Transcript ch 16--statistics File - Solanco School District Moodle

Unit Activation
 M & M distribution project
 How are probability and statistics related?
Statistics
HOW CAN WE REPRESENT A SET OF DATA SO THAT IT HAS
MEANING TO THOSE WHO NEED TO VIEW IT?
Statistics Review
16-1 & 2
HOW DO STATISTICS HELP ME RELATE TO THE WORLD
AROUND ME?
Greed
A STATISTICS REVIEW GAME
Set up your sticky note like this
with the sticky part on top
Instructions
1 ) E V E RY O N E B E G I N S T H E GA M E B Y S TA N D I N G
2) TWO SIX-SIDED DIE ARE ROLLED FOR THE INITIAL
SCORE
3 ) T H O S E T H AT A R E H A P P Y W I T H T H E I R S C O R E M AY
SIT DOWN AND RECORD THEIR SCORE ON THEIR
S T I C K Y N OT E
4) THE ROUND ENDS WHEN A ONE IS ROLLED OR
E V E RY O N E S I T S D O W N . I F A O N E I S R O L L E D
E V E RY O N E S TA N D I N G G E T S A Z E R O F O R T H E
ROUND
5 ) A GA M E C O N S I S T S O F 5 R O U N D S
6 ) AT T H E E N D O F F I V E R O U N D S, S T U D E N T S A D D
THEIR SCORES TOGETHER
7 ) T H E DATA I S T H E N U S E D T O R E V I E W S TAT I S T I C S
CONCEPTS
Roll two six-sided dice for the initial
score
Click to
Roll
Roll one six sided die
Click to
roll
Calculate your score
Place the papers on the board in numeric order
FIND THE:
 Mean
 Median
 Mode
 Create a Box and Whisker Plot
 Discuss outliers (not just extremes)
 Create a dot plot
 Create a stem plot
 State the similarities and differences between dot and
stem plots
 Play round two
Set up your sticky note like this
with the sticky part on top
Roll two six-sided dice for the initial
score
Click to
Roll
Roll one six sided die
Click to
roll
Calculate your score
Place the papers on the board in numeric order
 Create a back to back stem plot
 Compare and Contrast the two stem plots (Center,
Shape and Spread—range)
Homework
NONE.
Chapter 16-2a
HOW DO I INTERPRET GRAPHS AND CHARTS?
Statistics in the World
How many sectors are in this circle
graph?
5
What percentage of people in Shrub
Oak preferred chocolate ice cream?
35
What percentage of people in Shrub
Oak preferred butter pecan ice
cream?
13
If a total of 50 people were surveyed,
then how many people preferred
vanilla ice cream?
13
Not given
0 to 100
6
Visit with friends
School clubs
53
44
Watch TV and earn money
Visit w friends, chat online, talk on phone, earn money, watch tv, school clubs
Choice 3
Discuss this as a class
What is wrong with the graph?
 a) the labels are missing
 b) scale is incorrect
 c) too much data is presented for this type of graph
 d) none of the above
How can we represent this data?
 what type of graphs do you think is best for this data and why?
 One option is to the right,
Is this the only option?
No you could use a bar graph too
Homework
WORKSHEET Graphs
Chapter 16-3
HOW TO WE FIND THE MEASURES OF VARIATION AND WHAT
DO THEY MEAN?
definitions
 Mean deviation—the average distance
each piece of
n
data is from the mean
meandev 
| x  x |
i 1
i
n
 Variance—the measure of the amount of variation in
a set of data
n
s2 
 ( x  x)
i 1
2
i
n 1
 Standard deviation—the square root of the variance
or the typical deviation from the mean in normal
data all data should fall within three SD of the mean
Example
 20, 15, 12, 18, 17, 15, 17, 16, 18, 25
x 
 Reorder
12, 15, 15, 16, 17, 17, 18, 18 20, 25
Q1= 15
Median= 17
Q3= 18
range = 25-12=13
iqr = 18-15=3
173
10
=17.3
Just Watch!!!!!!!!!
 Find the standard deviation by hand
i
xi
Xi -
xx
(xii-
x )22
1
12
-5.3
28.09
2
15
-2.3
5.29
3
15
-2.3
5.29
4
16
-1.3
1.69
5
17
-.3
.09
6
17
-.3
.09
7
18
.7
.49
8
18
.7
.49
9
20
2.7
7.29
10
25
7.7
59.29
totals
173
108.1
173
x
 17.3
10
n
s2 
s2 
 ( x  x)
i 1
2
i
n 1
108.1
 12.01
9
s  s 2  3.46
 By Calculator
 Press Stat
 Press enter/edit
 Enter the data in L1
 Press STAT
 Choose calc
 Choose 1 var stat

