3 5 A Appliedstatistics
3 5 A Appliedstatistics
3 5 A Appliedstatistics
5 Applied Statistics
Introduction
Todays consumers are constantly trying to judge the quality of products. But what is
quality? How and by whom is quality determined? Some would say the designer
creates specifications, which in turn dictate the quality of a product. That quality is
also based on the acceptable value of a part within a whole product. Statistics are
commonly used in manufacturing processes to control and maintain quality. This
activity will allow you to apply statistics in order to analyze and determine the quality
of a set of wooded cubes.
In this activity you will collect data and then perform statistical analyses to determine
measures of central tendency and variation of the data. You will also represent the
data using a histogram.
Equipment
Engineering notebook
Pencil
Dial caliper
Procedure
1. Part of the manufacturing quality control testing for a toy is to measure the depth
of a connector piece that must fit into another part. The designed depth is 4.1 cm.
Every tenth part produced on the production line is measured. The following data
was collected during a two minute production period.
4.1, 4.1, 4.0, 4.1, 3.9, 4.4, 3.9, 4.3, 4.0, 4.2, 4.0, 3.8
a. Calculate each of the following measures of central tendency. Show your
work.
Mean: 4.06_____________
Median: 4.05____________
Mode: 4.0 and 4.1__________
b. Calculate each of the following measures of variation for the data set.
Show your work. A table has been provided to help you calculate the
standard deviations. In the table round values in the last two columns to
four decimal places. Report the standard deviation statistics to four
decimal places.
Range: 4.4 3.8 = 0.6___
x-
(x - )2
4.1
.0333
.00110889
4.1
.0333
.00110889
4.0
-.0667
.00444889
4.1
.0333
.00110889
3.9
-.1667
.02778889
4.4
.3333
.11108889
3.9
-.1667
.02778889
4.3
.05542889
4.0
.2333
-.0667
4.2
.1333
.01776889
4.0
-.0667
.00444889
3.8
-.2667
.07112889
SUM
.00444889
.32764669
c. Create a histogram for the data using the grid below. The horizontal axis
should display each length measurement from the minimum to maximum
recorded lengths. You may choose to begin with a dot plot and then fill in
the bars. Be sure to label your axes.
7
6
5
Frequency4
3
2
1
3.8 4.0
4.1 4.2
4.3 4.4
Length
2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 3.5 Applied Statistics Page 2
Conclusion
1 How can statistics of a products dimensions be used to assess the quality of the
product?
You can refer back to the different measurements to decide things.
2. In which phase(s) of a design process might statistics be most useful? Why?
In the testing stage because you can change your ideas based on the
statistics.