Statistics, Part 2: The Normal Curve

Welcome back from the snow days! I hope you all had a good break.

Today in 1A (Monday for 2B and 3B), we reviewed from last time, and then looked at the NORMAL CURVE. 

• A lot of data, when you plot a HISTOGRAM of it, looks like 

• a hill with lots of values piled up close to the MEAN, and then 
• less and less as you go off to the sides. 

• Here are the basic notes for a normal curve:

• Then, we used a Z-TABLE to find the probability for a value to be less than -3, -2, -1, 0, 1, 2, and 3 for a NORMAL CURVE with MEAN = 0 and STANDARD DEVIATION = 1:
• Notes from 1A:

• Slightly changed notes from 2B and 3B (same information, just different format):
• We saw that the normal curve is SYMMETRIC, because P(z<-3)=P(z>3), P(z<-2)=P(z>2), and P(z<-1)=P(z>1).

• Next we used these answers to show the EMPIRICAL RULE for normal curves.

• A data set is called NORMAL if: 
• it looks normal, and
•  it follows the EMPIRICAL RULE:
• 68% of the data within +/- 1 standard deviation of the mean, 
• 95% of the data within +/- 2 standard deviations of the mean, and 
• 99% of the data within +/- 3 standard deviations of the mean.

• Finally, we used this EMPIRICAL RULE to check whether data was NORMAL. We did only the first set in class, but here are both for your reference:

Welcome Back! NEW UNIT NOTES.

Welcome back from February break!

• A few of you need to take or finish your test on logarithmic functions. See me if you aren't sure when you're making that up. 
• The grades were pretty good for the most part. You should be happy.
• And now for something completely different: STATISTICS.

Today (February 23 for 1A) and tomorrow (February 24 for 2B and 3B) we are learning about ONE-VARIABLE STATISTICS.

In this section, we learn how to find the MINIMUM, Q1, MEDIAN, Q3, MAXIMUM, MEAN, and STANDARD DEVIATION. Most of these you have seen before.

(1) First, we did the calculations by hand (you will NOT have to do this on the test):

(2) Then we had the calculator do the hard work, by using [STAT] [EDIT] [1] to put the data into L1 and [STAT] [CALC] [1] to get the SAME answers.

(3) We learned three different ways to plot our results: the DOT PLOT, the HISTOGRAM, and the BOX AND WHISKER PLOT.

(4) Then we practiced. Practice #4 is shown here. Please do Practice 1, 2, and 3 on your own. The answers are taped up on my board so you can check your work.

Next time, we will review this briefly before moving on.

Review for Test Unit 4.2

Your test is THURSDAY (1A) or FRIDAY (2B and 3B).

Also please turn in ANY remaining HOMEWORK papers NO LATER THAN FRIDAY 2:30 pm.

Here are the notes from the review. Happy studying!

Ask for help in Group Me, or find me or Ms. Wilson.

Page 1:

 

 Pages 2-3: Condensing and Solving

Page 4: Word Problems:

Page 5: Bonus problems:

Real-World Problems - Notes from Feb 5, Feb 6, Feb 9

We're looking at three different kinds of real world problems in class.
* Half-Life:  caffeine, medicine, etc., or carbon dating
* Cooling: hot water or coffee, or time of death (solving a murder!)
* Interest: investing money

These are the notes from today and Monday (2B and 3B) and tomorrow (1A). Note to 1A - we will likely skip the "cooling" problem, because we have less time before the test than 2B and 3B.

HALF-LIFE: (all classes)

COOLING: (2B and 3B only, and this is NOT on the test)

INTEREST: (all classes)

Condensing and Solving, Feb 3-4. Notes and Assignment.

We started with a warm-up. These three problems are DIRECTLY from last time's assignment. So that's 5+7.5+10 = 22.5 out of the 100 points you need on that assignment, DONE. (Just make sure you have it copied.)

Then, we learned how to put it all together:
Step (1) Condense BOTH sides of the equation
Step (2) Solve, either by REWRITE AND SOLVE or by DROP AND SOLVE

Examples, that lead to a LINEAR EQUATION:

Examples, that lead to a QUADRATIC EQUATION:

PREVIOUS HOMEWORK:

Previous, #1: 100 total points from your choice of problems from sheets A, B, and C
Previous, #2, take 3 from sheet A, 2 from B, or 1 from C and 1 from A, and show all steps on the yellow poster card.

 NEW HOMEWORK:

Work the problems on the colored sheets on my table, to get 100 total points:
* PINK sheets are CONDENSING ONLY (NO SOLVING) and are 5 points each
* GREEN sheets are CONDENSING AND SOLVING with LINEAR equations, and are 10 points each.
* GOLD sheets are CONDENSING AND SOLVING with QUADRATIC equations, and are 15 points each.