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- Тип файла:ppt / pptx (powerpoint)
- Всего слайдов:39 слайдов
- Для класса:1,2,3,4,5,6,7,8,9,10,11
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Слайды и текст к этой презентации:
№2 слайд
Содержание слайда: Interpretation of summary statistics
A random sample of people attended a recent soccer match. The summary statistics (Excel output) about their ages is here below:
What is the sample size?
What is the mean age?
What is the median?
What shape does the distribution of ages
have? (symmetric or non-symmetric)
What is the measure/s for spread in the data?
Is this a large spread?
What is the Coefficient of variation for
this data?
№5 слайд
Содержание слайда: Symmetric distribution - Empirical rule
Knowing the mean and the standard deviation of a data set we can extract a lot of information about the location of our data.
The information depends on the shape of the histogram (symmetric, skewed, etc.).
If the histogram is symmetric or bell-shaped, we can use the Empirical rule.
№10 слайд
Содержание слайда: Empirical rule: Application
A company produces batteries with a mean lifetime of 1’200 hours and a standard deviation of 50 hours.
The mean is 1’200 and standard deviation is 50, we find the following intervals:
= 1’200 1x(50) = (1’150 and 1’250)
= 1’200 2x(50) = (1’100 and 1’300)
= 1’200 3x(50) = (1’050 and 1’350)
№11 слайд
Содержание слайда: Interpretation of the Empirical rule: Lightbulb lifetime example
If the shape of the distribution is normal, then we can conclude :
That approximately 68% of the batteries will last between 1’150 and 1’250 hours
That approximately 95% of the batteries will last between 1’100 and 1’300 hours and
That 99.7% (almost all batteries) will last between 1’050 and 1’350 hours.
It would be very unusual for a battery to loose it’s energy in ex. 600 hours or 1’600 hours. Such values are possible, but not very likely. Their lifetimes would be considered to be outliers
№13 слайд
Содержание слайда: Class quizz
Empirical rule:
(1) Which shape must the distribution have to be able to apply the Empirical rule?
(2) Which two parameters give information about the shape of a distribution?
(3) What percent approximately of the values in a normal distribution are within one standard deviation above and below the mean ?
№22 слайд
Содержание слайда: Random experiment
In statistics a random experiment is a process that generates two or more possible, well defined outcomes. However, we do not know which of the outcomes will occur next.
Examples: Experimental outcomes:
Tossing a coin Head, tail
Throwing a die 1, 2, 3, 4, 5, 6
The outcome of a football match win – lose - equalize – game cancelled
№24 слайд
Содержание слайда: Sample space, S - Examples
Random experiment: Flip a coin
Possible outcomes: Head or tail
The sample space: S= {head, tail}
There are no other possible outcomes, therefore they are collectively exhaustive.
When head occurs, tail cannot occur – meaning the outcomes are mutually exclusive.
The sample points in this example are head and tail.
№25 слайд
Содержание слайда: Sample space, S - Examples
Outcomes of a statistics course:
The sample space: S = {AA, BA, BB, CB, CC, DC, DD, FD, FF, VF)}.
There are no other possible outcomes, therefore they are collectively exhaustive.
When one of the outcomes occur, no other outcome can occur, therefore they are mutually exclusive.
The sample points are the individual outcomes of the sample space, S = {AA, BA, BB, CB, CC, DC, DD, FD, FF, VF}.
№26 слайд
Содержание слайда: Sample space - example
The sample space, S = { Google, direct, Yahoo, MSN and all other}
Mutually exclusive: When a person visits Google it can not visit Yahoo at the same time
Collectively exhaustive: There are no other possible search engines
Sample points: Google, Direct, Yahoo, MSN, all others
№28 слайд
Содержание слайда: Event:
– subset of outcomes of a sample space, S
Random experiment: Throw a dice (Turkish: zar).
Possible outcomes, sample space, S is: {1, 2, 3, 4, 5, 6}
We can define the event “toss only even numbers”. Let A be the event «toss only
even numbers»:
We use the letter A to denote the event: A: {2, 4, 6}
If the experimental outcome are 2, 4, or 6, we would say that the
event A has occurred.
№29 слайд
Содержание слайда: Event :
Subset of outcomes of a sample space, S
Random experiment: Grade marks on an exam
Possible outcomes (Sample space): Numbers between 0 and 100
We can define an event, «achieve an A», as the set of numbers that
lie between 80 and 100. Let A be the event «achieve an A»:
A = (80, 81, 82 …….98, 99,100)
If the outcome is a number between 80 and 100, we would say that the event A has occurred.
№32 слайд
Содержание слайда: Mutually exclusive event
A and B are Mutually Exclusive Events if they have no basic outcomes in common
i.e., the set A ∩ B is empty, indicating that A ∩ B have no values
in common
Example: Tossing a coin: A is the event of tossing a head. B is the event of tossing a tail. They cannot occur at the same time.
№33 слайд
Содержание слайда: Collectively Exhaustive
Events E1, E2, …,Ek are Collectively Exhaustive events if E1 U E2 U….. Ek = S
i.e., the events completely cover the sample space
Example: Tossing a coin - possible events: head and tail
Events, head and tail are collectively exhaustive because they make up the entire
sample space, S
№38 слайд
Содержание слайда: Class exercise
The following sample space is defined a S = {2, 3, 15, 17, 21}
1) Given the event A = {3, 17}, define event
2) Given the events from the sample space, S: A = {3, 17 } and
B = {3, 15, 21}
Define
What is the intersection of A B ?
What is the union of A
Are events A collectively exhaustive? Explain
Are events A and B mutually exclusive? Explain
№39 слайд
Содержание слайда: Class exercise
The following sample space is defined a S = {2, 3, 15, 17, 21}
1) Given the event A = {3, 17}, define event = {2, 15, 21}
2) Given the events from the sample space, S: A = {3, 17 } and
B = {3, 15, 21}
- Define = {2, 17}
- What is the intersection of A B ? = {3}
- What is the union of A = {3, 15, 17, 21}
- Are events A collectively exhaustive? They are not collectively
exhaustive because the sample point 2 is not in the union.
- Are events A and B mutually exclusive? No, because event A and B have a sample point in
common, 3
Скачать все slide презентации Empirical rule - Probabilities. Week 5 (1) одним архивом:
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Conditional Probabilities Statistical Independence. Week 6 (1)
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Probabilities. Week 5 (2)
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The Chain Rule
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Conditional probability and the multiplication rule
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Calculating the probability of a continuous random variable – Normal Distribution. Week 9 (1)
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Discrete Probability Distributions: Binomial and Poisson Distribution. Week 7 (2)
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Discrete random variables – expected variance and standard deviation. Discrete Probability Distributions. Week 7 (1)
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Random variables – discrete random variables. Week 6 (2)
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Measures of variation. Week 4 (2)
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Measures of variation. Week 4 (1)