- A graph is one of the tools used by scientists to interpret raw data. When we plot a graph, we do not connect the points, but instead we draw the best line of fit. Our data points from the raw data almost never fall in the straight line that they belong. This is because of experimental error. When we fit a line to our points, we draw the line the points should have been on. This is somewhat like an average, in that the line we draw is the best representation of our data points. The line may or may not go through any of our points, but it will have about equal points above and below it, which are about the same distance from the line. The correct answers are then any point along the line, and not our raw data points.
- This takes practice and concentration to do well. In this lab we will use probability to practice finding a line on a graph.
MATERIALS:
6 pennies
Cup
Ruler
graph paperPROCEDURE:
1. You will be "flipping" 1 through 6 pennies 25 times for each group. Start with one penny and shake it in the cup, then pour it on the table. Count the total number of heads in 25 tosses. Record the total number of heads on the DATA TABLE.
2. Now repeat step 1 with two pennies, then 3, ect. until you have done six pennies 25 tosses. Record the total number of heads for each group on the DATA TABLE.
DATA TABLE: NUMBER OF
PENNIES (x)NUMBER OF HEADS
PER 25 TOSSES (y)
1
2
3
4
5
6GRAPHING:
3. On graph paper, plot your 6 sets of data points. The number of pennies per group will be the horizontal or "x" axis. Number it out to 8 pennies, even though you only used 6. The number of heads tossed per group will be the vertical or "y" axis. Try to use as much of the graph as possible.
4. Now, using a ruler, draw the best line of fit for your data points. Review the introduction so you are sure you know how to do this properly. Remember, for this graph x=0, y=0 is a point that your line will go through. Because if you tossed no pennies, you would get no heads. Be sure to extend the line past where x=8.
CALCULATIONS:
5. According to your graph, how many heads would there have been for 8 pennies tossed 25 times? Simply find where your line crosses the x=8 line, then go over to the "y" axis to find the value.
According to the graph, 8 pennies thrown 25 times = _______ heads.
6. Now calculate the mathematical value for 8 pennies thrown 25 times. The probability of a head being tossed with a penny, is 50%. REMEMBER: Percent must be converted to decimal form for multiplication.
The formula would then be:-
8 X 25 X 0.5
Theoretical number of heads for 8 pennies thrown 25 times. = _______ heads
- Compare the results from your graph, to the calculated theoretical value. If you were only one or two off in either direction, you did a great job fitting the line to your graph.
Back to Physical Science Table of Contents
Back to Lab Dad's Laboratory
- This takes practice and concentration to do well. In this lab we will use probability to practice finding a line on a graph.
USING A GRAPH
TO INTERPRET DATA
USING PENNIES
INTRODUCTION: