Math 20-2

Chapter 5 Statistical Reasoning

Lesson 5.3   Standard Deviation

GOAL

The goal of this lesson is stated at the top of page 254 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Determine the standard deviation for sets of data, and use it to solve problems and make decisions

Explore...

Try to answer the question in the sidebar on page 254.

Watch

Video Tutorial

Investigate the Math

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 254 - 256

Read/Work through the Investigate section on Pages 254-256 in your textbook.

Go through this material,  AS BEST YOU CAN,  before you view the video tutorials that follow.

Because this is an important idea, and difficult to explain,  the presentation that follows goes in small steps.

You are welcome to simply follow the textbook, if you can, but if you want a good foundation for the work that follows,  hopefully the sections that follow will help with this concept!

Introduction

The coach of a varsity girls’ basketball team keeps statistics on all the players.

Near the end of one game, the score is tied and the best starting guard has fouled out.

The coach examines the field goal stats for five guards on the bench in the last 10 games.

Video Tutorial  (Invest A)

?  How can the coach use the data to determine which player should be substituted into the game?

Video Tutorial  (Invest B)

Background on Standard Deviation

It’s easy to go through the steps and calculate the standard deviation, but... the textbook NEVER actually tells you WHY you do those steps.
This will only take a minute or two, but understanding 	WHY standard deviation is calculated the way it is will really help with understanding.

Technology

The method to calculate standard deviation is easy to describe, but tedious to do , especially with large data sets.

IN THIS COURSE,  you are expected to use your graphing calculator to find standard deviation.

However,  you are also expected to see HOW the calculation is done, at least a few times, so you have an understanding of the process.

So,  the lesson will use a few examples to illustrate the process, then move on to using a calculator.

Informal Definition

Informal

The Standard Deviation is a measure of how spread out numbers are.

Calculating standard deviation

The symbol for standard deviation is σ (sigma,  the Greek letter)

The formula is easy:   it is the square root of the Variance.

So now you ask, "What is the Variance?"

Calculating the variance

Variance is defined as

The average of the squared differences from the Mean.

To calculate the variance follow these steps:
	•	Work out the Mean (the simple average of the numbers)
	•	Then for each number: subtract the Mean and square the result (the squared difference).
	•	Then work out the average of those squared differences.

The standard deviation is then the square root of the variance.

Video Tutorial   (Variance)

Example

This is a great example of how to calculate the standard deviation and what that number tells us.

Video Tutorial  (Dogs)

Analyze the data for Paige

If you want to work with the data in Google Sheets,   here is the link to the page I used for the video.

Video Tutorial  (Paige)

Analyze the data for the whole team

If you want to work with the data in Google Sheets,   here is the link to the page I used for the video.

Video Tutorial  (Team)

Questions   I - M

Taken from the textbook  (page 255 - 256)

Video Tutorial  (Patrice)

Reflect

Taken from the textbook  (page 255 - 256)

Video Tutorial  (Reflect)

Apply the Math  (Examples)

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the examples as models.

Example 1  Using standard deviation to compare sets of data

TEXT Pages 256 - 257

Work through Example 1 on Pages 256 - 257 in your textbook.

Watch

Video Tutorial

Your Turn

I answered these questions in the Example 1 video.

Example 2  Determining the mean and standard deviation of grouped data

TEXT Pages 257 - 260

Work through Example 2 on Pages 257 - 260 in your textbook.

NOTE!!   Cole’s solution is to show you what your calculator is doing to find the Standard Deviation.
You are NOT expected to do this by hand!
You can read this explanation to help understand what your graphing calculator is doing.
I will give a bit of explanation of the process when I work through Danica’s solution.

Watch

Video Tutorial   Danica’s Solution: Using technology to determine   (OverBar[x]) and  σ

Your Turn

I answered these questions in the Example 2 video.

In Summary

Key Ideas and Need to Know 
Presents and summarizes  the main new concepts of the lesson

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Check Your Understanding questions require basic understanding of the ideas of the  lesson.

Practising questions will require you to dig deeper for a solution.

Closing  A summary question that often asks YOU to explain ideas in your own words.

Extending questions offer enrichment and extension.

Notes

Question 1,    If you want to use the data I typed into Google Sheets,  the link is HERE

Question 4,    I didn’t do a video for this one.
sample answer....
a) The mean number of beads in company B’s packages is much less consistent than the mean number of beads in company A’s packages.
b) company A

Question 5,    I didn’t do a video for this one.
Not trying to avoid work,  but there really isn’t anything for me to  show here.
Enter the numbers and use the calculator to analyze....
I found a way to copy and paste the numbers into a spreadsheet!   No typing required, just a small bit of cleanup!
If you want to try the analysis using Google Sheets,   HERE is the link to the page

Question 6,    I didn’t do a video for this one.

Question 8,    I didn’t do a video for this one.

Question 9,     I didn’t do a video for this one.

Question 10,     I didn’t do a video for this one.

Question 12,     I didn’t do a video for this one.

Question 13,    I didn’t do a video for this one.
sample solution
e.g., One twin is more consistent, while the other is less consistent, resulting in the same mean (85.0%) with different standard deviations (2.6%, 12.0%).
Jane’s scores: 80%, 85%, 82%, 87%, 86%, 84%, 87%, 85%, 85%, 89%
Jordana’s scores: 78%, 92%, 99%, 64%, 72%, 82%, 77%, 95%, 98%, 93%

Question 14,    I used to be very frustrated with these images, I could never get them to work!
I eventually found that if I...
a)    took off my glasses
b)   put my face right up against the image, so it was totally out of focus
c)   then slowly moved away from the image, kind of trying to keep it out of focus until the image sort of “popped” out of the page
Note that I couldn’t make this work on computer, I had to look at the image in the actual paper textbook.
I can see two sea horses,   maybe there are some other things, but they are quite prominent.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 7" , "Question 11" , "Question 14"}})