"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.
"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. |
"Okay, so...what?" questioned Marie.
"Well, I think there may be a pattern in all that data!" continued Mike.
"Well, we were, but... I just thought of something else. Something that calls for two data detectives!"
"The dynamic duo of Mike and Marie!" |
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. |
"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."
"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". |
""Look! When I put this magnifying glass over my graph, the range appears! The lowest extreme is $0.60 $0.65 $0.95 $1.00 . The highest extreme is $0.60 $0.65 $0.95 $1.00 . |
"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.
"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!"
"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!" |
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?