# Project #83232 - Standard deviation/histogram

Workshop 2: Histograms and Descriptive Statistics

The tools practiced in this workshop are:

·      Histograms

·      Descriptive statistics

Materials needed:

·      A small metric ruler (see .pdf of paper ruler available in Blackboard)

·      A bag of small marshmallows (available at most grocery stores for around \$1)

Situation:

Consider that you/your group works for a marshmallow manufacturing operation and you have been tasked with collecting data to document the current performance of your production process. This data is needed to establish a baseline measurement at the beginning of your Lean Six Sigma project so that you will have a measurement to compare against later once the process has been improved.

Please note that the customer specifications for your marshmallow production process are:

Target: 0.9 ± 0.3 cm (lower specification limit: 0.6 cm and upper specification limit: 1.2 cm)

Instructions:

Use information from your training manual in Measure Phase – Lessons 9-11 to assist you with the activities that follow. Be sure to follow the “best practices” for each tool you use in this workshop.

Pretending the marshmallows you have are from your production process, measure the diameter (the distance across the round end of the marshmallow) in centimeters (cm) of approximately 50 different marshmallows. Record your measurements in a spreadsheet in Microsoft Excel and use Microsoft Excel to calculate your descriptive statistics and create a histogram of your data.

Activities: (also see next page)

1.     For the marshmallows produced by your production process, what is the:

a.     Average diameter in centimeters (cm)?

b.     Standard deviation in cm?

c.     Range in cm?

2.     Create a histogram that summarizes your data set (i.e., measurements of the marshmallow diameter in centimeters):

3.     Near the end of your Lean Six Sigma project, after you have implement solutions to improve your marshmallow production process, you measure the process performance again and get the following results:

Diameter – Average: 0.95 cm; standard deviation: 0.11 cm; range: 0.8-1.2 cm

a.     Have you improved the process? Yes or no and why.

Hint: Perform a before and after comparison by comparing the baseline measurements in Activity #1a-c of this Workshop with the measurements given in this question.

b.     How well does the improved process fulfill customer requirements?

Hint: Perform another comparison by comparing the measurements given in this question to the customer specifications given in the “Situation” part of this Workshop.

 Subject Business Due By (Pacific Time) 09/25/2015 12:00 am
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