# Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching.

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<ul><li> Slide 1 </li> <li> 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 </li> <li> Slide 2 </li> <li> 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 </li> <li> Slide 3 </li> <li> 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 </li> <li> Slide 4 </li> <li> 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 </li> <li> Slide 5 </li> <li> 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 </li> <li> Slide 6 </li> <li> 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 </li> <li> Slide 7 </li> <li> 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 </li> <li> Slide 8 </li> <li> 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 </li> <li> Slide 9 </li> <li> 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 </li> <li> Slide 10 </li> <li> 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 </li> <li> Slide 11 </li> <li> 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 </li> <li> Slide 12 </li> <li> 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 </li> <li> Slide 13 </li> <li> 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 </li> <li> Slide 14 </li> <li> Basic Statistics Standard Deviation shows how much the data vary from the mean. x i = represents the individual data = 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 ) n - 1 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning Foundations of Technology </li> <li> Slide 15 </li> <li> 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 ) n - 1 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning Foundations of Technology </li> <li> Slide 16 </li> <li> Practice Questions What is the standard deviation for the following data set? (1, 4, 4, 6, 7, 8, 12) (x i ) n - 1 The mean for the data set is 6, therefore = 6. (x i ) = (1 6) + (4 6) + (4 6) + (6 6) + (7 6) + (8 6) + (12 6) = (-5) + (-2) + (-2) + (0) + (1) + (2) + (6) = (25) + (4) + (4) + (0) + (1) + (4) + (36) = 74 (x i ) = 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 </li> <li> Slide 17 </li> <li> 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 </li> <li> Slide 18 </li> <li> 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 </li> <li> Slide 19 </li> <li> 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 </li> <li> Slide 20 </li> <li> 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 </li> <li> Slide 21 </li> <li> 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 + </li> <li> Slide 22 </li> <li> 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 + </li> <li> Slide 23 </li> <li> 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 + </li> <li> Slide 24 </li> <li> 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 </li> </ul>

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