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

2. Objectives
Students 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. The Big Idea
Big Idea:
Computers assist in organizing and analyzing data used in the Engineering Design Process.

10. 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

11. Practice Questions
What is the mean for the following data set? , 4, 4, 6, 7, 8, 10
Equation for Mean = ∑x n

12. Practice Questions
What is the mean for the following data set? , 4, 4, 6, 7, 8, 12
∑x =
∑x = 42
∑x = 42
n 7
Mean = 6

13. 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

14. 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 = How many Numbers

15. Practice Questions
What is the median for the following data set? 1, 6, 12, 4, 4, 8, 7

16. 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

17. Practice Questions
What is the median for the following data set? 1, 6, 12, 4, 4, 7

18. Practice Questions
What is the median for the following data set? , 6, 12, 4, 4, 7
Ordered Data Set = 1, 4, 4, 6, 7, 12
Middle Numbers = 4, 6
= (4+6) = =

19. Basic Statistics
The Mode is the most frequently occurring number in a given data set. Example: 1, 2, 3, 4, 4

20. Practice Questions
What is the mode for the following data set? 1, 6, 12, 4, 4, 8, 7

21. Practice Questions
What is the mode for the following data set? 1, 6, 12, 4, 4, 8, 7 Mode = 4

22. 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.

23. 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.

24. 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.

25. 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

26. Basic Statistics
What is the standard deviation for the following data set? , 4, 4, 6, 7, 8, 12
Equation for Standard Deviation = ∑(xi – μ)² √ n - 1

27. Practice Questions
What 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 = = 3.51 √ n – 1 √ √ 6 √ How many Numbers

28. 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 = Range = (4 – 1) = 3

29. Practice Questions
What is the range for the following data set? 1, 4, 4, 6, 7, 8, 12

30. 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 = Range = (12 – 1) = 11

31. 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)

32. Basic Statistics
Engineering tolerances are expressed like a written language and follow the American National Standards Institute (ANSI) standards.
Example: Bilateral Tolerance ( )
Example: Unilateral Tolerance ( )
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

33. Practice Questions
What are the upper and lower specification limit for the examples below?
Example: Bilateral Tolerance ( )
Example: Unilateral Tolerance ( )
+0.005

34. Practice Questions
What are the upper and lower specification limit for the examples below?
Example: Bilateral Tolerance ( )
Upper Specification Limit = = 1.150
Lower Specification Limit = – = 1.100
The Range should equal the difference between the upper and lower specification limit.
Range = 0.050

35. Practice Questions
What are the upper and lower specification limit for the examples below?
Example: Unilateral Tolerance ( )
Upper Specification Limit = = 2.580
Lower Specification Limit = – = 2.570
The Range should equal the difference between the upper and lower specification limit.
Range = 0.010
+0.005