Interpreting Data, just for fun

Let's finish the week and the year with a bit of research. We will make more charts about the hot dog (subject of yesterday's posting on picture graphs).

Using a newly-announced Google tool, we can investigate the number of times the words hot dog appear in English literature. Yes, I know you are asking WHY? but hey, it's my blog! Why not?

In this case, I compared hot dog with hamburger and the frequency that they occurred (Y-axis)  in a random set extracted from a Google-scanned database of books published in English between 1908 and 2008 (X-axis). An entire century! What do we learn from this?

It looks like hot dogs were more popular than the hamburger (at least in literature) in the decade between 1920 and 1930. Then the hamburger took off and hasn't been caught since. It is interesting to see that the hamburger has dropped in frequency of mention in the last decade. That makes sense. Now let's add the taco. Being a specialty ethnic food, the taco ranks third in this comparison.

Next I thought of fried chicken, so I added it in to the comparison. Notice in the chart below that early in the last century,  fried chicken got plenty of treatment in literature. It was much more popular than the other foods until after WWII. Now it cruises along right next to hot dogs.

What food will it take to change this chart dramatically? Pizza! Sure enough, it changes the whole scale of the graph, because it appears at least 3-4 times more frequently than hamburger in literature.

That's enough for now. I have equipped you with the tools to waste your entire holidays if you like ... and after a short vacation, I will be back after the New Year in January.

PS = Chocolate? YES! Trumps over pizza ...

Displaying Data Discretely

When I propose to display data discretely, I mean to show it with picture graphs (a discrete unit of measure on the graph) versus line, pie or other kinds of charts. I didn't mean "Leave out the embarrassing facts!"

Picture graphs are the simplest forms of charts, and are closest to representing the reality of what you are displaying. They are easiest for kids to understand. For example, here's a chart showing hot dogs eaten at a picnic:

Notice that the kids who ate the hot dogs are shown. Once we understand the idea of a picture graph, we can add some additional information, so the viewer doesn't have to squint at the tiny picture to identify the kids:

If the names are added we don't really need to have their pictures, so we can simplify a bit. Here is the chart using only the names. Now it's getting more abstract (farther from reality).

I am going to add another level of complexity. I am asking you to imagine that each 1 of the hot dogs shown represents 2 hot dogs in reality. Andrew ate 4, Hannah had 2, etc. The hot dog pictures are not really meaning a single dog in a bun, but two units of hot-dogginess. We have to do math in our heads to calculate Devin's picnic intake of 5 hot dogs.

In order to show this, math gurus invented the legend, or explanatory note. We put a legend at the bottom of the chart indicating that one dog picture = 2 hot dogs. We could have made it 3, 5, 10 or whatever we wanted.

In preparation for another level of abstraction, I have now added grid lines to the chart and value labels at the bottom of each grid line. We still have the hot dogs (we are about to remove them).

Here's the final version of our chart. It's turned from a picture graph to a bar graph. No more drawing little hot dogs, no more pictures of kids, just a boring old chart.

Isn't math fun? I think I will run down to Costco and pick up a hot dog for lunch.

Displaying Data again

Yesterday I showed three ways to construct a pie chart, or circle graph. Today we can look at a line graph, which is one of the more complex ways we teach elementary school kids to display data.

Here's a sample chart or graph which comes from our fourth grade material.

The chart shows distance (across the bottom or X-axis) and elevation (on the vertical or Y-axis). The green line is drawn connecting various points that our rider noted during his training ride. These points are also described in a story that accompanies the chart.

For this problem, we asked students to identify the points labeled 1, 2 & 3 on the chart. These corresponded to things mentioned in the text. This process allows kids to become familiar with the concept of the chart without having to construct everything themselves. Then we asked a question based on the data. Here are the answers:

The next week we asked for a bit more. We described a bike race, with a narrative story, then asked them to plot the ride on a blank grid. They had to decide the units on the Y-axis, label both axes, label the graph, and plot points based on the text. Finally, they had to ask their own question based on the data, and provide the correct answer.

