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BA 275 Quantitative Business Methods Agenda Summarizing Quantitative Data The Stem-and-Leaf Display The Box and Whisker Plot The Empirical Rule Quiz #2 Announcement •TA: Shen. 8:00 – 9:50 am, Friday at 328 Bx. 1 Quiz #1 Part 1. One of the conclusions of the Nationwide Personal Transportation Survey was that "In 1990, women drove 76% more on average than they did in 1969. However, women still drove 7,000 miles less on average than men in a year." Question 1. What is the numerical value of 76% an example of? A. A population parameter based on driving behavior in 1990 B. A population parameter based on comparing driving behavior in 1969 and 1990 C. A sample statistic based on driving behavior in 1990 D. A sample statistic based on comparing driving behavior in 1969 and 1990 E. None of the above 2 Quiz #1 Part 1. One of the conclusions of the Nationwide Personal Transportation Survey was that "In 1990, women drove 76% more on average than they did in 1969. However, women still drove 7,000 miles less on average than men in a year.“ Question 2. What is the numerical value of 7,000 miles an example of? A. A population parameter based on comparing driving behavior in 1969 and 1990 B. A sample statistic based on driving behavior in 1990 C. A sample statistic based on comparing driving behavior in 1969 and 1990 D. A population parameter based on driving behavior in 1990 E. None of the above 3 Quiz #1 Part 3. A college researcher surveys a random sample of 500 students. Among other things, the survey asks whether students have observed any instance of racial discrimination on campus. One hundred students return completed surveys, and 53 report having observed such discrimination. The researcher then reports that racial discrimination is common on campus. This report is: A. Invalid because the sample is such a small percent of the student body B. Invalid because it is a volunteer sample C. Valid because the sample is random D. Valid because the sampling frame is the entire student population 4 statistics: x , s2, s, p̂ , etc. x1, x2, …, xn Sample of size n Qualitative Quantitative Organizing data: Estimation Hypothesis Testing Regression Analysis Contingency Tables Drawing conclusions from data: Random variables, Probability, Distributions Discrete: binomial distribution Continuous: normal distribution, Sampling distribution of the sample mean Describing uncertainty: X1, X2, …, Xn Selecting a random sample: parameters: , 2, , p, etc. POPULATION Statistical Analysis 5 CEO Data NO 1 2 3 4 5 6 7 8 9 10 AGE 53 36 48 53 46 50 59 48 43 45 SALARY 145 291 659 298 250 291 296 388 621 58 EDUCATION Bachelors Masters Doctorate Masters Doctorate Bachelors Bachelors Masters Masters Bachelors : : : : : : : : : : : : 54 55 56 57 58 59 60 55 51 58 44 51 70 43 736 368 217 206 536 213 573 Bachelors Bachelors Bachelors Bachelors Masters Masters Bachelors 6 Summary Statistics AGE SALARY ---------------------------------------------------Count 60 60 Average 51.4667 403.883 Median 50.0 350.0 Mode 50.0 Variance 79.609 47815.6 Standard deviation 8.92239 218.668 Minimum 32.0 21.0 Maximum 74.0 1103.0 Range 42.0 1082.0 Lower quartile 45.5 250.0 Upper quartile 57.0 539.5 Interquartile range 11.5 289.5 ---------------------------------------------------7 Stem-and-Leaf Display for AGE 2 5 11 25 (12) 23 11 4 2 3|23 3|678 4|013344 4|55556677788889 5|000000112333 5|555666677889 6|0111223 6|99 7|04 8 Box-and-Whisker Plot for Salary Box-and-Whisker Plot 0 200 400 600 800 1000 1200 Salary 9 Box-and-Whisker Plot for Salary Invisible line Q1 – 1.5 x IQR Box-and-Whisker Plot Invisible line Q3 + 1.5 x IQR IQR = 289.5 1.5 x IQR = 434.25 Q1 = 250.0 Q1 – 1.5 x IQR = -184.25 Q3 = 539.5 Q3 + 1.5 x IQR = 973.75 0 200 400 600 800 1000 1200 Salary Smallest observation Within the invisible lines = Minimum Largest observation Within the invisible lines ≠ Maximum 10 Two or Multiple-Sample Comparison SG+: Compare / Multiple Samples / Multiple-Sample Comparison Compare / Two Samples / Two-Sample Comparison Summary Statistics for AGE EDUCATION Count Average Median Standard devia ---------------------------------------------------------------------------------------------Bachelors 25 51.92 53.0 8.10309 Doctorate 10 47.3 47.0 9.00679 Masters 22 53.8636 52.5 9.34164 None 3 44.0 45.0 6.55744 ---------------------------------------------------------------------------------------------Total 60 51.4667 50.0 8.92239 EDUCATION Maximum Lower quartile Upper quartile ---------------------------------------------------------------------------------------------Bachelors 69.0 47.0 57.0 Doctorate 62.0 41.0 50.0 Masters 74.0 48.0 58.0 None 50.0 37.0 50.0 ---------------------------------------------------------------------------------------------Total 74.0 45.5 57.0 11 Two or Multiple-Sample Comparison SG+: Compare / Multiple Samples / Multiple-Sample Comparison Compare / Two Samples / Two-Sample Comparison EDUCATION Box-and-Whisker Plot Bachelors Doctorate Masters None 32 42 52 62 AGE 72 82 12 Questions: CEO 1. What is the mean age? The mean salary? 2. What is the median age? The median salary? 3. How many CEO’s in the sample are younger than 45 years old? 4. How many CEO’s in the sample are making more than $540K a year? 5. If the youngest and oldest CEO’s are removed from the sample, what is the new median? What is the new mean? Does the new variance (or standard deviation) increase or decrease? 13 Exercise 1.1 In your own words, define and give an example of each of the following statistical terms. Population Sample Parameter Statistic 14

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