Lesson 2.2: Mathematics & Scientific Thinking

​What Math Skills to Scientists Use?

• When scientists do math they rely on several types of skills to help analyze their data

  • ​Estimation

  • accuracy and precision

  • Significant figures

• In addition to these skills, they rely on tools to help them interpret large amounts of data

  • mean

  • median

  • mode

  • range​

​Estimation

• Sometimes it is not possible to get a perfectly accurate number when collecting data

  • Something may be too small or numerous to accurately count​

• Estimate: an approximation of a number based on reasonable assumptions​

• Example: You have billions of white blood cells in your body, but you can't count every one

  • Doctors take a sample and count how many there are​ in that sample, and then multiply up to estimate how many there are in total to determine if you have an infection

​Accuracy and Precision

• Do not mean the same thing in science

  • Accuracy: How close a value is to the correct value

  • Precision: how close a group of measurements are to one another

• Scientists use both to determine how good their results are and try and determine where they made a mistake

  • Can help determine if the equipment is faulty​

​Significant Figures

• The measurements we make are never completely precise

  • Example: You are measuring something and it falls between the lines on a ruler

• Significant Figures: show how precise a measurement is

  • Include all the numbers you can measure exactly + one estimated digit​

​Using Significant Figures

• Example: you put an object on your scale which reads 3.24 grams. you add that object to a beaker that has a mass of 20.559 according to the box

  • Our scale only measures up to two decimal places. we don't know if there are any other numbers after that 4

  • I​f we add the masses together, we can't assume that there is no digit being added to the 0.009, so we round our final value to the second decimal place because that is what we can be sure of.

​What Math Tools do Scientists use?

• Mean: The numerical average of a set of data

  • Add all the numbers up and divide by the total number of objects that you added​

  • Sample problem:

    • The data set to the left is the number of inches a plant grew every day for seven days. What was the average daily growth?​

      • Add together all the daily growth measurements

        • 0.94+1.38+8.43+3.31+0.03+0.19+1.45

      • Divide by the total number of measurements

        • there were seven days

​What Math Tools do Scientists use?

• Median: The middle value in a list of numbers

  • Find by sorting the numbers from least to greatest

    • For an odd data set: the median is the number right in the center of the list

    • For an even Data Set: Add the two middle numbers together and divide by two

  • Sample Problem: Find the median for the data table:

    • 0.03, 0.19, 0.94, 1.38, 1.45, 3.31, 8.43

      • Median is 1.38 ​

​What Math Tools do Scientists use?

• Mode:The number that appears most often in a data table

  • Not all data sets have a mode

• Range: The difference between the largest value in a data table and the smallest value

  • In this Data table, the largest value is 8.43 and the smallest is 0.03

    • Range = 8.43-0.03= 8.4

​Reasonable and Anomalous Data

• It is always important to ask if your data makes sense

  • Sometimes you make a mistake in measuring

• Anomalous Data: Data that does not make sense or fit with the data set

  • usually caused by human or equipment error, but sometimes just exists

  • Example: A scientist measuring the wind speeds of hurricanes gets a measurement that says the wind was traveling 56 km/hr

    • The wind has to be traveling at least 119 km/hr to form a hurricane, so the scientists may check their mode of measurement to make sure it is working properly

​Percent Error

• There are some measurements that we know for a fact and never change

• When we test objects based on those amounts, we may get different answers

• Percent Error: A way of measuring the accuracy of your measurement

• Shown by the Following Equation:​

​Percent Error Sample Problem

• A student estimated the mass of a block to be 240 grams. When the block was put on a scale, the mass was 265 grams. What was the student's Percent Error?

  • Step 1: Identify your variables

    • Experimental: 240

    • True: 265

  • Step 2: Plug your values into the equation