DATA Metric System (SI) Taking Measurements Organization Presentation

Your data are all the records you have gathered from an investigation. The types of data collected depend on the activity. Data may be a series of weights of volumes, a set of color changes, or a list of scientific names. No matter which types of data are collected, all data must be treated carefully to ensure accurate results. Data Sometimes the data seem to be wrong, but even then, they are important and should be recorded accurately. Remember that nature cannot be wrong, regardless of what you discover in the laboratory. Data that seem to be “wrong” are probably the result of the experimental error.

Metric System A decimal system of measurement whose units are based on certain physical standards and scaled on multiples of ___ A decimal system of measurement whose units are based on certain physical standards and scaled on multiples of ___ Based on units of 10 Based on units of 10 ten

Kilo (k) = 1000 Kilo (k) = 1000 Hecta (h) = 100 Hecta (h) = 100 Deka (D) = 10 Deka (D) = 10 Base = 1 Base = 1 Deci (d) = 0.1 Deci (d) = 0.1 Centi (c) = 0.01 Centi (c) = 0.01 Milli (m) = Milli (m) = Metric System The system is easy to use because it is based on multiples of 10 1 meter = 100 cm1 kilogram = 1000 grams1 gram = 1000 milligrams1 liter = 1000 milliliters1 kilometer = 1000 meters1 centimeter = 10 millimeters

Measurement in Science Scientists use a revised form of the metric system called Le Systeme International d’Unites (International System of Units) or SI Units

S.I. Base Units The International System of Units (S.I.) defines seven base units for the seven base quantities: Quantity Name Symbol lengthmeterm masskilogramkg timeseconds electric currentampereA thermodynamic temperaturekelvinK luminous intensitycandelacd amount of substancemolemol

S.I. Base Units

Length The distance from one point to another The distance from one point to another Meter – the SI unit of length Meter – the SI unit of length Tool used to measure length depends on the size of the object Tool used to measure length depends on the size of the object Larger objects (i.e. the room) Larger objects (i.e. the room) – meter stick – meter stick Smaller objects (i.e. pencil length) Smaller objects (i.e. pencil length) – centimeter ruler – centimeter ruler Frequently used SI units Length 1 millimeter (mm) = 1000 micrometers (  m) 1 centimeter (cm) = 10 millimeters (mm) 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters (m) 1 light-year = 9,460,000,000,000 kilometers (km)

Measuring Length Measure the distance from Point A to B Measure the distance from Point A to B What distance is Point A? Point B? What distance is Point A? Point B? What is the total distance between points? What is the total distance between points? 4.5 cm6.4 cm 6.4 cm – 4.5 cm =1.9 cm

Mass The amount of matter in something The amount of matter in something Mass is measured using a balance or triple beam balance Mass is measured using a balance or triple beam balance Or an electronic balance Or an electronic balance

Mass The SI unit for mass is the kilogram (kg) The SI unit for mass is the kilogram (kg) The gram is the base unit The gram is the base unit However, some measurements of mass like the mass of vitamins or medicines are so small that we use milligrams (mg) to measure their mass Frequently used SI units Mass 1 gram (g) = 1000 milligrams (mg) 1 kilogram (kg) = 1000 grams (g) 1 metric ton = 1000 kilograms (kg)

Measuring Mass Measured using a balance Measured using a balance What is the mass of this object? What is the mass of this object? 175 g

Area Area is a physical quantity expressing the size of a part of a surface. Area is a physical quantity expressing the size of a part of a surface. The term can also be used in a non- mathematical context to be mean "vicinity". The term can also be used in a non- mathematical context to be mean "vicinity". Surface area is the summation of the areas of the exposed sides of an object. Surface area is the summation of the areas of the exposed sides of an object. Frequently used SI units Area 1 square meter (m 2 ) = 10,000 square centimeters (cm 2 ) 1 square kilometer (km 2 ) = 1,000,000 square meters (m 2 )

Measuring Area Area = Length x Width Area = Length x Width 2 cm 1 cm The square has an area of 4 square centimeters (4 cm 2 ) Area = l x l 2 = 2 cm x 2 cm Area = 4 square centimeters (4 cm 2 )

Measuring Area Calculate the area of the following rectangles Calculate the area of the following rectangles 5 cm Area = cm 8 cm Area = 3 cm X 8 cm 2 cm X 5 cm 24 cm 2 10 cm 2 2 cm 3 cm

Volume The amount of space a substance takes up The amount of space a substance takes up Volume of a liquid is found using a graduated cylinder Volume of a liquid is found using a graduated cylinder Unit is liters (L) or milliliters (mL) Unit is liters (L) or milliliters (mL) Frequently used SI units Volume 1 milliliter (mL) = 1 cubic centimeter (cc) or (cm 3 ) 1 liter (L) = 1000 milliliters (mL) or 1 dm 3

