AG00302_.GIF (2950 bytes)"Whew! I'm glad we're finally through analyzing All That Data! Those survey results really piled up!" sighed Mike.
AG00309_.GIF (4281 bytes)"I can't believe we sorted through mounds of data just to find ONE fair price!" complained Marie.

BS01103_.WMF (7058 bytes)"What did you just say, Marie?"
"What?"
she asked, confused by Mike's question.
 
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"You said something about a heap of data," continued Mike.

"I SAID we sorted through mounds of data," replied Marie.

AG00303_.GIF (3152 bytes)
"Yes, that's it!
Marie, I think there's more to learn about all that data!"


AG00311_.GIF (5166 bytes)"What do you mean
there’s
wpe6.jpg (2100 bytes)
asked Marie.

"Come with me and I'll show you," Mike pleaded.
"Oh no! Here we go again!" moaned Marie.  Previous Page |  Next Page







 

      "Here, look at this graph."
"Yeah, so, it's the column bar graph you made from the "All That Data!" survey results.wpeC.jpg (13215 bytes)

"I know that! But look at the shape of the data.  Doesn't it remind you of something?"

Type in how you think Marie will describe the shape of the data.
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"Okay, so...what?"
questioned Marie.

"Well, I think there may be a pattern in all that data!" continued Mike.

AG00314_.GIF (5152 bytes)
"A pattern? Oh Mike, I thought you said we were THROUGH!"

AG00301_.GIF (2955 bytes)
"Well, we were, but...
I just thought of something else.
Something that calls for two
data detectives!"

wpe14.jpg (3094 bytes)

wpe17.jpg (3903 bytes)"The dynamic duo of Mike and Marie!" Previous Page |  Next Page

 








 

PE00504_.WMF (10328 bytes)"Marie, I think there are clues hidden in our data displays," Mike explained. "Clues waiting to be discovered! To test my theory, we need several column bar graphs." "Sounds like a plan! Let's get to work," said Mike. 
Mike needs several bar graphs.  Type in what you think he hopes to find.
  Previous Page |  Next Page
BS00877A.GIF (1713 bytes)"We already have one," reminded Marie. "How about I graph the girls' survey results from 'All That Data'? You can graph the boys' results!"








 

wpe6.jpg (9137 bytes)

Describe the shape of the girls' data.
"Okay, here's my graph. Now show me yours!" said Marie.


"Well, the boys' graph looks more like a mountain range!  Look at all those peaks and valleys!" commented Mike.Previous Page |  Next Page

wpeF.jpg (8706 bytes)








 

AG00310_.GIF (5450 bytes)
"Mountain Range? Range! I wonder if the range has something to do with the shape of the data?"
AG00304_.GIF (2881 bytes)
"I don't know!  Let's check the Data Detectives' Dictionary and see what it says about data and graphs!"

BS00649_.WMF (7716 bytes)Marie read, "Data detectives, also called mathematicians, use three magnifying glasses to search for clues.  One is used to find the RANGE of the data! To find the range, they ."
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SO00596_.WMF (2526 bytes)"Highest and lowest extremes?  Does that mean the highest peaks and lowest valleys?" questioned Mike.

AG00310_1.GIF (5450 bytes)"The lowest and highest extremes are the beginning and ending points of the data."

Look at this picture. To reach the top, we start climbing at the lowest extreme."


LOWEST
EXTREME

WB00957_.GIF (495 bytes)
NA02186_1.WMF (6172 bytes) HIGHEST
EXTREME

WB00957_.GIF (495 bytes)

"When we come off the mountain, we are at the highest extreme.
It is called the highest extreme because it's the highest value listed
in the range of data". Previous Page |  Next Page








 

AG00305_.GIF (2809 bytes)"That makes sense!" said Mike. "We can't have a mountain without a beginning and ending point, and we can't describe data without knowing where it starts and ends."

HH01619_.WMF (21892 bytes)""Look! When I put this magnifying glass over my graph, the range appears!


The lowest extreme is .
The
highest extreme is.
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wpe11.jpg (11046 bytes)








 

BS00649_.WMF (7716 bytes)Mike took the dictionary and read about the next magnifying glass.
"After describing the range, mathematicians look for clues at the center of the data."

NA00434_.WMF (12690 bytes)

"The center of the data?"
"You mean like the peak of the mountain?" asked Susan.
"Well, it says here that the center of the data, or where the data peaks, is described by Three Measures of Central Tendency."Previous Page |  Next Page








AG00308_.GIF (5439 bytes)"Three What?" exclaimed Marie.

AG00306_.GIF (3503 bytes)"Three Measures of Central Tendency:
Mean, Median, Mode."
"These terms are used to describe where the CENTER of the data TENDS to fall."

HH01619_.WMF (21892 bytes)"Let's look at the girls' graph with this one," suggested Marie.wpeF.jpg (8816 bytes)

"Look, I found that the
mean was $0.81 and the median was $0.80."

Check  the mode of the data.
$0.75 $0.80 $0.85
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BS00649_.WMF (7716 bytes)"The third magnifying glass is used to examine how the data is distributed, or shared, within the range," Mike continued.

"In the girls' graph, the data seemed to be evenly shared around the center.  That's why we had a steady climb and a steady descent," Marie summarized.

wpe6.jpg (9137 bytes)

wpeF.jpg (8706 bytes)

"But in the boys' graph, the data went up and down.  Look at those peaks and valleys.  I wonder what all this means?" commented Mike. Previous Page |  Next Page

 

 

 

 

 

AG00313_.GIF (5130 bytes)"It says that when data is evenly shared around the center, it is called a normal distribution
So, I guess it means that girls are NORMAL!"

AG00304_1.GIF (2881 bytes)"Give me that book back! It SAYS that a normal distribution is identified by a bell-shaped curve, kind of like our mountain."

"That's right! The girls' graph was normal, and the boys' graph was abnormal!
Now we have mathematical proof that girls are normal and boys are not!

"I can hardly call that logic mathematical ! Now, let's get back to work!"

BS00649_.WMF (7716 bytes)"Oh, alright!" consented Marie. "Does the dictionary say anything else?" Previous Page |  Next Page

 

 

 

 

"Mathematicians look carefully at the data in order to detect:

HH01619_.WMF (21892 bytes)
The RANGE of the data,

HH01619_.WMF (21892 bytes)
The DISTRIBUTION of the data."

PE00504_.WMF (10328 bytes)"Through careful inspection, they gather enough information to describe the data for others!" Mike concluded.

"Our Data Detective Kit is now complete, and I'm ready for our first case!" declared Mike. "Let's look at the "All That Data!" survey results.  I know there's a mystery hidden in that mound of data!" 
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wpe11.jpg (15778 bytes)

HH01619_.WMF (21892 bytes)Review the case (bar graph) that Mike and Marie will try to solve!

What "clues" do you see in the areas of range, central tendency, and distribution?