Name__________________________ Period _______________ Date_____________ American Graph-itti Collecting Data The purpose of all scientific investigation is to collect information. We call this scientific information data.
Examples of data might include your height, shoe size,
amount of rainfall in one year, the number of times each student is late to class (we really do this), etc. Data can be used to predict things like weather or earthquakes.
It can be
instrumental in making design improvements on technology like computers and DVD's. Data can also be used in diagnosing illness or medical conditions. As scientist, you'll need to be able to record information, evaluate experiments, and draw conclusions. To do all of this, you need to know how to use data tables and draw graphs, which is exactly what you are about to review.
Graph-it 1
Now you will conduct a brief experiment in which you will collect data. Your team will be counting the number of times a person blinks in 3 minutes. You will record the total number of blinks every 30 seconds. You will need the following materials: 1.
partner
2.
clock or watch with a second hand
3.
your student sheet for recording data (see page 2)
Directions: 1.
Have one person find an object or image to focus their gaze on for 3 minutes.
2.
A second person, the counter, should be seated so they can see the clock and the eyes of their partner. The counter will continuously count the number of blinks and record the total number every 30 seconds.
3.
When everyone is ready, begin timing while counting blinks.
4.
Continue counting for 3 minutes.
5.
Organize and record your data in a way that seems logical to you. Each person should record the group data on their own sheet.
Physical Science
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Name__________________________ Period _______________ Date_____________ Graph-it 1 Data:
Question: How does the organization of your data compare to other groups? Similarities:
Differences:
Data Tables The more data you collect during an experiment, the more problems you have keeping track of it. In order to make data from an experiment useful, you must record it in an organized manner. Scientist use data tables to organize data in columns so it is neat and readable. Data tables should always have a title. The title should clearly describe, to the reader, the data contained in the table. If not clearly labeled, the reader might not be able to understand and use the data in the table. For example: Mass of a Green Iguana Over Nine Months Variables and units provide important information about an experiment. Therefore, they are also included in a data table. The variable clearly describes what was being observed in an experiment. The unit tells the reader how the variable was measured.
Some examples of variables might include time, temperature, length,
volume, mass, etc. The units for these examples would be seconds, degrees Celsius, meters, liters, grams, etc. The variables are written first in the data table. They are located either at the left of a row or the top of a column. The units are written in parentheses beside the variable to which they correspond. Physical Science
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Name__________________________ Period _______________ Date_____________ Here is an example of a data table with variables and units written correctly: Mass of a Green Iguana Over Nine Months Time (months) Mass (grams)
The last piece of information recorded in a data table is the numerical values for each variable.
For example: time (5, 10, 15, 20 seconds), temperature (0, 25, 50
degrees Celsius), length (1, 2, 3 meters), volume (5, 10, 15 mL), and mass (100, 200, 300 grams), etc. Here is an example of a data table with all parts correctly written: Mass of a Green Iguana Over Nine Months Time (months)
0
1
2
3
4
5
6
7
8
9
Mass (grams)
25
31
40
47
55
59
68
70
75
82
Ordered Pairs The numbers in a data table are organized in groups called ordered pairs. Ordered pairs are pieces of data those are directly related to each other in the experiment. In a data table ordered pairs are located in horizontal rows (left to right) or in vertical columns (up and down) Below is an example of a data table in which 2 ordered pairs have been circled. The first ordered pair is (3 months, 47 grams) and the second is (7 months, 70 grams). There are ten ordered pairs in this data table. Mass of a Green Iguana Over Nine Months Time (months)
0
1
2
3
4
5
6
7
8
9
Mass (grams)
25
31
40
47
55
59
68
70
75
82
Graph It 2 Temperature of Water in Full Sun for Nine Minutes Time (months)
0
1
2
3
4
5
6
7
8
9
Temperature (°C)
21
21
21
22
22
23
24
25
28
30
Physical Science
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Name__________________________ Period _______________ Date_____________ Using the data table above answer the following questions: 1.
