Mr. Hedman’s Math Class

Hey guys, so this week we learned how to find the median-median line of data. This example is from our Population Prediction packet that we did in class. So you have to plot the following things, let “x” be the years and “y” be the population. Remember that the data is in millions! (data is in order)

Years: 1920, 1930, 1940, 1950, 1960, 1970, 1980, 1990, 2000

Pop.: 106, 123, 132, 152, 180, 204, 227, 250, 282

Step 1. Plot the points as a scatter plot.

Step 2. Make three groups of numbers called “chunks” and each chunk should have an equal amount of data points.

Ex: chunk 1: 1920, 1930, 1940

chunk 2: 1950, 1960, 1970

chunk 3: 1980, 1990, 2000

Step 3: Find the median of each chunk and label them M1, M2, M3.

Step 4: Find the slope of the line that goes through M1 and M3. Use the equation m = Y2 – Y1 / X2 – X1.

250-123/1990-1930= 127/60=2.12 so m=2.12

Step 4: Use the equation y=mx+b to find the y-intersept of the line going through M1 and M3.

123=2.12(1930)+b (Multiply 2.12 by 1930)

1234=4091.6+b (Then subtract 4091.6 from both sides to isolate b)and get b=-3969.

Step 6: Repeat the same thing using the same formula to find the y-intersept of M2.

180=2.12(1960)+b (Multiply 2.12 by 1960)

180= 4155+b (Subtract 4155 from both sides to isolate b)

b= -3975

Step 7: Find the median-median line of the data. Use the following equation:

(y-intersept from step 4) + (y-intersept from step 4) +(y-intersept from step 6)/3

-3969-3969-3975/3 = -3971

Final Equation: y=2.12x-3971

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How to find the median-median line:

1. After you make your graph, you divide the graph into three “chunks”

2. Find the medians (the middle points) of each chunk and label them M1, M2, and M3.

3. Draw a line that goes through M1 and M3, then find the slope of that line.

4. Find the y-intercept (the point where the line crosses the y-axis) of the line going through M1 and M3.

5. Draw a line through point M2 that is parallel to the M1, M3 line (this line will have the same slope) and find it’s y-intercept.

6. Find the equation for the M1, M3 line.

• the formula is: y-y₁=m (x-x₁)

7. Find the equation for the M2 line

8. Using the y-intercepts from both lines, plug the numbers into the equation:

_{(y-intercept M1, M3 + y-intercept M1, M3 + y-intercept M2)}
3

9. Use the slope from the M1, M3 line and the y-intercept from #8 (above) you plug those numbers in:

• y-y₁=m (x-x₁)

10. Solve, and you have your median-median line.

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Hey everyone, here’s what happened in math class today.

We had some good news and bad news. Well, the seminar that Edwards and Hedman went to is teaching them to hold us more accountable for our actions and to try new things in class. Maybe this news isn’t the best news.

Today we worked on a U.S. population packet. From this, we learn to actually CALCULATE the line of best fit. The first row worked with partners while the rest of us got our own packet.

Then we have classwork to do on the last page of the U.S. population packet.
Page 139 # 6
If we didn’t finish this in class, it is now homework.

We also got notebooks passed back today. If you got a zero on an assignment, just contact Mr. Hedman and maybe you can have your grade adjusted.

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Filed under: Scribe Summaries tagged best fit, US population

Here are some ideas for getting extra credit in math. Mr. Hedman reserves the right to decide how much extra credit to give. He will decide based on the presence and quality of the math content, the amount of effort that went into the project, and the project’s aesthetics, humor, etc.

Create a website for a famous mathematician (don’t duplicate your project person.)
You can click here to set up a free site at Squidoo.com

The website needs to include:

• Basic biographic information. (Similar to the project blogs.)

• A brief summary of the math concepts discovered (or invented.)

• A brief description of how the discovery affected society. Did it allow new inventions or other technology?  Did it change the way we look at the world?

• Links to at least three other sites which have additional information.

• Pictures, videos, etc. to make it look nice!

Please cite your sources and restate everything in your own words. Two people can work together on one page.

Video Tutorial
Create a YouTube tutorial explaining a concept we have learned and/or showing how to do a problem. The math needs to be correct and it needs to be entertaining. Two or three people can work together to create the video.

After school tutoring
(If people are willing to be tutored.)

Other ideas?
If you have an idea for an extra credit project. Let me know and I’ll consider it.

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