xi
12
15
15
16
17
17
18
18
20
25
x  average
 x  total of x' s
 x  total of x' s squared
2
Sx  st. dev of the SAMPLE
σ x  st. dev of the Population
n  number of items
min x  min value
Q1  1st quartile
med  median
Q3  3rd quartile
max x  max value
Finding the Mean Deviation with the Calc
 Enter the data in L1
 Go to the top of L2 and enter |xi - 𝑥|
 Run 1 variable statistics on L2
 The 𝑥 in this run is the mean deviation
Homework
Pg. 702
2, 4, 6, 7
The Normal Distribution
16-4
Activation
Roll two die 5 times recording your results. Take turns plotting the results on the
graph below.
2
3
4
5
6
7
8
9
10
11
12
The normal curve
 Normally Distributed data—data which is bell shaped and symmetric
about the mean in a way that 68% of the data fall within one st. dev.,
95% fall within two st. dev. And 99.7% falls within 3 standard dev.
- 3
13.5
2.35
%
%

-2
-1
68%
mean
95%
99.7%
13.5
%
1
2.35
%
2
3
Z-scores
Z-score—the number of standard deviations a
piece of data falls from the mean
z
xx

Example: if the mean is 10 and the st dev is 2
What is the z-score of 7
Open the book to pg 850.
7  10  3
z

2
2
What does a z-score mean?
Z-chart—because the data is symmetric we
can find the likelihood that we will have this
piece of data or one less than it.
7  10  3
z

2
2
z  .0668
*
6.68% of the data is less than or equal to 7 when the mean is 10 and the st dev is 2
Example
 Samples of a certain type of concrete specimen are selected, and the
compressive strength of each one is determined. The mean and st. dev are
3000 and 500 respectively. The sample box-plot appears relatively
normal. (i.e.—we can use z-scores)
 Approx. what % of the sample falls below 2500?
 Approx what percent falls between 2500 and 4300?
 Approx what percent falls above 4500?
Homework
Pg 708
15-18
16-5
SAMPLING
 Simple Random Sample—samples chosen so that
 Each item has an equal chance of being selected
 The choice of one item has no bearing on the choice of the next
 Example:
A scientist is testing the impact on weight gain and loss on rats fed a
certain supplement. He reaches into the cage and chooses the five largest
rats. Is this a random sample?
This is not random in fact it is what we call biased.
 Bias—when data is overly influenced for some reason.

In the last example the scientist was biased towards the larger rats.
 Examples:
 The county decides to survey the size of its constituents households by calling
every 10th person on the list?
 Is this random?

Yes –not necessarily the best way to achieve randomness but legitimate
 Is this biased?

