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Foundations of Technology
Basic Statistics
Teacher Resource – Unit 2 Lesson 2
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Foundations of Technology
The BIG Idea
Big Idea:
Computers assist in organizing and analyzing
data used in the Engineering Design Process.
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STEMCenter for Teaching and Learning™
Foundations of Technology
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 =
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STEMCenter for Teaching and Learning™
Foundations of Technology
∑x
n
Practice Questions
What is the mean for the following data set?
1, 4, 4, 6, 7, 8, 10
Equation for Mean = ∑x
n
© 2013 International Technology and Engineering Educators Association,
STEMCenter for Teaching and Learning™
Foundations of Technology
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
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STEMCenter for Teaching and Learning™
Foundations of Technology
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
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
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
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
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
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STEMCenter for Teaching and Learning™
Foundations of Technology
Basic Statistics
The Mode is the most frequently occurring
number in a given data set.
Example: 1, 2, 3, 4, 4
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STEMCenter for Teaching and Learning™
Foundations of Technology
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
Practice Questions
What is the mode for the following data set?
1, 6, 12, 4, 4, 8, 7
Mode = 4
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STEMCenter for Teaching and Learning™
Foundations of Technology
Basic 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 =
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STEMCenter for Teaching and Learning™
Foundations of Technology
∑(xi – μ)²
√ n-1
Basic Statistics
What is the standard deviation for the following
data set?
1, 4, 4, 6, 7, 8, 12
Equation for Standard Deviation =
© 2013 International Technology and Engineering Educators Association,
STEMCenter for Teaching and Learning™
Foundations of Technology
∑(xi – μ)²
√ n-1
Practice 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
√ n–1
=
√
74
7-1
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STEMCenter for Teaching and Learning™
Foundations of Technology
=
√
74
6
=
12.3
√
=
3.51
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
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
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
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STEMCenter for Teaching and Learning™
Foundations of Technology
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)
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STEMCenter for Teaching and Learning™
Foundations of Technology
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 +0.005)
- 0.005
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.
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STEMCenter for Teaching and Learning™
Foundations of Technology
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
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STEMCenter for Teaching and Learning™
Foundations of Technology
+0.005
- 0.005
)
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
Practice Questions
What are the upper and lower specification
limit for the examples below?
+0.005
Example: Unilateral Tolerance (2.575 - 0.005)
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