Bicycles a la Mode

Jenny saw this ad for an after-school job:

*** JOBS JOBS JOBS ***

Come work for the Acme

Bicycle Company. Our average

rate of pay is $10 per hour!

"Wow!" thought Jenny. "10 dollars an hour!"

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

Jenny got a job with Acme Bicycle Company, but her starting pay was only $1/hour. She began asking people how much they make.

"I only make $1/hour", said Fred.
"I make $1/hour, also", said Jed.
"Me? I make $1/hour", said Ted.

"How can this be!?" said Jenny. She was very angry. The advertisement said that the average rate of pay is $10/hour.
WB00896_1.GIF (766 bytes)

She went to see the owner.

"See for yourself", said the owner. He showed Jenny a list of the employees and how much they make:

The Acme Bicycle Company has 10 employees. 9 of them make $1/hour, and 1 of them makes $91/hour.

Recall: the average is computed by (1) adding up all of the values, and (2) dividing by the number of values.

Fred	$1/hour
Ted	$1/hour
Jed	$1/hour
Ned	$1/hour
Ed	$1/hour
Ced	$1/hour
Red	$1/hour
Zed	$1/hour
Gred	$1/hour
Owner	$91/hour

The owner hadn't lied! The average pay really is $10/hour. Even though he hadn't lied, Jenny thought that wasn't very truthful either. She quit that very same day.

Sometimes, an average can be deceptive. That's why there are other ways to describe data. Today we are going to look at the...

MODE

I think you'll like the mode. An average, or mean, can sometimes take a lot of computation. To figure out what the mode is quite a bit easier.

The mode is the value that shows up the most often in the data.

What is the mode pay rate at the Acme Bicycle Company?

Here is a list of weekly high summer temperatures (in centigrade) for Dallas Texas:

33°, 35°, 35°, 36°, 33°, 31°, 34°, 33°, 35°, 33°, 42°, 34°

What is the mode temperature on this list?

Yes! You got it! Try this quick exercise:

PE02481_.WMF (8460 bytes)

What is the mode of this list of data?

6, 0, 1, 1, 4, 6, 5, 1, 7, 7, 7,8, 1, 0, 1

Yes, figuring out the mode isn't too difficult, huh? It's easy to remember what the mode is, because "mode" sounds a lot like "most".

DID YOU KNOW?

Did you that "data" is a plural noun? You should say "These are the data" or "The data look fine" and not "This is the data" or "The data looks fine".

The singular form of "data" is "datum". If your list has only one value, you can refer to it as a datum. Otherwise, it is data. Pretty weird, huh?

What about this?

Look at this list of data: 4, 7, 8, 10, 15, 16. No value appears more than once. What do you think the mode is? Click one below:

In the list 4, 7, 8, 10, 15, 16 there is no number that shows up the most, so we say this list has NO MODE.

Here's something else that can happen. Look at these data:

10, 10, 10, 11, 14, 15, 20, 20, 20.

In this case, we have TWO numbers that show up the most, so this list of data has TWO MODES.

What are the modes of this list of data?

You've done great! To review:

The MODE is the number or numbers which show up the MOST

If every number appears once, then there is NO MODE

If more than one number appears the most, then there are MORE THAN ONE MODE.