Yes—not all constituents may have a home phone
Closer—Happyville
• Keep the worksheet face down until told differently
• When I tell you turn the worksheet over and estimate the average
household size in Happyville—you have five seconds turn the paper back
• Get everyone’s values and find the average of the estimates
• When I tell you turn the paper over and randomly choose any ten
households by circling them (you have 30 seconds)—turn the paper back
• Average the number of people in the 10 households
• Get everyone’s values and find the average of the averages
• Compare the two values
• Seed the random number generator
• Type in a value from 0 to 1000 press STO math prb rnd
• Then type math prb 5 (1,100) press enter until you have 10 unique
values
• Average the number of people in these 10 households
• Get everyone’s values and find the average of the averages
• Compare the three values
• Which values are closest together?
Homework
Pg 713
evens
Simulations
16-7
Activation
What is the probability of getting 5 heads
when you flip a coin ten times?
Is it sufficient to flip the coin just ten times?
Ten sets of ten?
What if the experiment had been what is the
probability of getting 5 correct answers on a
ten problem true false test?
Simulations
 Theoretical probability
 The actual probability of an event
 Experimental probability
 The results that you get when you run an experiment
 Simulation
 Used to approximate the probability when money or
time is too great a factor in running an actual
experiment
 Design
 The method used to run the simulation
 Trial
 One run of the method described
Example one:
 A restaurant is giving away 6 actions figures
to the latest movie with the purchase of each
child’s meal. If you are equally like to get
any figure, what is the probability of getting
one of each in the purchase of ten meals?
Click
to roll
Example Two:
 A basketball player has a free throw percentage of
80%. What is the probability of making two free
throws out of three baskets?
Example Three:
How does this change our simulation?
 A basketball player has a free throw
percentage of 78%. What is the probability
of making two free throws in a out of three?
Homework
Worksheet
Types of sampling
16-6
IS ONE TYPE OF SAMPLING BETTER THAN ANOTHER?
River Project
WHAT ARE THE TYPES OF SAMPLING AND HOW IS EACH
ACCOMPLISHED?
Harvest Time
A farmer has just cleared a new field for corn. It is a unique plot of land
in that a river runs along one side. The corn looks good in some areas
of the field but not others. The farmer is not sure that harvesting the
field is worth the expense. He has decided to harvest 10 plots and use
this information to estimate the total yield. Based on this estimate, he
will decide whether to harvest the remaining plots.
Convenience Sample
The farmer decided to harvest the 10 easiest plots to harvest.
X
X
X
X
X
River
X
X
X
X
X
He then had second thoughts and decided to hire you, a
statistics student, somewhat knowledgeable about these
matters but far cheaper than a statistician. You are still to
choose 10 plots but try different sampling methods to
determine which one will give the best estimate of the actual
yield.
Simple Random Sample
Use a random number table to select 10 plots.
Describe the method used and mark the plots.
River
Stratified Sample (vertical)
Determine a method that will allow you to choose
one box in each column. Describe the method and
select the plots
River
Stratified Sample (horizontal)
Determine a method that will allow you to choose
one box in each row. Describe the method and
select the plots
River
Determining best method
The table below represents the yield per plot. You
will need this to determine which method is best
and why.
0
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
Determining best method
Method
Convenience
sample
Simple Random
sample
Vertical strata
Horizontal strata
Mean yield
per plot
Estimated
Total yield
Observations
1) You looked at four different methods of choosing plots. Is there a
reason, other than convenience, to choose one method over another?
2) How did your estimates vary according to the different sampling
methods used?
Homework
None
Hypothesis testing
HOW MUCH OF A DIFFERENCE IS ENOUGH?
Distracted Driver Project
1. Get a standard deck of 52 cards (i.e. no jokers)
2. Work with your group to determine a method for simulating this experiment
using the cards. Take five minutes to determine your method.
3. We will discuss the methods before proceeding and all use the same
method.
4. Shuffle and deal two piles of 24 cards. The pile on the left will be the cellphone drivers. Record the number who missed. Why don’t we need to
count the cards in the other pile?
5. Make a chart like the one below and repeat the experiment 9 more times
recording the number of cell phone misses.
6. In the original experiment, 7 of 24 drivers using cell phones missed the
freeway exit, compared to only 2 of the 24 drivers talking to a passenger. In how
many of your 10 simulation trials did 7 or more drivers in the cell phone group
miss the exit?
7. Place your results in the class dot plot on the board. In what percent of the
class’s simulation trials did 7 or more people in the cell phone group miss
the freeway? (be careful to keep the rows and columns of dots even)
8. Since 7 of the cell phone talkers missed the exit in the actual experiment,
do you think it’s possible that cell phones and passengers are equally
distracting to drivers based on the simulation results of the class? Why or
why not?
Homework
None