Statistics activity
Introduction.
Statistics is the mathematical science of the collection, analysis, and interpretation of data. Statistics can
be used to summarize data – descriptive statistics – or modeled in order to account for randomness and
uncertainty, which can be used to draw inferences about the process under study (this is called
inferential statistics). Probability, on the other hand, is the way in which we predict outcomes of
experiments. Statistics and probability are closely related, as you shall see in this activity.
Activity.
Part I. Flipping coins.
1.
In this activity you will find rules for predicting coin flips. Before flipping the
coin, predict whether the coin will land heads or tails for a single toss and write
your prediction in the table. Toss the coin and write the results in the table.
Complete a total of ten trials.
Trial
Prediction
(H or T)
1
2
3
4
5
Results
(H or T)
Trial
Prediction
(H or T)
Results
(H or T)
6
7
8
9
10
2.
How many tosses did you predict correctly? ______
Write a brief conclusion about predicting the outcome of a single coin toss based on your results.
3.
Now you are going to flip the coin a total of 100 times and count the number of heads and the
number of tails. As before, first record your prediction.
Prediction:
Heads ______
Tails ______. How did you arrive at this prediction?
Toss the coin 100 times and record your results below.
Results:
Heads ______
Tails ______. Was your prediction accurate?
Explain your answer. How do you know if a prediction is “accurate” or not?
Was your prediction for a single flip accurate according to your reasoning in the answer above?
Consider the discussion of two students:
Student A: “There is no way to know how many heads and tails you will get when you flip a coin
10 times or 100 times. Each time you flip it, you can’t say for sure whether it will be heads or
tails.”
Student B: “I agree you cannot predict heads or tails for a single flip, but if you make a lot of
flips, you will always get about half of them to end up heads and about half tails.”
Do you agree with Student A or B? A __ B __ both __ neither __. Explain your answer.
4.
Summarize (a) the rules you found for predicting a single coin flip and (b) the rules for predicting a
large number of coin flips.
Part IIa. Rolling a single die.
1.
In this activity you will find rules for predicting the results of rolling dice. Before
rolling, predict how often the numbers one through six will appear when you roll a
fair die. Express the frequency in terms of a fraction. For example, the probability
of tossing “heads” with a coin is one in two or ½. Write your predictions in the
table below.
Number
Rolled
1
2
3
4
5
6
Prediction
Did all the members of your group agree with these values? Check them with your teacher before
continuing.
2.
Roll the die 30 times and annotate the number rolled in the table below. Hint: use slashes – ///.
Number
Rolled
1
2
3
4
5
6
Total
Actual
Were your predictions accurate? Why or why not? How could you improve this experiment?
Part IIb. Rolling two dice.
1.
In this activity you will find rules for predicting the results of rolling dice. Obtain
two dice from your teacher. Predict the frequency with which each number will
occur and express the frequency in the form of a fraction. Now roll the two dice
100 times (again use slashes – /// – instead of numbers to keep track of totals).
100 Trials =
Number
2
3
4
5
6
7
8
9
10
11
12
Predicted
probability
Number rolled
Total
Actual
probability
2.
After completing your table, compare your results with your classmates.
Do the class results confirm your predictions? Yes _____ No_____. Why or why not?
3.
Summarize (a) the rules you found for predicting the number that will appear when you roll a
single die and (b) the rules for predicting the number that will appear when you roll two dice.
Part III. A couple of extensions.
Select only one extension and complete the procedure.
1.
Write an experiment using three dice. Set up a table and include the
predicted probabilities of rolling each number.
2.
Write an experiment using a single die and a coin. Include the predicted
probabilities of rolling each number and flipping a heads or tails. Hint: You
may want to graph this as a sample space in order to calculate all the possible
outcomes.