Transcript Practice Questions

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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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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∑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
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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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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
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Foundations of Technology
Practice Questions
What is the median for the following data set?
1, 6, 12, 4, 4, 8, 7
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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
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Foundations of Technology
Practice Questions
What is the median for the following data set?
1, 6, 12, 4, 4, 7
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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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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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Foundations of Technology
Practice Questions
What is the mode for the following data set?
1, 6, 12, 4, 4, 8, 7
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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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Foundations of Technology
Basic Statistics
Standard Deviation
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.
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Foundations of Technology
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.
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Foundations of Technology
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.
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Foundations of Technology
Click on graph to
learn more about
Standard
Deviation.
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
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Basic Statistics
What is the standard deviation for the following
data set?
1, 4, 4, 6, 7, 8, 12
Equation for Standard Deviation =
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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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=
√
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
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Practice Questions
What is the range for the following data set?
1, 4, 4, 6, 7, 8, 12
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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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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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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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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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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
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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
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Foundations of Technology
Resources:
Pierce, Rod. (15 Jan 2014). "Standard
Deviation and Variance". Math Is Fun.
Retrieved 3 Jul 2014 from
http://www.mathsisfun.com/data/standarddeviation.html
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STEMCenter for Teaching and Learning™
Foundations of Technology