Introduction to Basic Statistics

1
Forging new generations of engineers
2
Introduction to Basic Statistics
3
Lesson Concepts Addressed
Statistical analysis of measurements can help to
verify the quality of a design or
process. Engineers use graphics to communicate
patterns in recorded data.
4
Related Performance Objectives
It is expected that students will

• Generate a data set of linear measurement.
• Calculate the mean, mode, median, and range of a
  data set.
• Create a histogram of recorded measurements
  showing class interval and frequency.

5
Mean
The mean is the sum of the values of a set of
data divided by the number of values in that data
set.
(pronounced X-bar)
6
Mean
S x
x

n
x individual data value n of data values
in the data set S summation of a set of values
7
Mean
Data Set
3 7 12 17 21 21 23 27 32 36 44
Sum of the values 243
Number of values 11
S x
243
x


Mean
22.09
n
11
8
Mode
The most frequently occurring value in a set of
data is the mode.
Symbol M
Data Set
27 17 12 7 21 44 23 3 36 32 21
9
Mode
The most frequently occurring value in a set of
data is the mode.
Data Set
3 7 12 17 21 21 23 27 32 36 44
Mode 21
10
Mode
The most frequently occurring value in a set of
data is the mode.
Note If two numbers of equal frequency stand
out, then the data set is bimodal. If more than
two numbers of equal frequency stand out, then
the data set is multi-modal.
11
Median
The median is the value that occurs in the middle
of a set of data that has been arranged in
chronological order.

Symbol x pronounced X-tilde
12
Median
The median is the value that occurs in the middle
of a set of data that has been arranged in
chronological order.
Data Set
27 17 12 7 21 44 23 3 36 32 21
Median 21
13
Median
Note A data set that contains an odd of values
always has a Median. For an even of values, the
two middle values are averaged with the result
being the Median.
Data Set
3 7 12 17 21 21 23 27 32 36 44
Median 21
14
Range
The range is the difference between the largest
and smallest values that occur in a set of data.
Symbol R
Data Set
3 7 12 17 21 21 23 27 32 36 44
Range 44-3 41
15
Histogram
A histogram is 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
histogram to show the most common, or average,
dimension that exists among a group of identical
manufactured parts.
16
0
3
-1
-3
3
2
1
0
-1
-1
2
1
0
1
-1
-2
1
2
1
0
-2
-4
0
0
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
17
Histogram
Specific values, called data elements, are
plotted along the X-axis of the graph.
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
Data Elements
18
Histogram
Large sets of data are often divided into limited
number of groups. These groups are called class
intervals.
-5 to 5
6 to 16
-6 to -16
Class Intervals
19
Histogram
The number of data elements is shown by the
frequency, which occurs along the Y-axis of the
graph.
7
5
Frequency
3
1
-5 to 5
6 to 16
-6 to -16
20
Normal Distribution
Is the data normal?
Translationdoes the greatest frequency of the
data values occur about the mean value?
21
Normal Distribution
Mean Value
Frequency
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
Data Elements
22
Normal Distribution
Is the process normal?
Further Translationdoes the data form a bell
shape curve when plotted on a histogram?
23
Normal Distribution
Frequency
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
Data Elements