stats QUIZ IN CLASS 1
subjective approach
ex of ________ Granting Bank Loans Physician's Diagnosis of Illness Cause Jury Deliberation New Product Introduction Most business applications which involve uncertainty utilize subjective assessment to measure that uncertainty.
statistics
The science of data collecting, organizing, analyzing, interpreting, and presenting data.
Joint probability:
---- The probability of two or more events occurring together.
Marginal probability:
---- The probability that any one single event will occur -Marginal probabilities appear in the margins.
Complement of Event A:
----- Event consisting of all sample points that are "not in A". The complement of A is denoted by A'
Addition Rule:
----- The probability of the union of two events.
Exhaustive Events:
------ All possible outcomes must be included. A= Aces B= Black Cards C= Diamonds D= Hearts -Events A, B, C, and D are collectively exhaustive (but not mutually exclusive - an ace may also be a heart) -Events B, C, and D are collectively exhaustive and also mutually exclusive
Mutually Exclusive Events:
------ Events that cannot occur together (no sample points in common).
Subjective Approach:
-------- Probability based on individual's past experience, personal opinion, analysis of situation -When there are no precise mathematics and no large number of historical trials available Examples- -When you wake up in the morning, look out the window and figure that because there are no clouds it won't rain today, so don't take your umbrella with you -What is the probability that the price of Apple stock will rise within the next 30 days?
Conditional Probability
-------: The probability of one event, given that another event has occurred -B is the event known to have occurred and A is the uncertain event whose probability you seek, given that B has occurred.
Contingency Table
-----: A cross-tabulation of frequencies into rows and columns. -like a frequency distribution for two variables
inferential descriptive descriptive descriptive descriptive -inferential
4. Tell if descriptive or inferential statistics have been used. a. By 2040 at least 3.5 billion people will run short of water(World Future Society). -____ b. Nine out of ten on the job fatalities are men (Source: USA TODAY Weekend). -____ c. Expenditures for the cable industry were $5.66 billion in 1996 (Source: USA TODAY). -____ d. The median household income for people aged 25-34 is $ 35,888 (Source: USA TODAY). -____ e. Allergy therapy makes bees go away (Source: Prevention). -____ f. Drinking decaffeinated coffee can raise cholesterol levels by 7% (Source: American Heart Association).-___ g. The national average annual medicine expenditure per person is $1052 (Source: The Greensburg Tribune Review). -____ h. Experts say that mortgage rates may soon hit bottom (Source: USA TODAY). _____
QUANTITATIVE
5 types of ____ GRAPHS 1. histogram 2. frequency polygon 3. ogive 4. dot plot 5. stem and leave plot
Ratio Ordinal Interval Ratio Ratio -Ratio Ordinal Ratio -Ratio nominal
5. Classify each as nominal-level, ordial-level, interval-level, or ratio-level measurement. a. Pages in the 25 best-selling mystery novels. -____ b. Rankings of golfers in a tournament. -___ c. Temperatures inside 10 pizza ovens.- ____ d. Weights of selected cell phones. -___ e. Salaries of the coaches in the4 NFL. -____ f. Times required to complete a chess game. ___ g. Ratings of textbooks (poor, fair, good, excellent). -____ h. Number of amps delivered by battery chargers. -___ i. Ages of children in a day care center. ____ j. Categories of magazines in a physicians office (sports, women's, health, men's, news). -____
Qualitative Quantitative Quantitative -Qualitative Quantitative Quantitative Quantitative
6. Classify each variable as qualitative or quantitative. a. Marital status of nurses in a hospital. -___ b. Time it takes to run a marathon. -___ c. Weights of lobsters in a tank in a restaurant. -____ d. Colors of automobiles in a shopping center parking lot. ___ e. Ounces of ice cream in a large milkshake. -___ f. Capacity of the NFL football stadiums. -_____ g. Ages of people living in a personal care home. -____
Discrete -Continuous Discrete Continuous -Continuous Discrete Continuous