Here's the completed graph:

Is this rocket science? No. Is it difficult to do? Yes. Does it help to visualize this if you took the bike ride first? Yes. Math is a representation of the reality around us, but it is not totally independent of that reality.

Displaying Data

In Excel Math we teach kids how to plot points on a graph, and to make charts.

Believe it or not, this can be done without using Excel or another spreadsheet or without Powerpoint or another display program. Close that window! and work along with me.

We still can do it the old-fashioned way, by thinking and drawing. For example,

Here are the recent viewers in the top 4 countries from which this blog is viewed. 

USA 7447, UK 1199, Canada 874, Aus 436. 

I got these figures from the Visitors box in the left-hand margin of this screen.

Let's make a pie chart - that's a hard one. Here's how I would construct it:

1. Add all the viewer numbers 7447+1199+874+436=9956 or roughly 10,000

2. Calculate the percentage of viewers in each country. Because it's very close to an even number, we will just estimate. USA 75%, UK, 12%, Canada 9%, Aus 4% = 100%

3. We could draw this freehand, but let's do it the proper way and calculate the degrees of the pie that belong to each country. There are 360 degrees in a circle, so the USA gets 75% of 360, or 270 degrees, the UK gets 43 degrees, Canada 32 degrees and Aus gets the other 15 degrees of the circle.

4. We think up a title for the chart. How about  Percentage of Viewers in Top 4 Countries

5. We draw a circle and divide up the pie using a protractor or by eye.

6. Here's a hand-drawn version captured with my phone camera. This took me about 90 seconds to draw, including looking around in the drawer for my green highlighter.

7. Here's my high-quality version, created using Adobe Illustrator. This took me about 10 minutes to create:

8. Finally, here's a chart made using Microsoft Excel. It took me about 60 seconds to make it, including entering the data. Why do you think they invented the spreadsheet Chart Wizard!

That's partly because I already knew what I wanted to show. I didn't have to stop at the front screen (shown at the top above) and ponder the dozens of variations of charts. That could have added 5 minutes.

Of course by now, the numbers have changed. Rats!

Digging into the Data

In our Excel Math curriculum we help kids to study a problem, then re-evaluate data, re-present it in different ways, and learn more about it using their math skills. Let me give you an example.

I read an article today about increasing shoe production in Indonesia. Shoe makers there are getting some of the shoe business that used to be performed in China. But the article was all text - about various companies and countries. Apples and oranges really, too hard to compare. Things like "China share of output currently at 80 per cent, expected to fall to 70 per cent over the next two years", etc. I decided to make some graphs.

Looking at these two pie charts, you can readily see how the NIKE company has balanced their production across three countries, while Payless is heavily oriented towards China. They are in the process of "balancing" their production to reduce exposure to rising currencies.

In this case, my point is not about where your sport shoes are made, but how to visually depict the data so it's more informative.

Another quote in the article said that Indonesia is expected to produce 300 million pairs of shoes this year, with a value of approximately $2.5 billion US dollars. I wondered,  

How much is that per pair?

You can't do it easily in your head and it's not easy on my hand-held calculator either because there are too many zeros to display. We can solve this on paper, and drop zeros to simplify the task:

2,500,000,000 ÷ 300,000,000  =  2,5∅∅,∅∅∅,∅∅∅ ÷ 3∅∅,∅∅∅,∅∅∅ = 25 ÷ 3 = $8.33

or we can do it on a spreadsheet:

Here's how it looks on the calculator that pops up on my spreadsheet software. You can see that the average value (to "the country of Indonesia"; NOT the sales price) is about $8 per pair. This value represents some labor and some materials, and possibly some packaging.

The same article told me that one of the shoe companies sold 170,000,000 pairs of shoes resulting in revenues of $3.3 billion. Let's do a little math on the numbers.

