Quality Control
in the M&M Factory

CLASSROOM ACTIVITY: Quality Control In The M&M Factory

A classroom activity that introduces statistical methods to evaluate the variability in a system.

Purpose:

In this exercise you will learn some simple statistical procedures and how they apply to quality control. You will learn:

• How to calculate standard deviation and the significance of this value.
• How to construct a frequency histogram.
• About the nature of variability in manufacturing processes.

Background:

A. Using Standard Deviation As A Measure Of Variability

There is always variation in any system or process. When producing a product, such as a biotechnology product, it is important to reduce that variability as much as possible. For example, if a company is selling an enzyme that is supposed to have an activity of 200 Units/mg, then they want every lot of that enzyme to have an activity of 200 Units/mg -- they do not want the activity to sometimes be 182 Units/mg, or 222 Units/mg, or any values other than 200 Units/mg.

The first step in reducing the variability in a process is to be able to evaluate it. The field of statistics provides us with techniques to evaluate and record variability. In this laboratory exercise, we will discuss two simple statistical methods to evaluate and report the variability in a product. The product that we will examine is M&Ms and the feature of the product that is of interest to us is the color of the candies.

The standard deviation (SD) is a common mathematical measure of variability in a set of values. The calculation of SD is discussed in your textbook. We will use the SD in this exercise to measure and report the variability in the number of M & Ms in packages.

B. Using Histograms To Display Variability

Graphs are used to illustrate numerical values. A frequency histogram is a graphical method to display the distribution of a set of values. A frequency histogram shows how many there are of various classes of things. For example, a frequency histogram might indicate how many field mice there are of various sizes in a field, or how many students got grades of As, Bs, Cs, and Ds in a course.

When a histogram is made, the items are first categorized into classes or types. For example, for course grades, there are four classes or types: A, B, C, and D. These classes are plotted on the X axis of a graph. The number in each class is plotted on the Y axis. The number of items in each class determines how high the bar will be, that is, how far up the bar goes on the Y axis.

In practice, we distinguish between situations where classes are continuous and those where they are discrete. For example, height and weight are continuous variables. A mouse might be 19 g or 20 g or any weight in between. In contrast, course grades are discrete. A student may get an A- or B+, but there is no grade in between. When variables are continuous, the bars are usually plotted so that they touch one another. When variables are discrete, the bars are usually plotted so that they do not touch one another. In the case of our M & M data, the values are discrete. There might be 40 M & Ms in a bag or 41, but (unless some are broken) there cannot be any value in between.

It is possible to construct a frequency histogram for any data set consisting of the values for a single variable. The procedure for doing so is given in the box below followed by an example:

An Example Of Preparing A Histogram

Consider these hypothetical values for the grades of 43 students:

Step 1: Divide the data into classes. This is easy; there are four classes, A, B, C, and D.

Step 2: Count the number in each class.

Step 3: Arrange the values into a table:

 

FREQUENCY TABLE
VALUE (Grade)	FREQUENCY THAT GRADE APPEARS
A	12
B	19
C	9
D	3

 

Steps 4 and 5: Prepare the graph.

Activities:

1. Open your bag of M & Ms and pour them onto a paper plate or towel. Count and record:
   
   1. The total number of M & Ms in your bag.
   2. The number of M & Ms of each color
2. Record your data on the blackboard.
3. Based only on your own data, construct a histogram of color versus frequency.
4. Based on the classes data as a whole, construct a histogram of color versus frequency.

Discuss the two histograms.

1. Are the two histograms the same or different? Explain.
2. Based on your own histogram, are the colors of M & Ms evenly distributed? Based on the entire class's data, are the colors evenly distributed?
3. What do you predict a histogram would look like if we checked hundreds of bags of M & Ms?
4. Based on the data for the entire class, calculate the mean number of M & Ms per bag, and the standard deviation of the number of M & Ms per bag.
5. Based on the data for the entire class, construct a frequency histogram for the number of M & Ms per package.
6. Discuss the mean and the standard deviation.
   
   
   1. What does the mean tell you?
   2. What does the standard deviation tell you?
7. If you were to count the number of M & Ms in hundreds of bags, what do you think the frequency histogram would look like? Draw your prediction.
8. Where do you think variability in the M & M packages comes from?
9. Why is it important to be able to measure variability in a process?
10. Why is it important to find methods to reduce variability in a process?

NOTE:

According to the “M & M hotline” the ratios of colors are:

These colors were chosen based on surveys of consumer preferences.

The printable version of this document.

Contact Us:

Lisa Seidman
lseidman@matcmadison.edu
(608) 246-6204

Jeanette Mowery
jmowery@matcmadison.edu
(608) 243-4307

Updated: April 26, 2006

Maintained by Joan Millard