The title is _________________________________________________________.
2.
The two variables are ________________________ and _______________________.
3.
The unit for the first variable is _________________________.
4.
The unit for the second variable is ________________________.
5.
List the ordered pairs: a. __________________
f. __________________
b. __________________
g. __________________
c. __________________
h. __________________
d. __________________
i.
__________________
e. __________________
j.
__________________
6.
The temperature of the water when the experiment began was ________________.
7.
The water had been in the sun _________ when it reached a temperature of 23 °C.
8.
Using the guidelines you have been given for constructing data tables, correctly complete each of the data tables below: Height of an Oak Tree in Centimeters Over Ten Years
Time
1
2
3
4
5
6
7
8
9
10
Height
48
100
180
240
350
420
500
540
610
695
Time (years)
1
2
3
4
5
6
7
8
9
10
Height (centimeters)
48
100
180
240
350
420
500
540
610
695
Height of an Oak Tree in Centimeters Over Ten Years (years)
1
2
3
4
5
6
7
8
9
10
(centimeters)
48
100
180
240
350
420
500
540
610
695
540
610
695
Height of an Oak Tree in Centimeters Over Ten Years Time (years) Height (centimeters)
Physical Science
48
100
180
4
240
350
420
500
NPS
Name__________________________ Period _______________ Date_____________ Choosing a Graph A graph is a picture of information in a data table.
A graph shows the
relationship between all of the number in a data table. There are many types of graphs that can be used to display your data. Line graphs, bar graphs, and pie graphs are primary examples. The type of data you collect determines the type of graph you use. A line graph compares the relationship or trend between two variables. The information on a line graph is represented by data points that are connected by a line. A line graph shows the trend, what actually happens, between two variables over time. Examples of data that would be graphed using a line graph might include: the amount of time it takes water to reach a temperature of 100 °C, the mass of a green iguana over nine months, and the growth of an oak tree over time (see data tables on previous pages). A bar graph compares the trend of data over time and the relationship between each set of ordered pairs. The information on a bar graph is represented by thick blocks, drawn to scale. A bar graph focuses mainly on the differences between the ordered pairs in the data. For example, the amount of rainfall in four different cities, the height of individual members of a group, or the grade distribution in a class, would all be best illustrated on a bar graph. A pie graph uses a circle to display data. Each section of the graph represents a portion of the whole. When all of the portions are added together their sum must be 100%. The focus of a pie graph is to show the relationship between the parts of the whole.
Examples of data that could be shown in a pie chart would include the
percentage of elements in the earth's crust, the amount of types of water found on Earth, the portion of each type of fuel used in the United States. Rainfall Over 6 Months 15
10 rainfall (cm)
rainfall (cm)
Monthly Rainfall for Jan.-Apr.
Rainfall for Jan.-Apr.
10
5
8 6
Jan
4
Feb
2
Mar Apr
0
0 1
2
3
4
time (months)
Line Graph
Physical Science
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6
Jan
Feb
Mar
Apr
time (months)
Bar Graph
5
Pie Graph
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Name__________________________ Period _______________ Date_____________ Graph It 3 Using the information on the previous page, determine which type of graph would best display each set of data. __________ 1. The temperature of each of the science classrooms in the building. __________ 2. The number of each type of animal compared to the total number of animals in a ecosystem. __________ 3. The number of waves that reach the beach every minute for 1 hour. __________ 4. The number of raisins in three different brands of cereal. __________ 5. The amount of air pressure as you go up a mountain.
Give a brief justification for each of your answers above. 1.
2.
3.
4.
5.
