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Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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Page 1: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Unit 2: Engineering Design Process

Foundations of Technology

Basic Statistics

Lesson 2: Basic Statistics

Page 2: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

ObjectivesStudents learn to:

• Collect data and information and use computers and calculators to organize, process, and present the collected data and information.

• Collect information and evaluate its quality.

• Draw reasonable conclusions about a situation being modeled.

Page 3: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Objectives

• Contribute to a group endeavor by offering useful ideas, supporting the efforts of others, and focusing on the task.

• Work safely and accurately with a variety of tools, machines, and materials.

• Actively participate in group discussions, ideation exercises, and debates.

Page 4: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Vocabulary

• Data: information that is collected throughout the engineering design process to optimize designs and improve efficiency during production.

• Statistics: the collection and organization of data (science) as well as the analysis and presentation of those data (mathematics).

• Mean: the average of a given data set.

Page 5: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Vocabulary

• Median: the middle number in a given data set.

• Mode: the most frequently occurring number in a given data set.

• Standard Deviation: how much variation exists from the average (mean) in a given data set.

Page 6: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Vocabulary

• Range: the difference between the largest and smallest values in a given data set.

• Tolerance: the amount a characteristic (product/part/dimension/etc…) can vary without compromising the overall function or design of the product.

• Normal Size: the size used in the general description of a part/product.

Page 7: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Vocabulary

• Criteria: guidelines to help develop a solution.

• Constraints: limitations of the design when developing a solution.

• Alternative Solutions: are necessary so that ideas remain unique and are not traditional.

Page 8: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

• Basic Size: the converted normal size (fraction to decimal) which can produce some deviation.

• Upper Specification Limit: the highest acceptable value for a characteristic.

• Lower Specification Limit: the lowest acceptable value for a characteristic.

Page 9: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

The Big Idea

Big Idea:

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

Page 10: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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

Page 11: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Practice Questions

What is the mean for the following data set?

1, 4, 4, 6, 7, 8, 10

Equation for Mean = ∑x n

Page 12: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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

∑x = 42 n 7

Mean = 6

Page 13: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Practice Questions

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

Page 14: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Basic Statistics

The Median is the middle number in a given ordered data set. Out of 5 numbers.

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

How many Numbers

Page 15: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Practice Questions

• What is the median for the following data set?

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

Page 16: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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

Page 17: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Practice Questions

• What is the median for the following data set?

1, 6, 12, 4, 4, 7

Page 18: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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

Page 19: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Basic Statistics

• The Mode is the most frequently occurring number in a given data set.

Example: 1, 2, 3, 4, 4

Page 20: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Practice Questions

• What is the mode for the following data set?

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

Page 21: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Practice Questions

What is the mode for the following data set?

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

Mode = 4

Page 22: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Basic Statistics

Standard Deviation (SD): is a UNIT. It is used to measure how "weird" something is. Inches measure distance. Grams measure mass. SD's measure weirdness.

Things that equal the norm measure 0 standard deviations. Things above the norm register with positive standard deviations. Things below the norm register with negative standard deviations.

Page 23: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Basic Statistics

Understanding standard deviation:When you construct something you are going to have error. Let's say I have a relatively skilled crew build 100 bridge pilings according to a certain specification. There is going to be some wiggle in the height of the piling. A few mm taller a few mm shorter on each build. Now the mean of these builds should be REALLY REALLY close to what is on the specification. From this set of builds you can determine a standard deviation.

Page 24: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Basic Statistics

Understanding standard deviation:You can now set a tolerance for what a good build is. In some circumstances being within 2 SD of the norm is good enough. If these pilings are holding up a bridge that needs to carry the space shuttle to the launch pad you may want the piling to be to 1/2 of a standard deviation (space shuttles don't deal well with bumps). When a new piling is built you measure it, convert the height to SD and then decide whether it’s in its tolerance. If it is, great! If it isn't you tear down and rebuild the piling.

Page 25: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Basic Statistics

Calculating Standard Deviation

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

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

Page 26: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Basic 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

Page 27: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Practice QuestionsWhat is the standard deviation for the following data set?

∑(xi – μ)² xi = (1, 4, 4, 6, 7, 8, 12) √ 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 √

How many Numbers

Page 28: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Basic 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

Page 29: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

Practice Questions

• What is the range for the following data set?

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

Page 30: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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

Page 31: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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)

Page 32: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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.

+0.005- 0.005

Page 33: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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 )+0.005

- 0.005

Page 34: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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

Page 35: Unit 2: Engineering Design Process Foundations of Technology Basic Statistics Lesson 2: Basic Statistics

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

+0.005

- 0.005