027 -2.61145 2.352 10.0256 30.54946 274.26608 210.1 7.91581 8,878.53 50.128 41.90578 41.79656 #N/A 0.96236 0.70711 2.72867 0.75 1.4346 2.91469 4.592 27.4304 12.13531 1,154.46432 269.3 13.09351 14,641.65 137.152 53.60551 53.35235 #N/A 0.08447 0.70711 1.53432 0.75 0.12592 -1.86272 1.83333 5.56667 0.9265 87.09617 747.6 8.53655 46,642.28 66.8 62.25533 62.21065 #N/A 0.07054 0.58177 2.81066 0.91655 0.08105 0.4325 1.63333 3.40667 -1.896 17.04327 452.4 4.95258 34,131.4 20.44 75.37729 75.35447 #N/A -0.30154 0.69007 1.46857 0.83557 -0.4129 -1.96668