Using what you know about order of operations and previous math courses, look at the formula above and write out a procedure or "pseudo code" that will take a given data set (e.g., 5 numbers) and calculate sample standard deviation.
Overview
In groups of 3-4, students will be presented with the formula for sample standard deviation. They will write their own pseudo code or procedure for calculating sample standard deviation from a given data set. Students will test out their code and compare their output to their graphing calculator output. If the outputs don't match, they must debug their code until it matches the calculator output. After writing the correct code, students will answer some follow-up questions that dive deeper into standard deviation
Standards
Computational Thinking in STEM
- Data Practices
- Analyzing Data
- Manipulating Data
- Visualizing Data
- Modeling and Simulation Practices
- Using Computational Models to Understand a Concept
- Computational Problem Solving Practices
- Computer Programming
Activities
- 1. Standard Deviation - Unplugged
- 2. Using your model
- 3. Evaluating your model
- 4. What happens when we add data points?
- 5. Why do we need to understand standard deviation?
Student Directions and Resources
In groups of 3-4, students will be presented with the formula for sample standard deviation. They will write their own pseudo code or procedure for calculating sample standard deviation from a given data set. Students will test out their code and compare their output to their graphing calculator output. If the outputs don't match, they must debug their code until it matches the calculator output. After writing the correct code, students will answer some follow-up questions that dive deeper into standard deviation
1. Standard Deviation - Unplugged
Here is the formula for sample standard deviation, as it appears in our textbook and AP formula sheet:
Question 1.1
2. Using your model
Question 2.1
Use your procedure or "pseudo code" to find the sample standard deviation for this 5 number data set. Write your solution in the textbox below. Be sure to show all steps.
3 7 9 11 15
3. Evaluating your model
Question 3.1
Grab your graphing calculator and enter the same data set into List 1 (L1). Next, go to STAT --> CALC --> 1 Var Stats to display descriptive statistics. The sample standard deviation will be listed under "Sx". Does this value match your answer to Question 2.1? If it does, move on to question #4. If not, re-write your procedure or "pseudo code" in the text box below. As a reminder, your procedure must take a list of values and using the formula, calculate sample standard deviation. Make sure the output of your procedure matches the calculator output.
3 7 9 11 15
Question 3.2
If your procedure was incorrect the first time, please write what went wrong in the text box below.
4. What happens when we add data points?
Question 4.1
If we added the value "1" to our set, what effect would it have on the sample standard deviation? Why?
(If you're not sure, use your procedure or graphing calculator and find the new standard deviation with this point added.)
Question 4.2
If we added the value "20" to our set, what effect would it have on the sample standard deviation? Why?
(If you're not sure, use your procedure or graphing calculator and find the new standard deviation with this point added.)
Question 4.3
If we added the value "9" to our set, what effect would it have on the sample standard deviation? Why?
(If you're not sure, use your procedure or graphing calculator and find the new standard deviation with this point added.)
5. Why do we need to understand standard deviation?
Recall the gas price problem from earlier in this unit. You owned a trucking company and were trying to figure out how much to budget for gasoline (per gallon). For the questions that follow, let's assume that the current mean US gas price is $3.43/gallon with a standard deviation of $0.13/gallon.
Question 5.1
What would be an amount ($ per gallon) that would be way too high to budget for gasoline? Justify your answer.
Question 5.2
What would be an amount ($ per gallon) that would be way too low to budget for gasoline? Justify your answer.
Question 5.3
Make a prediction for the shape of the distribution of US gas prices. Justify your answer.
