Worked+Problems-+Mean+Median

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:**
 * Population Prediction** - Marlene Figueroa [West]
 * (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**

1. Once you turn on your [|calculator] press the Stat button. 2. Scroll over to Enter 3. Enter your first set of numbers to l1 and your second set of numbers to l2. Years- 1992,1993,1994,1995 Pop. - 200,500,700,900 If this was your information you would enter the years in l1 and the population in l2 4. Now that you’ve finished you can press 2nd and quit. 5. Press Stat again and scroll over to where Calc is. 6. Now move down to where med-med are, just press enter twice and you’ve got the median-median line.
 * TI-83** - Martha Landeros


 * How to Find the Median-Median Line -** AJ Quon [S]

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. 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: 10. Solve, and you have your **median-median line**.
 * the formula is: y-y1=m (x-x1)
 * y-y1=m (x-x1)