7. a. Number of pizzas sold by Pizza Express each day. -____ b. Relative humidity levels in operating rooms at local hospitals. ____ c. Number of bananas in a bunch at everal local supermarkets. -___ d. Lifetimes (in hours) of 15 iPod batteries. -____ e. Weights of the backpacks of first graders on a school bus. ___ f. Number of students each day who make appointments with a math tutor at a local college. -___ Blood pressure of runners in a marathon. -____
POSITIVELY SKEWED
: Which one of the following best describes the histogram?____
contingency table...marginal probability........Joint probability....adddition rule..........mutually exclusive events ....collectively exhaustive...mutually exclusive........an ace may also be a heart)...EXHAUSTIVE....CONDITIONAL PROBABILITY...RELATIVE FREQUENCY ...larger .... accurate...relative frequency approch
A cross-tabulation of frequencies into rows and columns Like a frequency distribution for two variables.. ______ The probability that any one single event will occur Marginal probabilities appear in the margins._______ _____: The probability of two or more events occurring together. -The probability of a joint event, A and B: :ex. P(A and B) =Number of outcomes satisfying A and B / Total number of outcomes in sample space _______The probability of the union of two events. P(A or B) = P(A) + P(B) - P(A and B) ______ Events that cannot occur together (no sample points in common). When event A occurs it excludes event B in the same trial. 50 P(A or B) = P(A) + P(B) Example: A car repair is either covered by the warranty (A) or not (B) _____ EVENTS . All possible outcomes must be included. A= Aces B= Black Cards C= Diamonds D= Hearts ALL ARE _____ BUT NOT_____ WHY???______
larger
Any good measure of variation will give a __ value of spread for the Metals fund than for the Income fund.
Cross Tabulation
Bivariate Data: ____ Also referred to as -Cross-classification table - Contingency Table -pivot table -joint frequency distribution -shows rel. bw two diff. variables -lists the frequency of each combination of the values of the two variables
Subjective Approach
Examples of ----- - Granting Bank Loans - Physician's Diagnosis of Illness - Jury Deliberation - New Product Introduction -most business operations which involve uncertainties utilize subjective assessment to measure that uncertainty
Actuarial science Classical Approach
Examples of Relative Frequency Approach Practical issues for actuaries ------ is a high-paying career that involves -calculate payout rates on life insurance, pension plans, and health care plans -Life and auto insurance Demand planning - Assessing chances of 20 or more customers arriving before 10 AM -Material and component parts order requirements - Assessing proportion of parts in a lot of 1000 that will be usable. -Applications limited to situations where there are a large number of identical trials. ----------: Based on equally likely events. -lottery -casino gambling -teaching probability -beads in a bowl -decks of cards -coin tosses =very few practical business applications
average middle
FINDING THE MEDIAN If n or N is even, the median is the ____of the two middle numbers If n or N is odd, the median is the _____number
nominal data ordinal data interval data ratio data
Four common levels of data include? ___(lowest) ,____ ,____ , ___(highest)
Empirical Rule
Interpreting Standard Deviation Knowing the mean & standard deviation allows business executives to derive useful information The information depends on the shape of the distribution of the data To determine the shape of the distribution, construct a histogram of the data If the histogram is bell-shaped Use the ____
Sturges Rule:
K= 1 + 3.3 * log(n), where k is classes and n is number of observations
Sorting Frequency Distributions and Histograms Charts 20 Crosstabulation
Organizing and Presenting Data Graphically 4 Techniques reviewed here?????? SFCC ___ ____ ___ ____
Visual Numerical
Organizing and Presenting Data Graphically Some type of organization is needed ___ (charts and graphs) provides insight into characteristics of a data set without using mathematics. 19 ____ (statistics or tables) provides insight into characteristics of a data set using mathematics.
