7 th Grade Chapter 11 Displaying and Analyzing Data Chapter 12 Using Probability

Probability4/19 The result of an actionOutcome Event An outcome or group of outcomes Theoretical Probability Number of favorable outcomes Number of possible outcomes Outcome you want Total outcomes possible

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

Finding probabilities from 0 to 1 Since probabilities are written as fractions they can be thought of as between 0 and 1. A probability of 0 means it would never happen—an impossible event A probability of 1 means it would always happen—a certain event 0 Impossible ½ or 0.51 Certain  less likelymore likely 

Suppose you have a spinner with 4 equally spaced colors: red, blue, green, and purple. What is the probability that the spinner will land on orange? What is the probability that the spinner will land on blue? What is more likely, that the spinner will land on blue or green, or that that spinner will land on purple?

Odds Unfavorable outcomes Favorable outcomesOdds in Favor What you want What you don’t want ExampleWhat are the odds in favor of picking a black puppy out of a litter of 12 puppies if 4 puppies are black and your eyes are closed?

Odds Favorable outcomes Unfavorable outcomesOdds against What you don’t want What you want ExampleYou have a standard 6 sided dice. What are the odds against rolling a 3? What are the odds against rolling a multiple of 2?

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Lists each data item with the number of times it occurred Frequency Table and Line plots 4/20 Frequency Table Display the set of data in a frequency table: Example Number01234 Frequency22222 Range Difference between the largest and smallest values in a data set

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 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 You try

Mean, Median, and Mode4/21 Average, the sum of the data divided by the number of data points Mean Find the mean: 2, 5, 6, 12, 6, 8, 12Example

The mean number of hours middle schoolers watch TV is 5 hours per night. How much TV do they watch in a week? (Mean # hour)(# of nights) (5)(7) 35 hours per week

The middle value when the data set is in order from least to greatest Median Find the median: 2, 5, 6, 12, 6, 8, 12Example 2, 5, 6, 6, 8, 12, 12 Median: 6 Find the median: 3, 11, 6, 7, 5, 8, 1, 3 1, 3, 3, 5, 6, 7, 8, 11 5 and 6 share the middle so find the mean (5 + 6)/2 11/2 5.5

The number in the data set that repeats the most mode exampleFind the mode: 2, 5, 6, 12, 6, 8, 12 6 and 12 share the mode Workbook Page19-20 You try

Random Samples and Surveys4/22 A group of objects or peoplepopulation sample Part of a population Random Sample Each member of a population has an equal chance of being selected in the sample

Identify the population and 3 different sample groups Example 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

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

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Estimating Population Size4/26 Set two proportions equal to each other Proportional Reasoning Population size Sample Population Proportion Sample Population Sample observed Population observed =

Example 1 out of 6 female American High School Students will have a baby before graduation. What does this statistic predict for the current 7 th grade class at OHS? Assume there are 35 girls x 35 = 1 35 = 6x 35 = 6x 5.83 = x

Example There are 20 marked sea otters in a costal region. In a survey, marine biologist counted 42 sea otters, of which 12 were marked. How many sea otters are in that area? x = 12x = x = 840 x = 70

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Sample Spaces4/27 The result of an action Outcome Event An outcome or group of outcomes Sample Space List of all possible outcomes

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

You cannot always count the possible outcomes Multiplication can be used Counting Principle 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 1 st digit2 nd digit3 rd digit4 th digit possible unique combinations

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

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Permutations and Combinations 5/3 An arrangement where order is important Permutation ExampleFind 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. #choices P #events Notation

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 3 P 2. We can list them as: CA CT AC AT TC TA Letter1Letter possibilities List Math

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 ( 10 P 4 ), It is unrealistic to make a list Letter 1Letter 2Letter 3Letter possibilities List Math

1. 4 P P P P 8 You Try

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

7! = ! Factorialn!= n (n-1) (n-2) (n-3) ! = 5040 Find 6 C 4 6P4 6P4

ExampleFind 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 3 C 2. We can list them as:

CA CT AT 2! # permutations 6 List Math

1. 4 C C C C 8 You Try