8th Grade Chapter 12 Data Analysis and Probability

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8th GradeChapter 12Data Analysis and Probability
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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
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 197 - 198
You try
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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 orderif 2 numbers are in the
  middle, average them)
• Find the range

Review
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• 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
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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
20.5 Median Data set
14.5 Median 1st half
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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
20.5 Median Data set
14.5 Median 1st half
26 Median 2nd half
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• 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
14.5 Median 1st half
26 Median 2nd half
Middle Quartile
Lower Quartile
Upper Quartile
Quartiles
The medians divide the data into four sections or
quarters
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• The smallest number in the data set

Least value
7
Greatest value
The biggest number in the data set
29
Use the least and greatest value to draw an
adequate number line
Number line
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• Mark the least value 7 with a point

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• Mark the lower quartile 14.5 with a vertical line

Connect the point and the line

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• Mark the middle quartile 20.5 with a vertical
  line

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• Mark the upper quartile 26 with a vertical line

Connect the tops and bottoms of the vertical lines

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• Mark the greatest value 29 with a point

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• 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
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Counting Outcomes and Theoretical
Probability 4/22

• The result of an action

Outcome
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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• 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
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Try your name
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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 1000.

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 203-204

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Random Samples and Surveys 4/23

• 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 203-204

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Independent and Dependent Events 4/26

• The outcome of one event does not affect the
  outcome of another

Independent Events
Example
Rolling dice Flipping Coins Slot
Machines Lottery Pulling marbles out of a bag and
replacing them each time
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• The probability of A then B

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

Formula
P(A, then B) P(A) P(B after A)
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?
Example
P(red, then blue) P(red) P(blue after red)
4 6
10 9
24/90
4/15
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• Workbook
• Page 205-206

You Try
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Permutations and Combinations 4/27

• 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
42

1. 4C2
2. 6C4
3. 9C4
4. 10C8

You Try