All That Data

Hi! Welcome to our meeting. I am glad that you could join us!

In the last lesson, "The Mean, Green Machine", our committee was planning a spring fundraiser.

We want to sell pizza slices during
the boys' and girls' ballgames.

Let me show you what we know.

We named Mike's calculator the "mean, green machine."

Thanks to Mike's mean, green machine, we know that the mean cost of a slice of pizza is $0.58.

Now we just need to find a fair price to charge. Click on each step to see our plan for solving this problem.

	Step 1 Understand the Problem
Step 2 Decide on a Plan
Step 3 Carry out the Plan
Step 4 Look Back and Review
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Since the last meeting, each member asked 15 or 20 people the following question: "If a slice of pizza costs $0.58, what would be a fair price to charge?

Today we'll share our data with the group.

We plan to use the
range,
mean,
median, and
mode to help us understand
ALL THAT DATA!
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Peggy shared first. "I asked 15 people, and used a chart to keep up with the data. It looks like the range of prices is from $0.70 to $1.00. I can't find the mean, median, or mode ."

Peggy's Chart of Fair Prices: $0.70, $0.80, $0.85, $0.85, $0.90, $0.75, $0.75, $0.80, $0.80, $0.90, $0.75, $0.70, $0.85, $0.95, $1.00.

Why do you think Peggy can't find the other information?

Have you ever used a table to organize data?

Well, maybe you could organize your data. I used a table to help me. These are the 20 answers I got from my survey.

Let me show you what I found!
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Price	# of Responses	Total Value
$0.60	///	$1.80
$0.65	/	$0.65
$0.70	///	$2.10
$0.75	/	$0.75
$0.80	///	$2.40
$0.85	///	$2.55
$0.90	//	$1.80
$0.95	///	$2.85
$1.00	/	$1.00

The range of prices
was .

The median price was .

The mode price was.

The mean price was found by up the total values and by the 20 responses.

The underlined words are hints. Use them in this lesson when you're stumped.
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Price	# of Responses	Total Value
$0.60	///	$1.80
$0.65	/	$0.65
$0.70	///	$2.10
$0.75	/	$0.75
$0.80	///	$2.40
$0.85	///	$2.55
$0.90	//	$1.80
$0.95	///	$2.85
$1.00	/	$1.00
TOTAL	20 Responses	$15.90

"Hey! Your table looks like my line plot!" cried Marie. "I also surveyed 20 people. I kept track of the data this way."

My range of prices was .

The median price was .

The mode price was .

Find the mean price .

Price	# of Responses	Total Value
$0.70	XXX	$2.10
$0.75	XX	$1.50
$0.80	XXXX	$3.20
$0.85	XXXXX	$4.25
$0.90	XX	$1.80
$0.95	XXX	$2.85
$1.00	X	$1.00
TOTAL	20 Responses	$16.70
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"This is the bar graph I made of my 15 responses. I found the range, median, and mode. How can I find the mean?"
What can John do to find the mean?

John's Survey Results
P R I C E R A N G E	$0.60
	$0.65
	$0.70
	$0.75					MEDIAN
	$0.80					MODE
	$0.85
	$0.90
	$0.95
	# of Responses	1	2	3	4

"I also used a graph," replied Susan, "and I ran into the same mean problem."
So I added up the price of EACH response. Then, I divided this total value by 15 since I had 15 responses."

"Help me find the mean price."

Susan used a graph to organize her data.

$0.65, $0.65, $0.70, $0.75, $0.75,
$0.75, $0.75, $0.75, $0.80, $0.80,
$0.85, $0.85, $0.85, $0.90, $0.90.

"I found the mean to be $0.78," said Mike.

"Your mean, green machine comes through again!" stated Susan. "Let's use it to find the mean of your 15 data results."

Use Mike's circle graph to find:

1.The range of prices ,

2.The mode price , and

3. The mean price .

Data can also be organized in a circle graph.

"Cool!" said Susan. "My mean was $0.78, and your mean rounded to $0.78!"

"Well that's just great!" said Marie. "But I'm tired, and we still don't have an answer!"

"What if we combine our results and put ALL THAT DATA on one table?" I suggested.

The members liked the idea. We all gathered around to help. Susan and Mike offered to make graphs on the computer.
(That just "thrilled" Marie!)

All That Data! Survey Results
Price	# of Responses	Total Value
$0.60	XXXXXX	$ 3.60
$0.65	XXXXXXXX	$ 5.20
$0.70	XXXXXXXXXXXXX	$ 9.10
$0.75	XXXXXXXXXXXXXX	$10.50
$0.80	XXXXXXXXXXXXXXXXXXXX	$16.00
$0.85	XXXXXXXXXXXXXXXXX	$14.45
$0.90	XXXXXXXXXX	$ 9.00
$0.95	XXXXXXXX	$ 7.60
$1.00	XXXX	$ 4.00
TOTAL	100 Responses	$79.45

Altogether, we had surveyed 100 people! Use the line plot to complete these sentences.

The of prices is $0.40.
The median price is .
The price is $0.80.
The mean price is .

Use the hints in the underlined words, and don't forget your

And the survey says...

Susan made a horizontal bar graph.

On this graph it's easy to see:

the range,
the median,
the mode,
the mean.

Check all that apply!

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wpeE.jpg (13215 bytes)

Mike made a column bar graph.

Why is it easy to see the range and mode on these bar graphs?

Together they made the circle graph.

This circle graph uses percents (%) in its data display.

Twenty percent (20%) means that 20 out of the 100 people chose $0.80.

What percentage of people chose $0.65?

We found that: 1. The mean price was $0.79. 2. The median price was $0.80. 3. The mode price was $0.80.
From this data, we decided that $0.80 would be a fair price to charge!

"Well, I'm impressed!" said Marie. "Now we have the data to prove that we are charging a fair price. I'd like to see someone argue with all that data!"

"No one will argue with you, Marie," said Susan. And with that, the meeting was dismissed.