3,300,000,000 ÷ 170,000,000  =  3,30∅,∅∅∅,∅∅∅ ÷ 17∅,∅∅∅,∅∅∅ = 330 ÷ 17 = $19.41

My math says about $20 per pair total revenue to the company. Presumably this includes shipping the shoes out to stores, inventory, sales expense, etc. Plus the $8 earned in Indonesia, China or Vietnam.

If we wanted to learn more about the economics and politics of the shoe industry it would take a lot more research. Today we can just go away knowing that those three countries make many sport shoes, and get about $8 a pair for their work.

Ring Them Bells, Part V

Let's finish our week of Bell Math.

I found lots of software related to bells. The first category was factory and school bell software, to ring bells to indicate work shifts or classes are over. Then there was some software for churches, so they could "ring bells" using a computer and speakers.Then I got complete side-tracked by a bunch of sites ranting about "Ma Bell" (AT&T) and its issues! And discussions on how to draw a bell curve using Microsoft Excel.

I took a short trip through Apple's App store, where I found a few bell programs.

• Virtual Cow Bell
• Jingle Jingle Bell
• Dinner Bell
• H.Bell
  
• Hand Bell
• Handbell
• Golden Handbell
• Dingaling
• Mobel

The reviews were generally negative on most of these apps. Why? Because they don't sound like bells. Not surprising, considering an iPhone has a tiny speaker.

There is some uniqueness to the sound of a bell that is very hard to quantify. Bell sounds are unlike many other sounds that can be reproduced by speakers or headphones. As yesterday's post indicated, some of the sound is generated in our ears, and not from the source (bell or speaker).

Finally, I found some nifty software called Abel, Mabel and Mobel. Abel runs on PCs and Mabel on Macs. Mobel is for iPhones. The creator of these programs gives all the profits to restoration of real bells.

Of course, if you really want to hear bells, go find some real ones! Most ringers welcome new folks. Be prepared to use your logic, timing, math and arms.

Or get your own! You can buy here. Use your math while shopping, and you will learn that an average church bell is 28 inches in diameter and weighs 400+ pounds. I found a source that shows typical weights for bronze bells, by bell diameter. Here are a few:

6 inch weighs 12 lbs.
12 inch weighs 35 lbs.
18 inch weighs 125 lbs.
24 inch weighs 320 lbs.
30 inch weighs 560 lbs.
36 inch weighs 980 lbs.
42 inch weighs 1620 lbs.
48 inch weighs 2300 lbs.
54 inch weighs 3200 lbs.
60 inch weighs 4500 lbs.

This data should be in a table.
So I made one.


Finally, my wife asked me to explain the poor grammar in my choice of the Bell Post titles. It's the title of a song I like, by Bob Dylan. I also found another recording by Liza Minelli that was completely different - but the same title. There appear to be at least 100 different songs available with Bells in the title!

We can end with Ring Them Bells' cryptic lyrics:

Ring Them Bells

Ring them bells, ye heathen
From the city that dreams
Ring them bells from the sanctuaries
’Cross the valleys and streams
For they’re deep and they’re wide
And the world’s on its side
And time is running backwards
And so is the bride

Ring them bells St. Peter
Where the four winds blow
Ring them bells with an iron hand
So the people will know
Oh it’s rush hour now
On the wheel and the plow
And the sun is going down
Upon the sacred cow

Ring them bells Sweet Martha
For the poor man’s son
Ring them bells so the world will know
That God is one
Oh the shepherd is asleep
Where the willows weep
And the mountains are filled
With lost sheep

Ring them bells for the blind and the deaf
Ring them bells for all of us who are left
Ring them bells for the chosen few 
Who will judge the many when the game is through
Ring them bells, for the time that flies
For the child that cries
When innocence dies

Ring them bells St. Catherine
From the top of the room
Ring them from the fortress
For the lilies that bloom
Oh the lines are long
And the fighting is strong
And they’re breaking down the distance
Between right and wrong

Copyright © 1989 by Special Rider Music

I'd like this set for of 6 bells for Christmas, just in case you are feeling generous: