1. 5. Collect and Analyze Data as part of experimentation
Example of a data table
5. Collect and Analyze Data as part of experimentation
Data is always collected in a table or chart.
Data is often presented in a graph. (line or bar)
Example of a line graph

2. How Do Scientists Use Math to Analyze Data?
Timing ≈ 0.5 min
Recap: Calculating percent error and knowing the precision and accuracy of your measurements are important in analyzing data.
Connect: It is also important to be able to study the patterns and relationships in your data.
Preview: Graphs often help you find patterns and trends in your data. Next, we will look at some common types of graphs that you may see in chemistry.

3. Displaying and Interpreting Data: Graphs
Show trends clearly
Allow for easy data set comparison
Provide less precise data points
Are less useful for numeric analysis
Timing ≈ 0.5 min
[Animate stem] Another common way of displaying data in science is with a graph.
[Animate bullet 1 and graph] Graphs show trends clearly. For example, this graph makes it obvious that the data in trial 1 follow a nonlinear trend [teacher show] but the data in trial 2 follow a linear trend [teacher show].
[Animate bullet 2] Graphs also allow for more rapid comparison of data sets as a whole. For example, by studying this graph, you can see that trial 2 yielded product more rapidly than trial 1 at first, but then trial 1 began to be more productive [teacher show on graph].
[Animate bullet 3] Although graphs make trends easier to see, it is difficult to read data points from graphs precisely.
[Animate bullet 4] Therefore, they are typically less useful if you need data for a numerical analysis.

4. Common Type of Graphs
A line graph shows change in a given variable when a second variable is changed.
Independent variable on x-axis
Dependent variable on y-axis
May include multiple lines
One line for each group or sample
Often used to show change over time or response of one variable to another
Timing ≈ 1 min
[Animate definition]
(teacher relate this statement to definition) Line graphs are often used to show the relationship between a dependent variable and an independent variable.
[Animate bullet 1] The independent variable is a factor that can be varied or manipulated in an experiment (e.g. time, temperature, concentration, etc). It is graphed on the x-axis [teacher circle]. The scale of the axis depends on the data you are graphing. The range of the axis values should include all of the data you are graphing, but they should not include too much extra space. [teacher show that the x-axis in the sample ends after last data point]
[Animate bullet 2] The dependent variable is the factor that depends on another variable and is measured by the scientist, reflecting the influence of the independent variable. It is plotted on the y-axis [teacher circle]. The same rules apply for the scale of this axis.
In the graph, pressure is the independent variable that is manipulated to various values. Volume, as the dependent variable, is then measured for each of the manipulated pressures (teacher, use graph).
[Animate bullet 3] You can have multiple lines on a graph. [teacher draw another line for a different gas on the graph, explaining that if you have the same range of pressure values you can graph the data on the same graph]
[Animate bullet 4] Line graphs are commonly used to show the dependence of one variable on another.

5. Common Type of Graphs
A scatterplot shows individual data points; may show a best-fit line.
Does not imply dependence of one variable on another
May include multiple data sets
Different point style/color for each data set
Often used to determine mathematical relationship between two variables
May include best-fit line
Timing ≈ 1 min
[Animate definition]
(teacher relate this statement to definition) A scatter plot is used to show the relationships between individual measurements, or data points.
[Animate bullet 1] Unlike a line graph, a scatter plot does not suggest that there is a dependent variable and an independent variable.
[Animate bullet 2] Like a line graph, a scatter plot can show multiple data sets. [teacher draw in another set of data using a different color]
[Animate bullet 3] Scatter plots are often used to determine the relationship between two variables. For example this graph shows that mass and volume are directly related--as one increases, the other increases.
[Animate bullet 4] Scatter plots often include a best-fit line or curve. [teacher sketch in a best-fit line for each data set] Notice how a best fit line does not connect each plotted point, but represents all the points. The best-fit line can be used to estimate the mathematical relationship between the variables.

6. Common Types of Graphs
A bar graph shows the magnitude of individual measurements or values associated with categories.
Can be used for data with only one numeric value per point
May include multiple data sets
Different bar color for each data set
Often used to compare categories or magnitudes of data
Timing ≈ 1 min
[Animate definition] A bar graph shows the magnitude of a measurement across different categories.
[Animate bullet 1] Unlike data in a line graph or a scatter plot, the data in a bar graph have only one numerical value that is being compared. For example, this graph compares the number of valence electrons in various elements. The size of the bar indicates the magnitude of the value.
[Animate bullet 2] Like a line graph and a scatter plot, a bar graph can show multiple data sets. [teacher draw in another set of data using a different color]
[Animate bullet 3] Bar graphs are often used when you need to compare the size of a measurement across different categories or samples.
Bar graphs are used for “show” because they often look pleasing to the eye.

7. Line vs. Bar
In this class you will be using either a line, or a bar graph, but how do you know when to use which graph?
Use a line graph when a there is a direct correlation between the two variables being plotted.
Use a bar graph when the two variables are not directly correlated.

8. Best-Fit Lines
In graphs, sometimes data do not fall along the same line.
Allow for estimates of mathematical relationships in “messy” data
Can be lines, curves, or other mathematical operations that represents most points.
Timing ≈ 0.5 min
[Animate stem and graph] Explain (teacher, use graph to explain) that sometimes data do not fall along the same line. In some cases, it is appropriate to draw a line that approximates the best fit for a series of data points.
[Animate bullets 1 and 2] A best-fit line or curve helps visualize patterns in the data.
[Animate bullet 3] Because the calculations for determining a best-fit line are repetitive and easy to mess up, typically these lines are found using technology, such as spreadsheet software.

9. Graphing Data
When setting up a graph it is important to keep in mind that a graph is a visual picture of the data.
LOOKS COUNT when it comes to graphing.
Appropriate graphs that are scaled correctly and neatly are excellent tools for analyzing results.

10. Graphing Guidelines
Title your graph – make an appropriate title for what is being represented (should be descriptive of data plotted).
Label axes – leave space for labeling each axis (INCLUDE UNITS).
Always plot the independent variable (control) on the horizontal (x) axis.
Choose an appropriate scale – make sure that each box on each axis is given the same interval value, and that the data will fit on the paper according to your scale, but at the same time, be visually pleasing.

11. Quick Break
Shawshank Redemption

12. Measurement
Measuring and measurement tools are an essential part of the scientific process.
The International System of Units (SI), also called metric system, will be used in this class and in most science classes.

13. The Metric vs. English Controversy

14. The Metric System Metric System Versus the English System Simplicity
The metric system uses ONE unit for each category of measurement
Gram (mass), liter (volume), meter (distance)
The English system utilizes many different names for each major measurement (units of mass, volume, distance)
DISTANCE: Rod, furlong, hand, foot, yard, mile, nautical mile
VOLUME: Pinch, gill, teaspoon, tablespoon, ounce, cup, pint, quart, gallon, peck, bushel
MASS/WEIGHT: Penny, grain, ounce, pound, short ton, standard ton

15. The Metric System Metric System Versus the English System Consistency
All metric units are multiple of 10 or utilize decimal placement
The English system has no consistency between units
DISTANCE: Rod, furlong, hand, foot, yard, mile, nautical mile
VOLUME: Pinch, gill, teaspoon, tablespoon, ounce, cup, pint, quart, gallon, peck, bushel
MASS/WEIGHT: Penny, grain, ounce, pound, short ton, standard ton

16. The English System

17. The Metric System Metric System Versus the English System Conversions
Metric units are inter-converted by moving the decimal place
Metric units are expressed by prefixes and exponential notation

18. The Metric System Metric System Versus the English System
Standard Units
Mass … grams (g)
Distance … meters (m)
Volume … liters (l)

19. The Metric System Units
Mass
The amount of matter a substance contains
The measure of inertia in a substance
This value never changes unless the substance changes
Grams (g)
Measured using a Triple Beam Balance, Electronic or Analytical Balance

20. The Metric System Units
Distance
Dimensions … L W H
Meters (m) = inches
Calibrations (metric ruler, meter stick, odometer)

21. The Metric System Units
Volume
The amount of space a substance occupies or takes up
Liters (l) … often we use milliliters (ml)
Types of Volume Measurements
1) regularly shaped solids  cubic volume (L x W x H)  cm3
2) volume of a liquid  direct volume using a graduated cylinder
3) irregularly shaped solids  water displacement

22. The Metric System Units
Density
A special relationship between mass and volume
d = m/v  mass/volume
Information concerning Density
1) g/ml g/cm3 g/l
2) ice floats  less dense than liquid
3) helium floats  less dense than air
I “love” density

23. Density The amount of matter (mass) in a given space (volume)
Density describes how tightly packed the molecules in a substance are.
Density = mass/volume
More DENSE
Less DENSE

24. The Metric System Units
Density
Why would the two sides be balanced (as shown in the picture)?
The mass of the objects must be the same since they balance out
The volume is different
Density accounts for them being balanced

25. Identify the Correct Units
A chemical reaction produces solid sulfur as a product. Which unit should be used to describe the mass of the sulfur produced? O milliliters O grams O kilometers O Kelvin
The volume of a gas must be measured at several points during an experiment. Which units should be used to describe the volume of the gas? O liters O centimeters O degrees Celsius O milligrams
Timing ≈ 0.5 min
Entry Audio: It is important to know the correct units for different types of measurements.
Hint 1 Audio: Which unit is a unit of mass?
Hint 2 Audio: Which unit is a unit of volume?
Exit Audio: Knowing the correct units for different quantities is only half the story. You must also know how to convert from one unit to another, which we study next.

26. Convert between English and SI Units
Laura measures the length of a piece of equipment in inches. Which metric unit is the most appropriate for her to use for her measurement?
O meters
O centimeters
O kilometers
Timing ≈ 0.5 min

27. The Metric System
Metric System Uses Prefixes
terameter
decigram

28. The Metric System

29. Getting to know your prefixes
Notice that each unit is a multiple of ten from the one next to it.
Prefixes: (from biggest to smallest)
kilo (k)- (1,000 times bigger than base unit)
hecto (h)- (100 times bigger than base unit)
deka (dk)- (10 times bigger than base unit)
BASE UNIT (meters, liters, grams)
deci (d)- (10 times smaller than base unit)
centi (c)- (100 times smaller than base unit)
milli (m)- (1,000 times smaller than base unit)

30. An easy way to remember prefixes
King (kilo)
Henry (hecto)
Died (deca)
By (base unit)
drinking (deci)
chocolate (centi)
milk (milli)

31. Metric Conversions
Converting in the metric system is simply an exercise in moving the decimal place.
You start at the prefix of your known value.
You move (left or right) to the prefix you are trying to find.
You move the decimal point in the same direction for the same number of places to find the new answer.
Base unit
Kilo Hecto Deka (l,g,m) Deci Centi Milli

32. Sample problem Kilo Hecto Deca (l,g,m) Deci Centi Milli
How many kilometers are in centimeters?
Base unit
Kilo Hecto Deca (l,g,m) Deci Centi Milli
Start at “centi” since that is our given prefix.
Go 5 places to left to get to kilometers (our unknown).
Move the decimal in our known value 5 places to left.
432.3 cm becomes km

33. Conversion Practice 567,000 0.078 780 3,450 753 345 m = _______ dm
567 g = __________ mg
78 L = ___________ Kl
.0078 km = _______ cm
345 m = _______ dm
7.53 dkg = ______ dg
0.078
753
780
Base unit
Kilo Hecto Deca (l,g,m) Deci Centi Milli

34. Quick Break
Airplane

35. Uncertainty in Measurement
Uncertainty in measurement depends on the skill and carefulness of the person and the limitations of the instruments
We certainly want our dentists, doctors, mechanics, pharmacists, nurses, chefs, and other service providers to be accurate and precise in their care
CTRiesen

36. Uncertainty in Measurement
Why be precise?
CTRiesen

37. Uncertainty in Measurement
Precision
Usually refers to instrumentation
Indicates the reliability or reproducibility of a measurement
Examples
The following measurements on a thermometer [91.9 C, 92.0 C, 92.0 C, 91.9 C] show consistency and high reproducibility and are, therefore, the thermometer readings are considered precise
CTRiesen

38. Precision
Precision indicates how close together or how repeatable the results are. 
You can be precise, but not accurate (meaning you get the same wrong value again and again).
Ideally, you’d like to be both accurate and precise (meaning you are getting the correct value again and again).

39. Uncertainty in Measurement
Precision
Usually refers to to instrumentation
Measure the bug to the left using the most precise unit on the centimeter ruler
The bug is more than 1 cm, but less than 2 cm
There are millimeters calibrations as well (more than 5 but less than 6 mm)
We can ESTIMATE once between the 5th and 6th mm …
The bug is 1.54 cm long
CTRiesen

40. Uncertainty in Measurement
Accuracy
Usually refers to people and inaccurate measuring OR to an instrument that may be measuring precisely, but is not accurate (see example below)
Indicates how close a measurement is to the accepted value
Examples
The values of temperature [91.9 C, 92.0 C, 92.0 C, 91.9 C] for the boiling point of water are inaccurate … the accepted value at sea level is 100 C (student probably used an “immersion thermometer” rather than non-immersion thermometer)
CTRiesen

