Math in Science

 Estimate  Accuracy  Precision  Significant Figures  Percent Error  Mean  Median  Mode  Range  Anomalous Data

 All scientists use some sort of math in their work  Scientists use math to collect, organize, analyze, and present data.  Some math skills used in science when working with data include estimation, accuracy and precision, and significant figures.

 ESTIMATE: An approximation of a number based on reasonable assumptions.  An estimate is NOT a guess.  It is ALWAYS based on known information.  Scientists rely on estimations when they cannot obtain exact numbers.  Estimates might be based on insufficient measurements, calculations, models or samples.  Estimating from a sample often involves making a visual analysis as well as calculating.

 PAGE 23 IN THE WORKBOOK (PULL UP ON THE BOARD, USE INTERACTIVE CD)

 ACCURACY: refers to how close a measurement is to the true or accepted value  PRECISION: refers to how close a group of measurements are to each other.

 First, use a high-quality measurement tool (example: laser)  Next, measure carefully  Repeat the measurement a few times  If your measurement is the same each time, you can assume that it is reliable.  A reliable measurement is both accurate and precise.

 Page 24 in the workbook, pull up on the board.

 SIGNIFICANT FIGURES: Communicate how precise measurements are.  The precision of a measurement depends on the instrument you use to take the measurement.  EXAMPLE: if the smallest unit on a ruler is centimeters, then the most precise measurement you can make will be in centimeters.

 Some math tools used in science include calculating percent error; finding the mean, median, mode, and range; and checking the reasonableness of data.

 PERECENT ERROR: are calculations that are a way to determine how accurate an experimental value is.  A LOW PERCENT ERROR: means that the result you obtained was accurate.  A HIGH PERCENT ERROR: means that your result was not accurate.  It may not have been accurate because you did not measure carefully or because something was wrong with your measurement tool.

 MEAN: is the numerical average of a set of data. To find the mean, add up the numbers and then divide the sum by the total number of items you added.  LETS DISCUSS SOME EXAMPLES AND TRY OUT SOME PROBLEMS AS A CLASS

 MEDIAN: The middle number in a set of data.  To find the median, list all the numbers in order from least to greatest.  The median is the middle number.  If the list has an even number of entries, add the two middle numbers together and divide by two to find the median.  WHAT IS THE MEDIAN OF THIS LIST OF NUMBERS  1, 4, 6, 7, 12, 23, 33, 45, 65

 MODE: The number th at appears most often in a list of numbers.  What is the mode of this list of numbers? Discuss with a partner and share with your classmates.  1, 1, 2, 4, 23, 45, 60, 61, 61, 61, 62, 67, 72, 72

 RANGE: the range of a set of data is the difference between the greatest value and the least value in the set.  LETS FIGURE OUT AS A CLASS, THE RANGE OF THIS SET OF DATA.  12, 19, 21, 33, 40  How would we figure this out? What is the range?

 Anomalous data: Data that does not fit in with the rest of the data sets.  Investigating the reason for anomalous data can lead to new information and discoveries.

 If you were asked to measure the temperature outside of your home in August, and the data for the first four nights are 80 degrees, 78 degrees, 81 degrees, and 79 degrees. But, on the last night, someone recorded it was 60 degrees out. Is that data reasonable? Does it make sense for the temperature to drop almost 20 degrees in the August? No, so the data does not fit in with the rest of the information, meaning the data is anomalous.

 ON YOUR OWN, WRITE IN YOUR CLASSWORK SECTION THE ANSWERS TO THE FOLLOWING QUESTIONS:  (PAGE 29 IN WORKBOOK, BRING UP ON BOARD)