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Forging new generations of engineers
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Introduction
toBasic Statistics
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Lesson Concepts Addressed
Statistical analysis of measurements
can help to verify the quality of adesign or process.
Engineers use graphics tocommunicate patterns in recorded
data.
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Related Performance Objectives
Generate a data set of linearmeasurement.
Calculate the mean, mode, median,
and range of a data set. Create a histogram of recorded
measurements showing class interval
and frequency.
It is expected that students will
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S xn
x=
Mean
(pronounced X-bar)
The meanis the sum of the values of a
set of data divided by the number ofvalues in that data set.
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x= individual data value
n= # of data values in the data set
S= summation of a set of values
S xn
x=
Mean
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3 7 12 17 21 21 23 27 32 36 44
Data Set:
Sum of the values = 243
Number of values = 11
Mean =24311
= 22.09S xn
x= =
Mean
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The most frequently occurring
value in a set of data is the mode.
Symbol M
Mode
27 17 12 7 21 44 23 3 36 32 21Data Set:
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3 7 12 17 21 21 23 27 32 36 44Data Set:
Mode = 21
The most frequently occurring
value in a set of data is the mode.
Mode
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Note: If two numbers of equal frequency
stand out, then the data set isbimodal. If more than two numbers
of equal frequency stand out, then
the data set is multi-modal.
The most frequently occurring
value in a set of data is the mode.
Mode
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The medianis the value that
occurs in the middle of a set of datathat has been arranged in
chronological order.
Symbol x pronounced X-tilde~
Median
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Data Set:
Median = 21
Median
The medianis the value that
occurs in the middle of a set of datathat has been arranged in
chronological order.
27 17 12 7 21 44 23 3 36 32 21
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Note: A data set that contains an odd # of values
always has a Median. For an even # ofvalues, the two middle values are averaged
with the result being the Median.
Median
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Data Set:
Median = 21
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The rangeis the difference
between the largest and smallestvalues that occur in a set of data.
Range = 44-3 = 41
Symbol R
Range
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Data Set:
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A histogramis a common data distribution
graph that is used to show the frequency with
which specific values, or values within
ranges, occur in a set of data.
An engineer might use a histogramto showthe most common, or average, dimension that
exists among a group of identical
manufactured parts.
Histogram
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0 1 2 3 4 5 6-1-2-3-4-5-6
0
3
-1
3
2
-1
-1
1
2
-3
0
1
0
1
-2
1
2
-4
-1
1
0
-2
0
0
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Specific values, called data elements,
are plotted along the X-axis of the graph.
Histogram
0 1 2 3 4 5 6-1-2-3-4-5-6
Data Elements
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Large sets of data are often divided into
limited number of groups. These groups
are called classintervals.
Histogram
-5 to 5
Class In tervals
6 to 16-6 to -16
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The number of data elements is shown by
the f requency, which occurs along the Y-
axis of the graph.
Histogram
Freque
ncy
1
3
5
7
-5 to 5 6 to 16-6 to -16
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Is the data normal?
Translationdoes the greatest
frequency of the data values occur
about the mean value?
Normal Distribution
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Frequency
Data Elements
0 1 2 3 4 5 6-1-2-3-4-5-6
Mean Value
Normal Distribution
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Is the process normal?
Further Translationdoes the data
form a bell shape curve when
plotted on a histogram?
Normal Distribution
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Frequency
Data Elements
0 1 2 3 4 5 6-1-2-3-4-5-6
Normal Distribution
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