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Page 1: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Foundations of Technology

Basic StatisticsBasic Statistics

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Teacher Resource – Unit 2 Lesson 2

Page 2: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

The BIG IdeaThe BIG Idea

Big Idea:

Computers assist in organizing and analyzing data used in the Engineering Design Process.

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 3: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Basic StatisticsBasic 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 4: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 5: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice 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

∑x = 42 n 7

Mean = 6

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 6: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Basic StatisticsBasic 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 7: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice Questions

What is the median for the following data set?

1, 6, 12, 4, 4, 8, 7

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 8: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 9: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice Questions

What is the median for the following data set?

1, 6, 12, 4, 4, 7

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 10: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 11: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Basic StatisticsBasic 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 12: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice Questions

What is the mode for the following data set?

1, 6, 12, 4, 4, 8, 7

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 13: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 14: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Basic StatisticsBasic Statistics

Standard Deviation shows how much the data vary from the mean.

xi = 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 = ∑(xi – μ)² √ n - 1

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 15: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Basic StatisticsBasic Statistics

What is the standard deviation for the following data set?

1, 4, 4, 6, 7, 8, 12

Equation for Standard Deviation = ∑(xi – μ)² √ n - 1

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 16: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice Questions

What is the standard deviation for the following data set? (1, 4, 4, 6, 7, 8, 12)

∑(xi – μ)²√ n - 1

The mean for the data set is 6, therefore μ = 6.∑(xi – 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

∑(xi – μ)² = 74 = 74 = 12.3 = 3.51√ n – 1 √ 7 - 1 √ 6 √

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 17: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Basic StatisticsBasic Statistics

The Range is the distribution of thedata 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 18: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice Questions

What is the range for the following data set?

1, 4, 4, 6, 7, 8, 12

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 19: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 20: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Basic StatisticsBasic 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, STEMCenter for Teaching and Learning™ Foundations of Technology

Page 21: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Basic StatisticsBasic 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, STEMCenter for Teaching and Learning™ Foundations of Technology

+0.005

- 0.005

+–

Page 22: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice 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, STEMCenter for Teaching and Learning™ Foundations of Technology

+0.005

- 0.005

+–

Page 23: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice QuestionsWhat 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, STEMCenter for Teaching and Learning™ Foundations of Technology

+–

Page 24: Basic Statistics Foundations of Technology Basic Statistics © 2013 International Technology and Engineering Educators Association, STEM  Center for Teaching

Practice QuestionsPractice QuestionsWhat 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, STEMCenter for Teaching and Learning™ Foundations of Technology

+0.005

- 0.005


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