41. Accuracy
Accuracy indicates how close a measurement is to the accepted value.

42. Accuracy Versus Precision
Production: Please recreate diagrams.
Accuracy is the closeness of measured values to the accepted value.
Precision is the reliability or reproducibility of a measurement.
Accurate and precise
Precise, not accurate
Timing ≈ 0.5 min
[Animate accuracy definition] Accuracy is the closeness of measured values to the accepted value.
[Animate precision definition] Precision is the reliability or reproducibility of a measurement. In other words, it relates to the closeness of the measured value to other measured values. What do these mean?
[Animate accurate and precise diagram] The picture with the points in the bull's-eye [teacher circle] is an example of accuracy. The bull’s eye is the accepted value. To be accurate is to hit the bull's-eye. It also shows precision because it shows the points are close together.
[Animate precise, not accurate diagram] The second bull's-eye in the example [teacher circle] portray precision due to the grouping of the points but not accuracy because the points do not hit the bull’s eye.
[Animate neither precise nor accurate diagram] The last bull's-eye [teacher circle] is an example of poor accuracy and poor precision. There is a loose grouping and the grouping is not near the bull's-eye (accepted value).
Sources:
Neither accurate nor precise

43. Is the Measure Accurate or Precise?
A single penny has a mass of 2.5 g. Abbie and James each measure the mass of a penny multiple times. Which statement about these data sets is true? O Abbie's measurements are both more accurate and more precise than James'. O Abbie's measurements are more accurate, but less precise, than James'. O Abbie's measurements are more precise, but less accurate, than James'. O Abbie’s measurements are both less accurate and less precise than James'.
Penny masses (g)
Abbie’s data
James’ data
2.5, 2.4, 2.3, 2.4, 2.5, 2.6, 2.6
2.4, 3.0, 3.3, 2.2, 2.9, 3.8, 2.9
Timing ≈ 1 min
Entry Audio: Consider again the measurement of the mass of a penny. Suppose a penny has an actual mass of 2.5 g.
Hint Audio: Accurate data are close to the accepted value. Precise data are reproducible, being closely grouped together.
Exit Audio: Accuracy and precision of data are important to a scientist. All measurements have some uncertainty. In the next slides, we learn about determining the precision of a measuring tool.

44. Determining the Right Tool
Which tool would give the most precise volume?
Timing ≈ 1 min
Each of these tools are used to measure the volume of liquids. They have different degrees of precision based on the graduations (decimal place indicated: 10 ml versus 1 ml versus 0.1 ml).
A 25-mL beaker (teacher circle) typically has markings for every 10 mL. Therefore, you can estimate volume to the nearest mL with this beaker.
This 100-mL graduated cylinder (teacher circle) has markings for every mL [teacher point to 1-mL marking]. Therefore, you can estimate volume to the nearest 0.1 mL with this graduated cylinder.
This buret has markings for every 0.1 mL (teacher point to 0.1 mL marking). Therefore, you can estimate volume to the nearest 0.01 mL with this buret.
The tool you choose for a given measurement depends on how precisely you need to measure the quantity in question.
Source:
Graduated cylinder: Graduation marks to 1 mL
Beaker: Graduation marks to 10 mL
Buret: Graduation marks to 0.1 mL

45. Determining Precision of Tools
DD1:
1 cm
*0.1 cm
0.01 cm
Consider the ruler shown below. The smallest graduation on this ruler is 1 cm 0.1 cm 0.01 cm
Which measurement shows the correct degree of precision for this ruler? O 1.5 cm O 1 cm O 1.55 cm
Timing ≈ 0.5 min
Entry Audio: You've just learned that different tools have different degrees of precision. How precise of a measurement can you make with a given tool?
Hint 1 Audio: The units indicated on a tool are typically the ones that are labeled with lines and/or numeric values.
Hint 2 Audio: Remember that the precision of a tool is defined as the smallest unit of graduation on the tool.
SOURCE:

