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Sweetening Statistics with

Statistical Concepts:
What M&Ms Can Teach Us.
M&Ms can provide an ideal way to make statistics
immediately understandable to students who are timid about
the subject. By simply weighing a few bags of the peanut
variety and counting their contents, students gather useful
data. Through applying statistics to this data on the weight,
color, quality, and other factors of the M&Ms, students
take an everyday item such as candy and transform it into a
powerful learning tool.
Are the M&Ms weights accurate?

According to the package, each small bag of peanut M&Ms should weigh
49.3 grams. To determine if the bag weights are on target, ask the students to
measure the weight of say, 30 bags of M&Ms and conduct a 1-sample t-test.

In our analysis, the t-test results include a very small p-value of 0.000. Since
the p-value is much smaller than an -level of 0.05 or even 0.01, we can
reject the null hypothesis and conclude that the average bag weight is not
equal to 49.3 grams.
Results generated using Stat > Basic Statistics > 1-Sample t.
In this case, however, its good news for consumerswe can see from the
average weight of 52.040 grams that, in fact, the average bag weight is
significantly more than the 49.3 grams target.

Can two people measure the

same weights?
If one person measures 30 bags of M&Ms and their friend measures the
same 30 bags using the same scale, will they get similar measurements?
Students can test this hypothesis using a paired t-test.

In our analysis, the p-value of 0.394 is larger than our chosen -level of 0.05.
Therefore, we fail to reject the null hypothesis and can conclude that there is
not a significant difference between the average measurements taken by the
two friends.

Are there equal amounts of

each color in a bag? Results generated using Stat > Basic Statistics > Paired t.

A pie chart lets us easily visualize the counts of each color. For
example, there were 138 blue M&Ms and only 63 red M&Ms in
our sample. But is the difference between these counts statistically
significant? A chi-square test can tell us.

The p-value of 0.000

suggests that the
observed counts are
significantly different
than what we would
expect to see if there
were an equal number
of red, orange, yellow,
green, blue, and
brown M&Ms.
Results generated using Stat > Tables > Chi-Square Goodness-of-Fit
Graph created using Graph > Pie Chart. Test (One Variable).
Do enough M&Ms have the m?
M&Ms are easily identified by the signature m printed on each piece of candy. It must
pose a challenge to stamp the familiar symbol on a surface as uneven as a peanut M&M. Its
not surprising, therefore, that sometimes this m is not perfectly printed.

Suppose there is a requirement that no more than 15% of M&Ms have a misprinted m. If
we count the total number of M&Ms and the number with misprints, we can conduct a
1 proportion test.

Of the 622 M&Ms we evaluated, 87 had misprints. Using a 1 proportion test and an
Results generated using Stat > Basic
alternative hypothesis of greater than 15%, we get a p-value of 0.776. Because the p-value is
Statistics > 1 Proportion.
greater than an equal to 0.05, we can conclude that the proportion of misprinted M&Ms is
15% or less.

Is there a correlation between the

number of M&Ms in each bag and
the bag weights?
You may suspect that as the number of M&Ms in each bag increases, so does the weight of
the bags. We can use a scatterplot to examine this relationship and a correlation test to see
Graph created using Graph > Scatterplot. if this theory is true.

The scatterplot of our data shows that, in general, as the number of M&Ms in a bag
increases, so does the weight. In addition, the correlation p-value of 0.011 indicates that
we can reject the null hypothesis and conclude that there is a significant positive, linear
relationship between the bag weights and the number of M&Ms inside.

Results generated using Stat > Basic Additional Considerations

Statistics > Correlation.

Although measuring Gage repeatability and reproducibility is well beyond the scope of a
typical university statistics course, you can also use M&Ms to teach more advanced statistical
techniques. For instance, we used Minitab to create a Gage R&R measurement plan,
followed the plan to measure 10 bags of M&Ms twice each in a random order, and then
analyzed the measurement results.

The resulting total Gage R&R percent study variation of 1.14% is well below the 10% ideal,
indicating that very little variation was due to the measurement system. In addition, the
R Chart is in control, while the XBar Chart is out-of-control. Therefore, our measurement
system is acceptable.
Results generated using Stat > Quality Tools
> Gage Study > Gage R&R Study (Crossed).
MBREM18.STAT
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