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

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7th GradeChapter 11Displaying and Analyzing
DataChapter 12Using Probability
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Probability 4/19

• The result of an action

Outcome
Event
An outcome or group of outcomes
Theoretical Probability
Number of favorable outcomes
Number of possible outcomes
Outcome you want
Total outcomes possible
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• In the name
• Trisha Leanne McDowell
• What is the probability of randomly choosing a
  vowel if the letters were scrambled?

Example
Outcome you want (vowels)
Total outcomes possible (number of letters in
name)
7
20
Try your name
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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 happenan
impossible event
A probability of 1 means it would always happena
certain event
?less likely
more likely?
0 Impossible
½ or 0.5
1 Certain
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• 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?
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Odds
Favorable outcomes
Odds in Favor

• Unfavorable outcomes

What you want
What you dont want
Example
What 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?
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Odds
Unfavorable outcomes
Odds against

• Favorable outcomes

What you dont want
What you want
Example
You 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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• Workbook
• Page 199-200

You try
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Frequency Table and Line plots 4/20
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
Display the set of data in a frequency table 1 4
0 3 0 1 3 2 2 4
Example
Number 0 1 2 3 4
Frequency 2 2 2 2 2
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• 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.
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• 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 numberif there is
already an x above your number, then put your x
above that x
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• 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 183-184
You try
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Mean, Median, and Mode 4/21

• Average, the sum of the data divided by the
  number of data points

Mean
Find the mean 2, 5, 6, 12, 6, 8, 12
Example
2 5 6 12 6 8 12
7
51
7
7.29
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• 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
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• The middle value when the data set is in order
  from least to greatest

Median
Find the median 2, 5, 6, 12, 6, 8, 12
Example
Median 6
2, 5, 6, 6, 8, 12, 12
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
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• The number in the data set that repeats the most

mode
example
Find the mode 2, 5, 6, 12, 6, 8, 12
6 and 12 share the mode
Workbook Page19-20
You try
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Random Samples and Surveys 4/22

• A group of objects or people

population
sample
Part of a population
Random Sample
Each member of a population has an equal chance
of being selected in the sample
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• 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
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• A question that does not influence the sample

Fair Questions
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
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• Workbook
• Page 191-192

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Estimating Population Size 4/26

• Set two proportions equal to each other

Proportional Reasoning
Population size
Sample Population
Sample Population
Sample observed Population observed
Proportion

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

1 35 6x
35 6x
5.83 x
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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?
12 42
20 x

12x 42 20
12x 840
x 70
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• Workbook
• Page 193-194

You Try
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Sample Spaces 4/27
Outcome

• The result of an action

An outcome or group of outcomes
Event
Sample Space
List of all possible outcomes
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Theoretical Probability
Number of favorable outcomes
Number of possible outcomes
Outcome you want
Total outcomes possible
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Counting Principle

• You cannot always count the possible outcomes

Multiplication can be used
Multiply the possible outcomes of each event
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• 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
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• WZZK is running a contest. If you call in and
  the last four digits of your Social Security
  Number are randomly generated, you will 10000.

What is the probability of winning?
Outcomes you want (your SS)
Possible outcomes (all the combinations)
1
10000
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You try

• Workbook
• Pages 205-206

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Permutations and Combinations 5/3

• An arrangement where order is important

Permutation
Notation
choicesPevents
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.
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• 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
3 2
Math
Letter1 Letter2
6 possibilities
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• 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),

It is unrealistic to make a list
List
10 9 8 7
Math
Letter 1 Letter 2 Letter 3 Letter 4
5040 possibilities
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1. 4P2
2. 6P4
3. 9P4
4. 10P8

You Try
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Combination

• An arrangement where order does not matter

Notation
choicesCevents
Combinations are the number of permutations
divided by (the number of events factorial)
Formula
choicesCevents choicesPevents events!
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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
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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

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List
CA   CT   AT
permutations
Math
2!
6
2 1
6
2
3
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1. 4C2
2. 6C4
3. 9C4
4. 10C8

You Try