1. Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology Teacher Resource – Unit 2 Lesson 2

2. The BIG Idea Big Idea: Computers assist in organizing and analyzing data used in the Engineering Design Process. © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

3. Basic Statistics The Mean is the average of a given data set: x = represents the data set ∑ = the sum of a mathematical operation n = the total number of variables in the data set Equation for Mean = ∑x n © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

4. Practice Questions What is the mean for the following data set? 1, 4, 4, 6, 7, 8, 12 Equation for Mean = ∑x n © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

5. Practice Questions What is the mean for the following data set? 1, 4, 4, 6, 7, 8, 12 ∑x = 1 + 4 + 4 + 6 + 7 + 8 + 12 ∑x = 42 n 7 Mean = 6 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

6. Basic Statistics The Median is the middle number in a given ordered data set. Example: 1, 2, 3, 4, 4 If the given data set has an even number of data, the Median is the average of the two center data. Example: (1, 2, 4, 4) Median = (2+4) = 6 = 3 2 2 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

7. Practice Questions What is the median for the following data set? 1, 6, 12, 4, 4, 8, 7 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

8. Practice Questions What is the median for the following data set? 1, 6, 12, 4, 4, 8, 7 Ordered Data Set = 1, 4, 4, 6, 7, 8, 12 Median = 1, 4, 4, 6, 7, 8, 12 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

9. Practice Questions What is the median for the following data set? 1, 6, 12, 4, 4, 7 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

10. Practice Questions What is the median for the following data set? 1, 6, 12, 4, 4, 7 Ordered Data Set = 1, 4, 4, 6, 7, 12 Middle Numbers = 4, 6 = (4+6) = 10 = 5 2 2 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

11. Basic Statistics The Mode is the most frequently occurring number in a given data set. Example: 1, 2, 3, 4, 4 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

12. Practice Questions What is the mode for the following data set? 1, 6, 12, 4, 4, 8, 7 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

13. Practice Questions What is the mode for the following data set? 1, 6, 12, 4, 4, 8, 7 Mode = 4 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

14. Basic Statistics Standard Deviation shows how much the data vary from the mean. x i = represents the individual data μ = represents the mean of the data set ∑ = the sum of a mathematical operation n = the total number of variables in the data set Equation for Standard Deviation = ∑(x i – μ)² √ n - 1 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

15. Basic Statistics What is the standard deviation for the following data set? 1, 4, 4, 6, 7, 8, 12 Equation for Standard Deviation = ∑(x i – μ)² √ n - 1 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

16. Practice Questions What is the standard deviation for the following data set? (1, 4, 4, 6, 7, 8, 12) ∑(x i – μ)² √ n - 1 The mean for the data set is 6, therefore μ = 6. ∑(x i – μ)² = ∑(1 – 6)² + (4 – 6)² + (4 – 6)² + (6 – 6)² + (7 – 6)² + (8 – 6)² + (12 – 6)² = ∑(-5)² + (-2)² + (-2)² + (0)² + (1)² + (2)² + (6)² = ∑(25) + (4) + (4) + (0) + (1) + (4) + (36) = 74 ∑(x i – μ)² = 74 = 74 = 12.3 = 3.51 √ n – 1 √ 7 - 1 √ 6 √ © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

17. Basic Statistics The Range is the distribution of the data set or the difference between the largest and smallest values in a data set. Example: 1, 2, 3, 4, 4 Largest Value = 4 and the Smallest Value = 1 Range = (4 – 1) = 3 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

18. Practice Questions What is the range for the following data set? 1, 4, 4, 6, 7, 8, 12 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

19. Practice Questions What is the range for the following data set? 1, 4, 4, 6, 7, 8, 12 Largest Value = 12 and the Smallest Value = 1 Range = (12 – 1) = 11 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

20. Basic Statistics Engineering tolerance is the amount a characteristic can vary without compromising the overall function or design of the product. Tolerances generally apply to the following: Physical dimensions (part and/or fastener) Physical properties (materials, services, systems) Calculated values (temperature, packaging) © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology

21. Basic Statistics Engineering tolerances are expressed like a written language and follow the American National Standards Institute (ANSI) standards. Example: Bilateral Tolerance (1.125 0.025) Example: Unilateral Tolerance (2.575 ) Upper and lower specification limit are derived from the acceptable tolerance. Bilateral and Unilateral are just two examples of how tolerance is expressed using ANSI. © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology +0.005 - 0.005 + –

22. Practice Questions What are the upper and lower specification limit for the examples below? Example: Bilateral Tolerance (1.125 0.025) Example: Unilateral Tolerance (2.575 ) © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology +0.005 - 0.005 + –

23. Practice Questions What are the upper and lower specification limit for the examples below? Example: Bilateral Tolerance (1.125 0.025) Upper Specification Limit = 1.125 + 0.025 = 1.150 Lower Specification Limit = 1.125 – 0.025 = 1.100 The Range should equal the difference between the upper and lower specification limit. Range = 0.050 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology + –

24. Practice Questions What are the upper and lower specification limit for the examples below? Example: Unilateral Tolerance (2.575 ) Upper Specification Limit = 2.575 + 0.005 = 2.580 Lower Specification Limit = 2.575 – 0.005 = 2.570 The Range should equal the difference between the upper and lower specification limit. Range = 0.010 © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching and Learning™ Foundations of Technology +0.005 - 0.005