Physical Science
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Name__________________________ Period _______________ Date_____________ Parts of a Line Graph In science class you will use a line graph most of the time because you will be comparing the relationship between two variables. All parts of a data table must be included in a graph. The same title, variables, units, and data must be used. There are two axes on a two-dimensional line graph, the horizontal and the vertical. The horizontal axis is known as the “x” axis and runs along the bottom of a graph. The vertical axis, also called the “y” axis, runs up and down along the side of a graph. Each axis must be labeled with the proper variable and units. The variable that you change is called the independent or manipulated variable. The independent variable is always placed on the x axis. The name of each variable is placed is placed along its axis and the units for each variable are written in parentheses beside it. “Time” is almost always the independent variable in an experiment. The variable that changes as a result of the independent variable is called the dependent or responding variable. The dependent variable goes on the y axis. The lines on an axis are labeled in even intervals. Intervals are the even spacing of numbers along the axis of a graph. These intervals are determined by the range of the data and the number of spaces on a graph. The range on a graph is the difference between the largest and smallest numbers in the data. Each ordered pair shows the location where two lines intersect on the graph. The place where the two lines intersect is called a data point. There is a data point for each ordered pair in a data table. Plotting is the process of locating each data point on the graph. You may have seen graphs with data points connected by a line. The type of line drawn depends on the arrangement of the data points. If the pattern is clear, draw a straight or curved line that passes through each data point.
distance (meters)
Distance a Worm Traveled 9 8 7 6 5 4 3 2 1 0 1
2
3
4
5
6
7
time (minutes)
Physical Science
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Name__________________________ Period _______________ Date_____________ Draw a “best fit” line or smooth curve if there is no clear pattern. This line should pass through as many data points as possible to form a smooth line that follows the general pattern (not all data points may touch the line).
heartbeats (number)
Num ber of Heartbeats Over Tim e 9 8 7 6 5 4 3 2 1 0 0
2
4
6
8
tim e (m inutes)
If the points are totally scattered, do not try to create a pattern by connecting points with a line. However, be sure the data points are very visible. Quakes Along the San Andreas
quakes (number)
25 20 15 10 5 0 0
2
4
6
8
tim e (days)
Graph it 4: Label each part of the graph 1. _________________________
1 Rainfall Over 6 Months 1
2. _________________________
rainfall (cm)
15
3 1 1
3. _________________________
4 1
10
4. _________________________
1
5
5 1
5. _________________________
7 1
1
6. _________________________
1
0 1 2 1
2
3
4
tim e (m onths)
5
6
7. _________________________
6 1 1
Physical Science
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Name__________________________ Period _______________ Date_____________ Multiple Line Graphs A single line graph has only one line because it shows data for only one trial. Sometimes it is necessary to compare different data from similar trials. This produces a graph with two or more lines called a multiple line graph. There are still only two variables; however you are comparing ordered pairs of different trials. Look at the example below. Traveling Rate of Three Boats Time(sec) 5 10 15 20 25 30 35 40 45 50 Distance Boat A (m) 3 16 25 39 53 64 75 86 97 110 Distance Boat B (m) 4 18 30 46 61 72 84 95 105 118 Distance Boat C (m) 7 15 23 33 44 57 65 74 83 91 In this data set the two variables are time and distance, but there are three boats. There will be three different sets of ordered pairs. To determine the ordered pairs, you must match the independent variable data (time) with each set of dependent variable data (distance). For example, the ordered pairs for 5 seconds would be: boat A (5, 3), boat B (5, 4), and boat C (5, 7). When plotting data it is important to plot only one set of data at a time. You would begin by plotting all of the data for boat A, then draw the line, and label it. Then you would plot all of the data for boat B, followed by boat C. Graph it 5 List the ordered pairs for each boat above in the space provided. 1.
2.
3.
Boat A ________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
________
Boat B
Boat C
Physical Science
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Name__________________________ Period _______________ Date_____________ Constructing a Line Graph 1.
Title your graph.
2.
Label the x axis with the independent variable and its units.
3.
Label the y axis with the dependent variable and its units.
4.
Count the number of lines on the x axis.
5.
Determine the range of data for the independent variable (the difference between the largest and smallest numbers of the data). NOTE: THE SMALLEST NUMBER WILL ALWAYS BE ZERO for this class, so that we can compare data more easily.
