If you have some free time this week, you might want to teach your child how to create their own statistical tables and charts. This practice can either be presented as a chore or a game, but games seem to make their marks more quickly than forced efforts. Then, when your child encounters this practice in math class, she might become the star pupil.

While some tables and graphs might seem complex, they usually begin with what is known as a "frequency table." You will need graph paper (larger graphs, like ?", are good), pencils with erasers, a simple calculator, a ruler, and some crayons or markers.

Frequency Table: Say that you make a list of all the investments you made at BUYandHOLD during the twelve months in 2004 (start with January) I'll keep the figures low for computing ease:

$9, $12, $20, $20, $15, $9, $12, $10, $15, $20, $15, $9

The information above is called "raw data," and it might be difficult for you to decipher information from this format. But, if you count the number of times - or frequency - that each dollar amount appears, you can display the information like this:

Investment	Frequency
$9	3
$10	1
$12	2
$15	3
$20	3
Total	12

The chart above represents a simple way to clarify information, where the investment represents the category and the frequency equals the number of times each category appears in the "data set." The total number of frequencies (12) represents 100%. So, if you want to know the "relative frequency" for a category (or the frequency expressed in fractions or percentages), then you would divide the investment frequency by the total frequency. In other words, three out of twelve investments cost $9, so:

1. The relative frequency for $9 investments equals 3/12 or 25%
2. The relative frequency for $10 investments equals 1/12, or 8.3%
3. The relative frequency for $12 investments equals 2/12, or 16.7%
4. The relative frequency for $15 investments equals 3/12, or 25%,
5. The relative frequency for $20 investments equals 3/12 or 25%

Now, notice that the final percentages add up to 100%, but only because I round up the 16.6666% to 16,7%. Actually, you can round down the 8.3% to 8% and continue to round up the 16.7% to 17% to make this game a little easier. The next step involves formulating a graph from these figures.

Simple Graph: You can create a simple graph from the information in the frequency chart. You need to create a table that looks very similar to the charts shown at BUYandHOLD when you head to Research Stocks and click on one of the top ten holdings. First, draw a box (on graph paper) where the twelve months are listed along the bottom (Jan., Feb., Mar., etc.). Then list the prices along the side, starting with "0" and increasing in increments of five. That left-hand list would then read, "0 - 5 - 10 - 15 - 20."

Now, begin under the "10" along the left side above January to make the first dot, and continue to make dots above each month along the prices that are represented by those months. While the "10," "15," and "20" dollar amounts might be easy for the kids to find, you may have to help them understand where the "9," "12" stand. Now, just connect the dots, and they have a graph that illustrates your investment amounts during 2004.

Bar Chart: Make another box just like the one you made for the graph above and follow the same instructions up to the directions for connecting the dots. Now, however, instead of connecting dots they will take a ruler and draw a straight line from the month listed at the bottom up to the dot. Now, they can take their crayons and make each line a different color if they want.

Another way to create the graph and bar charts incorporates the categories (dollar amounts) along the bottom and the frequencies (number of times the categories occurred, like "1" for the ten dollar amount) along the left side. Remember to begin with "0" on the left side. Since there are no more than 3 frequencies for any given dollar amount, just number from 0 to 5 along the left side. Then, repeat the exercises above but let the kids try to keep track of the categories and frequencies without your help. This is where the practice becomes both a game and a skill.

Older kids can add the relative frequency (percentages) vertically along the right side of the bar chart. Then, they can analyze whether their frequencies along the left side match their relative frequencies along the right side. This type of chart is very easy to read as long as the kids don't create drop-shadows, 3-D effects, or any other fancy graphics that would make the visuals difficult to read. However, if they do get fancy with their charts, make the point that their efforts make great artwork, but they don't work as readable charts (for helpful hints about this information, read last week's article).

Have Fun!

Until Next Week,
Linda Goin