Measuring Volume Liquid volume measured using graduated cylinder Liquid volume measured using graduated cylinder Read volume at meniscus ( downward curve of water) Read volume at meniscus ( downward curve of water) What is the volume of this liquid? What is the volume of this liquid? 45 mL 45 mL

Measuring Volume Find the volume of these liquids Find the volume of these liquids 16 mL15 mL 12.5 mL

Volume Volume of a solid is found using the volume equation Volume of a solid is found using the volume equation length x width x height length x width x height In this equation, we are also multiplying the units together so units for the volume of a solid are… In this equation, we are also multiplying the units together so units for the volume of a solid are… m x m x m = m 3 OR cm x cm x cm = cm 3 m x m x m = m 3 OR cm x cm x cm = cm 3 Also know that 1 mL = 1 cm 3 = 1 cc (cubic centimeter) Also know that 1 mL = 1 cm 3 = 1 cc (cubic centimeter)

Measuring Volume Solid volume measured using volume equation (l x w x h) Solid volume measured using volume equation (l x w x h) What is the volume of a cube that is 2 cm x 2 cm x 2 cm? Volume = l 1 x l 2 x l 3 = 2 cm x 2 cm x 2 cm Volume = 8 cubic centimeters (8 cm 3 )

Measuring Volume Calculate the volume of the box Calculate the volume of the box 5 mm 2 mm 6 mm Volume = 60 mm 3 6 mm X 5 mm X 2 mm l x w x h

Water Displacement Some solid samples, such as an irregularly shaped rock cannot have their volume measured easily by using the volume equation (length x width x height) Some solid samples, such as an irregularly shaped rock cannot have their volume measured easily by using the volume equation (length x width x height) For these solids, scientists use a technique called Water Displacement For these solids, scientists use a technique called Water Displacement

Water Displacement Steps of Water Displacement Steps of Water Displacement 1. Add water to a graduated cylinder and record its volume (ex: 7 ml) 2. Place the irregularly shaped solid into the graduated cylinder already containing water and record the new volume (ex: 9 ml)

Water Displacement 3. Subtract the smaller volume (combined volume) from the larger volume (water only) to get the volume of the irregularly shaped solid. (ex: 9 ml – 7 ml = 2 ml) 4. We would say that the irregularly shaped solid takes up 2 ml of space. Since it is a solid, we need to state the volume using cm 3 so we would say that its volume is 2 cm 3

Volume = V 2 – V 1 Volume = 30 – 20 Volume = 10 mL Water Displacement = 10 cm 3 = 10 cm 3

Temperature The amount of heat in something The amount of heat in something Tool used to measure temperature is a thermometerTool used to measure temperature is a thermometer Celsius is the unit of measure in the metric system Celsius is the unit of measure in the metric system

Temperature SI unit for temperature is the Kelvin (K) SI unit for temperature is the Kelvin (K) Notice that there is no degree sign used! Notice that there is no degree sign used! Kelvin scale is easier for scientists to use Kelvin scale is easier for scientists to use To calculate Kelvin you add 273 to the Celsius temperature To calculate Kelvin you add 273 to the Celsius temperature Ex. 23 ○ C = = 296 K Ex. 23 ○ C = = 296 K

Reading a Thermometer What’s the temperature? What’s the temperature? -14 ○ C 24.5 ○ C ○ C

Reading a Thermometer What’s the temperature? What’s the temperature? -14 ○ C 24.5 ○ C ○ C

Time The period between 2 events The period between 2 events The SI unit of time is the second (s) The SI unit of time is the second (s) Measurement tool of time is a stopwatch Measurement tool of time is a stopwatch

Recording and Organizing Laboratory Data There are many ways to record and organize data, including: data tables, charts, and graphs. It is important to include the appropriate units when you record data. Remember that DATA are measurements or observations, not merely numbers. Data tables, graphs, and diagrams should have descriptive titles to ensure that another person can understand them without having been present during the investigation. Many important scientific discoveries have been made accidentally in the course of an often unrelated laboratory activity. Scientists who keep very careful and complete records sometimes notice unexpected trends in and relationships among data long after the work is completed. The laboratory notebooks of working scientists are studded with diagrams and notes; every step of every procedure is carefully recorded.

Data Tables and Charts For example, if you collected data on plant growth that included both the length of time it took for the plant to grow and the amount of growth, you could record your data in a table (as shown below). Data tables are probably the most common means of recording data. Although prepared data tables are often provided in lab manuals, it is important that you be able to construct your own. The best way to do this is to choose a title for your data table and them make a list of the types of data to be collected. This list will become the headings for your data columns. Time in Days Height of Plant (cm) Plant Growth Data Example Data Table These data are the basis for all your later interpretations and analyses. You can always ask new questions about the data, but you cannot get new data without re- peating the experiment.

