All That Data 2

"Whew! I'm glad we're finally through analyzing All That Data! Those survey results really piled up!" sighed Mike.

"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.

"You said something about a heap of data," continued Mike.
"I SAID we sorted through mounds of data," replied Marie.
"Yes, that's it! Marie, I think there's more to learn about all that data!"	"What do you mean there’s asked Marie.
"Come with me and I'll show you," Mike pleaded. "Oh no! Here we go again!" moaned Marie. \|

"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.
"A pattern? Oh Mike, I thought you said we were THROUGH!"	"Well, we were, but... I just thought of something else. Something that calls for two *data detectives!"*
	"The dynamic duo of Mike and Marie!" \|

"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. \|
"We already have one," reminded Marie. "How about I graph the girls' survey results from 'All That Data'? You can graph the boys' results!"

	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. \|

"Mountain Range? Range! I wonder if the range has something to do with the shape of the data?"	"I don't know! Let's check the Data Detectives' Dictionary and see what it says about data and graphs!"
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 ." \|

"Highest and lowest extremes? Does that mean the highest peaks and lowest valleys?" questioned Mike.
"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	HIGHEST EXTREME
"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". \|

"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."
""Look! When I put this magnifying glass over my graph, the range appears! The lowest extreme is . The highest extreme is. \|

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."
"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." \|

"Three *What*?" exclaimed Marie.	"Three Measures of Central Tendency: Mean, Median, Mode." "These terms are used to describe where the CENTER of the data TENDS to fall."
"Let's look at the girls' graph with this one," suggested Marie. "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 \|

"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.

"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. \|

"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!"	"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!"
"Oh, alright!" consented Marie. "Does the dictionary say anything else?" \|

"Mathematicians look carefully at the data in order to detect:
The RANGE of the data, The MEASURES OF CENTRAL TENDENCY, and The DISTRIBUTION of the data."	"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!" \|

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?