CHAPTER 1 LESSON 3 Math in Science

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

What Are Some Math Skills Used In Science? 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.

ESTIMATION 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.

Accuracy and Precision 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.

How can you be sure that measurement is both accurate and precise? 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.

Significant Figures 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.

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

Percent Error 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 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 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 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 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?

REASONABLE AND ANOMALOUS DATA 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.

EXAMPLE 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.