A3 5 AppliedStatistics
Activity 3.5 Applied Statistics
Introduction
Today’s 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: ___4.066667__________
Median: ____4.05________
Mode: _____4, 4.1 Bimodal________
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: _____0.6________
Standard Deviation of this data: ___.1648__________
Estimated Standard Deviation for all pieces produced: ______.1721_______
X
x-µ
(x-µ)2
3.8
-.2667
.0711
3.9
-.1667
.0277
3.9
-.1667
.0277
4.0
-.0667
.0044
4.0
-.0667
.0044
4.0
-.0667
.0044
4.1
.0333
.0011
4.1
.0333
.0011
4.1
.0333
Introduction
Today’s 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: ___4.066667__________
Median: ____4.05________
Mode: _____4, 4.1 Bimodal________
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: _____0.6________
Standard Deviation of this data: ___.1648__________
Estimated Standard Deviation for all pieces produced: ______.1721_______
X
x-µ
(x-µ)2
3.8
-.2667
.0711
3.9
-.1667
.0277
3.9
-.1667
.0277
4.0
-.0667
.0044
4.0
-.0667
.0044
4.0
-.0667
.0044
4.1
.0333
.0011
4.1
.0333
.0011
4.1
.0333