8th Grade Chapter 12 Data Analysis and Probability

Frequency Table and Line plots 4/19 Range Difference between the largest and smallest values in a data set Lists each data item with the number of times it occurred Frequency Table Example Display the set of data in a frequency table: 1 4 0 3 0 1 3 2 2 4 Number 1 2 3 4 Frequency

Make a frequency table for the ages of students in this classroom. 1. Determine the range of ages of so you know what ages to list on the table Age Frequency 2. Gather data to determine the frequency of each age.

Displays data with an X mark above a number line Line Plots Displays data with an X mark above a number line Write your favorite number (between 0 and 10) on the scrap of paper given to you When your number is called come up to the board and place an x above your number—if there is already an x above your number, then put your x above that x

Use the information from the line plot you make a frequency chart on your own paper Can you think of other data that could be arrange in a frequency chart or line plot? Workbook Page 197 - 198 You try

Box-and-Whisker Plots 4/20 15, 18, 21, 7, 29, 20, 9, 23, 25, 25, 29, 14, 8, 18, 26, 28, 27, 19, 7, 26 Write the numbers in order from least to greatest Identify the smallest number Identify the biggest number Find the median (the middle number when the numbers are in order—if 2 numbers are in the middle, average them) Find the range Review

7, 7, 8, 9, 14, 15, 18, 18, 19, 20, 21, 23, 25, 25, 26, 26, 27, 28, 29, 29 20.5 Median Data set

Find the median for the first half of the data Divide the data into quartiles 7, 7, 8, 9, 14, 15, 18, 18, 19, 20 Median of 1st half: 14.5 7, 7, 8, 9, 14, 15, 18, 18, 19, 20, 21, 23, 25, 25, 26, 26, 27, 28, 29, 29 14.5 Median 1st half 20.5 Median Data set

Find the median for the second half of the data Divide the data into quartiles 21, 23, 25, 25, 26, 26, 27, 28, 29, 29 Median of 2nd half: 26 7, 7, 8, 9, 14, 15, 18, 18, 19, 20, 21, 23, 25, 25, 26, 26, 27, 28, 29, 29 14.5 Median 1st half 20.5 Median Data set 26 Median 2nd half

The medians divide the data into four sections or quarters 7, 7, 8, 9, 14, 15, 18, 18, 19, 20, 21, 23, 25, 25, 26, 26, 27, 28, 29, 29 14.5 Median 1st half 20.5 Median Data set 26 Median 2nd half Lower Quartile Middle Quartile Upper Quartile Quartiles The medians divide the data into four sections or quarters

Least value The smallest number in the data set 7 Greatest value The biggest number in the data set 29 Number line Use the least and greatest value to draw an adequate number line

Mark the least value: 7 with a point •

• • Mark the lower quartile: 14.5 with a vertical line Connect the point and the line •

Mark the middle quartile: 20.5 with a vertical line •

• • Mark the upper quartile: 26 with a vertical line Connect the tops and bottoms of the vertical lines •

Mark the greatest value: 29 with a point • •

Drawing information from a Box-and Whiskers Plot 3rd Quarter has a biggest range Middle quartile: 50 Least value: 32 Upper quartile: 72 Greatest value: 80 Lower quartile: 45 2nd Quarter has the most concentrated data

Counting Outcomes and Theoretical Probability 4/22 The result of an action An outcome or group of outcomes Event Sample Space List of all possible outcomes

Theoretical Probability Number of favorable outcomes Number of possible outcomes Outcome you want Total outcomes possible

Example In the name: Trisha Leanne McDowell What is the probability of randomly choosing a vowel if the letters were scrambled? Outcome you want (vowels) Total outcomes possible (number of letters in name) 7 20 Try your name

Counting Principle You cannot always count the possible outcomes Multiplication can be used Multiply the possible outcomes of each event

We use the last four digits of our Social Security Numbers for lots of things. How many unique combinations are possible? Four digits so four events • • • 10 10 10 10 1st digit 2nd digit 3rd digit 4th digit 10000 possible unique combinations

WZZK is running a contest WZZK is running a contest. If you call in and the last four digits of your Social Security Number are randomly generated, you will $1000. What is the probability of winning? Outcomes you want (your SS#) Possible outcomes (all the combinations) 1 10000

You try Workbook Pages 203-204

Random Samples and Surveys 4/23 population A group of objects or people sample Part of a population Random Sample Each member of a population has an equal chance of being selected in the sample

Example Identify the population and 3 different sample groups Elections are in November. Pollsters spend a lot of time and money to try and determine who is going to win. Random sample: calling names out of the phone book Not random sample: calling registered Republicans or Democrats

Fair Questions A question that does not influence the sample A question that makes one answer appear better than another Biased Questions Do you prefer sweet, loving doggies or mean, psychotic cats? Example Do you prefer cats or dogs

Workbook Page 203-204

Independent and Dependent Events 4/26 Independent Events The outcome of one event does not affect the outcome of another Example Rolling dice Flipping Coins Slot Machines Lottery Pulling marbles out of a bag and replacing them each time

Formula The probability of A then B P(A, then B) = P(A) •P(B) Example You roll a dice twice, what is the probability you roll a 4 then a 5? P(4, then 5) = P(4) •P(5) 1 • 1 6 6 1/36

Dependant Events The outcome of one event does affect the outcome of another Example Pulling marbles out of a bag and not replacing them Counting Cards

Formula The probability of A then B P(A, then B) = P(A) •P(B after A) Example There are 4 red marbles and 6 blue marbles in a bag, what is the probability of pulling a red, then blue marble if none are replaced? P(red, then blue) = P(red) •P(blue after red) 4 • 6 10 9 24/90 4/15

You Try Workbook Page 205-206

Permutations and Combinations 4/27 An arrangement where order is important Notation #choicesP#events Example Find the number of ways to arrange the three letters in the word CAT in different two-letter groups where CA is different from AC and there are no repeated letters.

Because order matters, we're finding the number of permutations of size 2 that can be taken from a set of size 3. This is often written 3P2. We can list them as: List CA   CT   AC   AT   TC   TA Math 3 • 2 Letter1 Letter2 6 possibilities

We have 10 letters and want to make groupings of 4 letters We have 10 letters and want to make groupings of 4 letters. Find the number of four-letter permutations that we can make from 10 letters without repeated letters (10P4), List It is unrealistic to make a list 10 • 9 • 8 • 7 Math Letter 1 Letter 2 Letter 3 Letter 4 5040 possibilities

You Try 4P2 6P4 9P4 10P8

Combination An arrangement where order does not matter Notation #choicesC#events Formula Combinations are the number of permutations divided by (the number of events factorial) #choicesC#events= #choicesP#events #events!

Factorial n!= n • (n-1) • (n-2) • (n-3) • . . .• 1 7! = 7 • 6 • 5 • 4 • 3 • 2 • 1 7! = 5040 6P4 Find 6C4 4! 6 • 5 • 4 • 3 4 • 3 • 2 •1 15

Example Find the number of combinations of size 2 without repeated letters that can be made from the three letters in the word CAT, order doesn't matter; AT is the same as TA. Because order does not matter, we're finding the number of combinations of size 2 that can be taken from a set of size 3. This is often written 3C2. We can list them as:

List CA   CT   AT Math # permutations 2! 6 2 • 1 6 2 3

You Try 4C2 6C4 9C4 10C8