D
Q4.5: Which of the following is the sample space when 2 coins are tossed? ____ A. {HH, HT, TT} B. {H, T, H, T} C. {H, T} D. {HH, HT, TH, TT}
Census costly cumbersome
Reasons for Drawing a Sample Less time consuming than a census ___: Collecting data for the entire population Less ___ to administer than a census Less ___ and more practical to administer than a census of the targeted population It is possible to obtain statistical results of a sufficiently high precision based on samples
Individual Values Sum of all values
Requirements of probabilities ______ never negative 0 ≤ P(e) ≤ 1 i _____ k = Number of .5 elementary events in the sample spaces ei = ith elementary event
Skewness MODALITY modal class
SHAPES OF HISTOGRAMS -BELL SHAPED -SYMMETRIC ___ Long tail extending to either the right or the left -Positively Skewed OR Negatively Skewed ____-BIMODAL OR UNIMODAL A __ is the class with the largest number of observations
standard deviation
The distance of a value in a population (or sample) from the mean value of the population (or sample). A computed measure of how much scores vary around the mean score.
Mean median Mode outlier
WHICH MEASURE OF LOCATION IS THE BEST? ____ is generally used, unless extreme values (outliers) exist Then_____ is often used, since it i is not sensitive to extreme values. Certain situations may warrant use of the ___ ____ distort the data, know that the median describes "what is typical"
probability
What is _____?: The likelihood or chance that a particular event will occur Why study it? To infer something about the population based on sample observations
Frequency Distribution
What is a_____? A list or a table ... containing the values of a variable (or a set of ranges within which the data falls) ... and the corresponding frequencies with which each value occurs (or frequencies with which data falls within each range) Why use it? is a way to summarize data The distribution condenses the raw data into a more useful form... and allows for a quick visual interpretation of the data
continuous quantitative
What type of data is the income of a mortgage applicant?
categorical
What type of data is your Gender?___
event...elementary event
When estimating a probability.. ...you are assigning a numeric measure to the likelihood or chance of a particular____occurring. Example of Elementary Events. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH, and TT. Any one outcome like {HH} is called an___ of the sample space {HH, HT, TH, TT}.
D all the above
Which of the following is an experiment? Q4.4: Which of the following is an outcome? ____ A. Tossing a coin B. Rolling a single 6-sided die C. Choosing a business card from a jar D. All of the above
Communication Understanding the language of statistics facilitates communication and improves problem solving. Information Management Statistics help summarize large amounts of data and reveal underlying relationships. Quality Improvement Statistics helps firms oversee their suppliers, monitor their internal operations and identify problems.
Why Study Business Statistics? CIQ ___,____,____
x-axis
__(abscissa) labeling w/ class endpoints
grouped data
__- data that has been organized in a frequency distribution
variable
__-characteristic of any entity of being studied that is taking on different values. ex. return on investment, advertising decision, labor productivity, stock price... -most can produce a measurement used for analysis
dispersion center
___ -measures of deviation give info on the spread or variability of the data values -small standard deviation versus large(same ____, different variation)
discrete data
___ Data whose possible values are countable. The most common type of discrete variable is a counting variable. Number of people in a room Number of correct answers in a multiple choice exam
Pareto chart
___ 3rd type of qualitative data - viewed as part. application of bar graph -analysis uses this tally to produce a vertical bar chart that displays the most common types of defects ranked in order of occurance from left to right -Vertical bar graph on which bar height reflects frequency or impact of causes. -looks like a bar chart except that the highest-ranking item is listed first, followed by the second highest, down to the lowest-ranked item. -named after italian economist Vilfredo Pareto who observed over a hundred years ago that most of italy's wealth was controlled by few family's who were drivers behind economy
Arithmetic n N
___ Mean (Average) Measure of central location Most common measure of central tendency -effected by extreme values (outliers) ______sample size ___population size
bar graph horizontal vertical
___ a widely used qualitative measurement of data containing two or more categories along axis and series of bars for each category along other axis -categories are nonnumerical ____- referred to as bar charts ___ -reffered to as column charts
running totals
___ in ogive loops allows the program to keep running totals while evaluating data
graphical depiction qualitative quantitative
___ most effective measurements in presenting data in a form meaningful to decision makers - helps researcher determine shape of distribution ___-plotted along nonnumerical category ____-plotted along a numerical scale
J.M. Juran