Ways to Record Data Data Tables: Must have a title Must have a title Must include relevant data Must include relevant data Must have labeled columns Must have labeled columns Number of Flies on Meat per Day Day Number of Flies

Graphs Pie (circle) graphs Line graphs Bar graphs After data are collected, you must determine how to display them After data are collected, you must determine how to display them One way of showing your results is to use a graph One way of showing your results is to use a graph Three types of graphs are commonly used Three types of graphs are commonly used

Pie Graph: Used to show how a part relates to the whole Used to show how a part relates to the whole Needed to show percentages effectively Ways to Graph Data NCHS’s Biology Ice Cream Survey Vanilla21.0% Chocolate33.% Strawberry12.0% Raspberry 4.0% Peach 7.0% Neopolitan17.0% Other 6.0%

Ways to Graph Data (Continued) Line graph: used to show change over time Line graph: used to show change over time Bar graph: used to compare quantities in different categories Bar graph: used to compare quantities in different categories Be sure to include: Be sure to include: Title Title Axis labels Axis labels Key Key

Making a Line Graph Start with your data tableDraw and Label Axes Independent Variable on the x-axis Dependent Variable on the y-axis Would help to know that this experiment was done with paper towels Experimental Data IndependentVariable Submersion time (seconds)DependentVariable Average height liquid rose (mm) Average height liquid rose (mm) Submersion time (sec)

Making a Line Graph (Continued) Using your data table, write data pairs (10, 11) (15, 14) (20, 14) (25, 25) (30, 16) (35, 17) (40, 19) Experimental Data IndependentVariable Submersion time (seconds)DependentVariable Average height liquid rose (mm)

Making a Line Graph (Continued) Use your data pairs to determine the scales for the axes 2. Write Data Pairs (10, 11) (15, 14) (20, 14) (25, 25) (30, 16) (35, 17) (40, 19)

Start plotting your data pairs Making a Line Graph (Continued)

After plotting data, draw a line “of best fit”

Making a Line Graph (Continued) Complete the graph by summarizing its findings “As the length of time the paper towel was submerged increased, the height the liquid rose also increased.”

Making a Bar Graph Again, Start with your data tableDraw and Label Axes

Using your data table, write data pairs Making a Bar Graph (Continued)

Use your data pairs to determine the scales for the axes Making a Bar Graph (Continued)

Start plotting your data pairs

After plotting data, fill in bars Making a Bar Graph (Continued) Include a key if needed A B C D E F Brand of paper towel Water absorbed (mL)

Complete the graph by summarizing its findings Making a Bar Graph (Continued) Brands A and D were the most effective water absorbers. The least effective absorber was Brand B. Brands C, E, and F absorbed intermediate amounts of water. 5. Summarize Trends A B C D E F Brand of paper towel Water absorbed (mL)

Graphing Review Purposes: Purposes: Organize and analyze data Organize and analyze data Show patterns Show patterns Communicate information Communicate information Allow scientists to make predictions Allow scientists to make predictions Components: Components: Appropriate title Appropriate title Equal units on each axis with good use of spacing Equal units on each axis with good use of spacing Labels on each axis including units Labels on each axis including units (example, mm, sec., kg.) (example, mm, sec., kg.) Neatly created using a variety of color Neatly created using a variety of color

Types of Graphs Graph Review

Statistical Methods & Analysis of Errors

ERROR May be defined as a deviation from the absolute value or from the true average of a large number of results. TYPES OF ERRORS 1. D eterminate error - constant 2. I ndeterminate error – random or accidental

Determinate Error Usually present in each measurement and affect all observations in a series. Usually present in each measurement and affect all observations in a series. Example: Example: Errors in calibration Errors in calibration Operation in measuring Operation in measuring Impurities in the reagents or drugs Impurities in the reagents or drugs Biased personal errors Biased personal errors Pouring or mixing Pouring or mixing Weighing operations Weighing operations Matching colors Matching colors Making calculations Making calculations

Indeterminate Error Occur by chance Vary from one measurement to the next Yield a random pattern around an average Occur also in the filling of capsules Random fluctuations in temperature and other factors

PRECISION & ACCURACY ACCURACY – is the degree of closeness of a measured or calculated a measured or calculated quantity to its actual (true) quantity to its actual (true) value. value. PRECISION – also called REPRODUCIBILITY the degree to which the degree to which measurements or calculations measurements or calculations show the same similar results. show the same similar results.

Comparing ACCURACY & PRECISION HIGH Accuracy, LOW precision LOW Accuracy, HIGH precision

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