6.
Calculate the interval for the x axis using the following rule: Divide the range of the data (zero to the highest number) by the number of lines on the axis. Example: range number of lines
7.
Label the x axis using the intervals you have calculated. You do not have to label every line. You can mark every few lines depending on your interval.
8.
Repeat steps 4 through 7 for the dependent variable on the y axis.
9.
Plot your data points using the ordered pairs in the data table.
10.
Draw a smooth line connecting the data points.
11.
If there is more than one set of ordered pairs for your graph, plot each set one at a time and draw your lines using different colors or notation.
12.
For a multiple line graph, label each line or make a key.
Physical Science
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NPS
Name__________________________ Period _______________ Date_____________ Graph it 6 Construct a graph for each data table using the graphs provided.
Time (days) Rainfall (cm)
Total Rainfall Over the First Ten Days of January 1 2 3 4 5 6 7 8 0 0 0 1 1 2 3 5
What is the interval for each axis? X__________
Physical Science
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9 5
y__________
NPS
10 7
Name__________________________ Period _______________ Date_____________
Height of Three Varieties of Tomato Plants Over Nine Weeks Time (weeks) 0 1 2 3 4 5 6 7 Height of Plant A (cm) 4 16 25 39 53 64 75 86 Height of Plant B (cm) 4 18 30 46 61 72 84 95 Height of Plant C (cm) 4 15 23 33 44 57 65 74
8 97 105 83
What is the interval for each axis? X__________ Y ___________ How many data lines will appear on this graph?____________
Physical Science
12
NPS
9 110 118 91
Name__________________________ Period _______________ Date_____________ Best Fit Line Graphs In a best fit line graph the line(s) pass through many but not all data points. Scientists use a best fit line to show relationships and trends that do not have to be exact. This graph has a smooth continuous line, which represents a prediction for information or data between known data points. The process of predicting these unknown data points within the line is called interpolation. A best fit line graph can also be used to find values that are not within the range of measured data. You can extend the line following the trend in the data. This process of estimating beyond the known data is called extrapolation. Look at the graph below. Bacterial Population Over 8 Hours
bacteria (number)
300 250 200 150 100 50 0 0
2
4
6
8
10
time (hours)
This is a best fit line because it estimates the value of the data between the known points. To interpolate the number of bacteria at 5.5 hours, you would use the following procedure: 1. 2.
Draw a vertical line, perpendicular to the x axis, starting at 5.5 until it intersects the best fit line. Mark this point. Starting at the point you marked, draw a horizontal line until you intersect the y axis.
The number of bacteria at 5.5 hours is the point where your horizontal line intersects the y axis. The number of bacteria at 5.5 hours is approximately 45. The ordered pair for 5.5 hours is (5.5, 45). To extrapolate the number of bacteria at 8.5 hours you would use the following procedure: 1. 2. 3.
Extend the line to 8 hours beginning at the last known data point following the trend of the line. Draw a vertical line perpendicular to the x axis, starting at 8 until you intersect the best fit line. Mark this point. Starting at the point you marked, draw a horizontal line until you intersect the y axis.
Physical Science
13
NPS
Name__________________________ Period _______________ Date_____________ The number of bacteria at 8 hours is the point where your horizontal line intersects the y axis. The number of bacteria at 8 hours is approximately 250. The ordered pair for 8 hours is (8, 250). Graph it 7: Practice drawing best fit lines in the graphs below.
