Statistically speaking

Marisa O’Neil

Pick a card, any card.

Now, what are your chances of picking a black card or a red card?

Statistics -- a subject that strikes fear in the hearts of many

students -- can help predict the odds of drawing one card or another.

They can also show if someone stacked the deck with extra cards, as

students in Noureddine El Alam’s Advanced Placement statistics class

at Sage Hill School in Newport Coast learned.

“Someone hands you a deck of cards,” El Alam told his class Friday

as they lined up to draw one card each. “Make a guess as to the

proportion of red to black cards.”

As he drew the first card, 14-year-old Michael Cassel wagered he

had a 50% chance at pulling either one. But by the time each of the

seven students took a turn, the odds looked a little off. Each one

drew a black card.

Lesser students might lose hope. What are the chances of seven

students all pulling black cards from a deck?

Pretty good if their teacher stacked it with all black cards, as

they later found out El Alam did. But only drawing one card each

makes it hard to predict what the rest of the deck looks like.

Especially if someone tinkered with it.

“You have to be careful of sample size in a population of only

52,” Michael warned.

Taking one card in a deck of 52 might not give a good

representation of the population, in this case some kings, queens,

clubs and spades. But take, say, 10 cards -- now that’s a sample.

They drew the cards on a different deck, slipping them back in and

recording the results. Once the tally was in, they started forming

and rejecting hypotheses and discussing binomial distributions,

statistical means and formulas that would make the average math

student’s head spin.

And the class was ready to make its inferences.

“Are you willing to say there are more red than black cards in

this deck?” El Alam asked.

Using the mean they calculated, the students were ready to commit

and agree that the last deck had more red than black cards. Sure

enough, El Alam had replaced some of the red cards with black,

leaving that side of the deck with a definite, statistical advantage.

* IN THE CLASSROOM is a weekly feature in which Daily Pilot

education writer Marisa O’Neil visits a campus in the Newport-Mesa

area and writes about her experience.