46. Determining Precision of Tools
Consider the ruler shown below. Which measurement shows a valid estimate for this ruler? O 2.3 cm O 2.35 cm O cm
A scientist needs to know the temperature of a mixture to the nearest 0.05°C. Which thermometer would be most useful for the scientist? O one with markings every 1°C O one with markings every 5°C O one with markings every 0.1°C
Timing ≈ 0.5 min
Hint 1 Audio: An estimate of one decimal place after the smallest graduation on the measuring tool is also considered a significant figure in the measurement.
Hint 2 Audio: What is the rule for determining the precision of a tool relative to the markings on the tool?
Exit Audio: Every tool has a specific degree of precision. You cannot improve the precision of a tool, no matter how carefully you read it.
SOURCE:

47. Quick Break
Vacation

48. Percent Error
Percent error is a mathematical way of showing accuracy and precision
An estimate of accuracy in a measurement
Higher percent error indicates a less accurate data set
Must know experimental value and actual or accepted value to calculate percent error
Timing ≈ 1 min
[Animate definition] Scientists use percent error when determining the [Animate bullet 1] accuracy of a data set. [Animate equation] Percent error is determined by subtracting the measured value (called the experimental or observed value) and the accepted value, and then dividing by the accepted value. [use pencil highlighter around each successive phrase] The equation for percent error [teacher circle] provides the magnitude of error from the accepted value in a measurement and is always positive.
[Animate bullet 2] The higher the percent error, the less accurate the data set is.
[Animate bullet 3] To calculate percent error, you must know both the experimental (or measured) value and the accepted value of the quantity. It is good practice to take several measurements or perform multiple trials and then determine an average value. The average measurement would represent the experimental value in the equation for percent error.

49. Uncertainty in Measurement
How do we assess precision and accuracy in measurements?
We use percent error
CTRiesen

50. Uncertainty in Measurement
Percent Error
Percent error is a mathematical way of showing accuracy and precision
% Error = observed value - accepted value x 100%
accepted value
Accepted or Theoretical Value of the boiling point of water = 100 C
Observed or Experimental Value = 98 C
(98 C C) / 100 C x 100% = 2 % error
CTRiesen

51. Experimental Error Errors can arise from:
Instrument error: Calibration of the instrument has not been carried out or is faulty. Consequently, accuracy and precision are affected. 
Personal error: Observer making inaccurate observations. These type of errors can be overcome by taking an average based on several measurements, especially if data is collected by two or more independent observers. This overcomes the problem of personal bias resulting from poor observational habits which might produce a consistent observational error if only one investigator collects the data.
Sampling errors: These can also arise because of the size or nature of the sample used. Sample sizes can be either too small or not random enough. Replication of experiments also reduces errors.

52. Sample Problem
The accepted density value for Titanium is 4.5g/ml. Johnny measured Titanium’s density and received a value of 4.2g/ml. What is the percent error in his measurement?
4.2 – 4.5 x 100% = 6.7% is the percent error
4.5
NOTE: A 0% error means you got the correct accepted value. The larger the percent error value, the farther away you are from the accepted value (ideally, you want a low % error).

53. Problem Solving
In this class you will be asked to solve some problems from time to time using some equations and calculations.
To give you a way of organizing your information, I would like you to use this four step method to solve all problems in this class.

54. Four Step Problem Solving Method
Read the Problem and list the information given (knowns and unknowns).
Show the formula or equation you will use to solve the problem.
Solve the problem – show your work with units included.
Show your answer with the correct number of decimal places, or a whole number. It is extra important that your answer also includes units. Include a circle or a box around your final answer.

55. Problem Solving Practice
1. WHAT IS THE DENSITY OF AN OBJECT THAT HAS A VOLUME OF 14.3 mL, AND A MASS OF 20.0 g? M D V
Known/Unknown
Equation
Show work
Answer/units
D=20.0g /
14.3 ml
M=20.0g
V=14.3 ml
D=?
D=M/V
D= 1.4 g/ml

56. 2. WHAT IS THE MASS OF AN OBJECT THAT HAS A VOLUME OF 2
2. WHAT IS THE MASS OF AN OBJECT THAT HAS A VOLUME OF 2.0 mL, AND A DENSITY OF 10.4 g/mL? M D V
Known/Unknown
Equation
Show work
Answer/units
D=10.4 g/ml
V=2.0 ml
M=?
M=10.4 g/ml *
2.0 ml
M=D*V
M=20.8 g

57. Problem Solving Practice
3. WHAT IS THE VOLUME OF A GAS THAT HAS A MASS OF g, AND A DENSITY OF g/mL? M D V
Knowns/Unknown
Equation
Show work
Answer/units
M=0.025 g
D=0.007 g/ml
V=?
V=0.025 g/
0.007g/ml
V=M/D
V=3.6 ml