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Physical Science
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NPS
Name__________________________ Period _______________ Date_____________ Use the data table below to: A. Construct a best fit graph. B. Extrapolate the number of guppies at 11 weeks__________. C. Interpolate the number of guppies at 6.5 weeks__________. Guppy Population in a Twenty Gallon Aquarium Over Ten Weeks Time (weeks) 0 1 2 3 4 5 6 7 8 9 Guppies (number) 6 6 12 17 16 15 22 35 24 23
Physical Science
15
NPS
10 20
Name__________________________ Period _______________ Date_____________ Expansion: Just the Facts, Maam Examine the following graphs and answer the questions based only on the information you can gather from them. Do not make inferences - just stick to the facts. A student in a science class studied the effect of temperature on the growth of bacteria. The student obtained the following data: Temperature of growth chamber (oC) 5 10 15 25 50 70
Number of bacterial colonies 0 2 6 12 8 1
Which graph correctly represents the data from the experiment? 1
12
8
10
Number of
12
Number of
8
Colonies
6
Colonies
6
2
4
0
0 0 5 10 15 25 50 70
0 10 20 30 40 50 70
Temperature (°C)
Temperature (°C)
70
70
50
50
Temp.
30
Temp. 25
(°C)
20
(°C)
10
10
5
0
0 3 6 9 12 15 18
3 6 9 12 15 18
Number of Colonies
Physical Science
Number of Colonies
16
NPS
Name__________________________ Period _______________ Date_____________ A study is being done on the amount of water needed to grow plants. Five small plots are given different amounts of water. After two months the height of the plants is measured. The data are shown in the graph. What is the relationship between the variables?
45
40 Height of
35
Plants (cm)
30
25
20
10
20
30
40
50
Amount of Water (Liters/day)
a. Increasing the amount of water increases the height of the plants. b. Increasing the height of the plants increases the amount of water. c. As the amount of water increases, the height of the plants also increases. d. Increasing the amount of fertilizer increases the height of the plants.
Physical Science
17
NPS
Name__________________________ Period _______________ Date_____________ Expansion: Graphing Food Collecting data is a very important component of any investigation. Once you collect the data it must be analyzed (broken down and studied) further. You should look for patterns in the data that has been collected. This allows scientists to make predictions about the subjects being researched. This could in turn create a new theory or disprove an existing theory. Now you will attempt to collect some vital data about plain M&M’s. PROBLEM: Does the number of M&M’s dropped at one time affect which side they land on? HYPOTHESIS: Write the word HYPOTHESIS on the first line of your paper and write your hypothesis to the problem. EXPERIMENT: MATERIALS: 1 small cup (please do not put your mouth on this cup – we are going to use these in other classes). 1 – 2 paper towels 1 small handful of assorted plain M&M’s 1 sheet of notebook paper to record data 1 pencil (optional) 1 ruler – to make your data table grid look nice PROCEDURES: 1. Spread out the paper towel on your desk. 2. Construct a data table on your paper in a manner that allows you to conduct 10 trials. 3. Have your teacher check your data table and then get some plain M&M’s from your teacher. DO NOT EAT ANY! 4. Place 1 M&M in your cup. (You haven’t eaten any yet have you?) 5. Begin TRIAL 1 – shake M&M gently and roll it onto your paper towel (like playing Yahtzee). 6. Record how many M&M’s landed with the M facing up for TRIAL 1. 7. Begin TRIAL 2 – Repeat steps 4 - 6 until you have enough data for 10 trials (each trial you are adding 1 M&M for a total of 10 M&M’s). You may now eat your M&M’s or throw them in the trash. Please do not share. 8. Throw away your paper towels and return the cups to the teacher’s desk. 9. On a piece of graph paper, title your graph, and label the independent and dependent variables on the correct axes. 10. Using 10 as your largest number determine the range for the x and y axes. Calculate the intervals using the formula range/number of lines. 11. Number your axes using the appropriate intervals. (The interval for the x-axis may be different than that of the y-axis). 12. Plot your data points using the ordered pairs in your data table. 13. Draw a best fit line through your data points. 14. Below your data table, describe any possible patterns or trends that you see in your data and be ready to share this information with the class! 15. Interpolate the number of M&M’s landing M side up when 4.5 M&M’s are rolled (if possible) and extrapolate how many land M side up when 11 M&M’s are rolled. Physical Science 18 NPS