___ observed that poor quality can be addressed by attacking on few major causes that result in most of problems
y-axis
___(ordinate) w/ frequencies drawing a horiz. line from class endpoint to endpoint at each freq. value and connecting them
sample
___- a portion of the whole or representative of the whole. -researchers like to worth with this of a population rather than the entire population
nonparametric stats
___- if data is nominal or ordinal. can also be used to analyze interval or ratio data
interval data
___- next to highest level of data in which the distances b/w consecutive numbers have meaning and the data are always numerical
class midpoint
___- the midpoint of each class interval or sometimes referred as class mark or the value halfway across the class interval and calculated as the average between the tw classes endpoints
scatter plot
___- two dimensional graph plot displays pairs of points from two numerical variables to examine possible relativities bw variables
measurement
___- when a standard process is used to assign numbers to particular attributes or characteristics of a variable ex. labor productivity, customer satisfaction
frequency distribution
___-a summary of data presented in te form of class intervals and frequencies ..easy to construct, vary in final shape and decision, constructed according to individuals researchers taste -constructed according to RANGE of raw data
metric data
___-bc interval and ratio level data are gathered in precise instruments, used in production or engineering processes and referred as quantitative data -higher level data -interval and ratio -quantitative data -can use in parametric stats
population
___-collection of persons, objects, and items of interest ex. "all automobiles" -researcher defines as whatever he/she is studying
range
___-defined as the diff. bw the largest and smallest numbers
census
___-gather data from the whole population for a given measurement of interest
business statistics
___-is about measuring phenomena in the business world and organizing, analyzing and presenting it in a better more informed business decisions
ordinal data
___-measurement is higher than nominal level -can be used to rank or order people/objects
ungrouped data
___-raw data, or data that has not been summarized in any way
parametric stats
___-require that data be interval or ratio
nominal data
___-the lowest level of data meausurement -numbers using only this can be only used to classify or categorize ex. employee identification numbers bc only used to differenciate employees not make a value statement about them ex. sex, religion, ethnicity, geographic location, SS number
Standard Deviation extra squared average
___: Square root of the average of squared deviations of values from the mean -Most commonly used measure of variation -Explains how individual values in a data set vary from the -has same units of orig. data -Uses all values in calculation -Values far from the mean are given____ weight (because -deviations from the mean are_____ A measure of the "____" scatter around the mean Sample standard deviation, s: s =root s^2 Population standard deviation, σ: σ = σ^2
sorting
____ Shows range (min to max) Provides some signals about variability within the range May help identify outliers (unusual observations) If the data set is large, sorting is less useful
range
____ Simplest measure of variation Difference between the largest and the smallest Range = xmax - xmin disadvantages of it: -Ignores the way in which data are distributed -sensitive to outliers
Quantitative Qualitative
____ (Numerical) Ratio Real numbers (fixed zero, ratio of two observations) Bank Balance Account of $0 means you have no money Interval Ranking of integer numbers (distance between consecutive integers is equal) 100°F is 20°F hotter than 80°F which is 20°F hotter than 60°F ____ (Categorical) Ordinal Ranking of categories (differences between categories may not be equal Bond ratings, best to worst ranking, age categories Nominal Categories only Eye color, gender, ethnic/cultural groups, zip codes
Frequency Distribution Mutually exclusive All inclusive
____ More on Classes Classes must be: Equal-width ___(data value can be placed in only one class) ___ (contains all the possible data values) Class Boundaries: Never overlap In general, the lower limit is included in the class while the upper limit is excluded Class widths can typically be reduced as the number of observations increases, and therefore more classes can be used Distributions with numerous observations are more likely to be smooth and have gaps filled since data are plentiful (no empty classes)
Sample Statistics Population parameters
____ (known) inference---- ____ (unknown, but can be estimated from sample evidence)
Cumulative Frequency: Cumulative Relative Frequency:
____ A summary of a set of data that displays the number of observations with values less than or equal to the upper limit of each of its classes. ___ A summary of a set of data that displays the proportion of observations with values less than or equal to the upper limit of each of its classes.
QUALITATIVE
____ Data graphs or 1.pie charts 2. bar charts 3. pareto charts
mode outliers
____ the value in a data set that occurs most frequently -NOT ejected by extreme values (___) -used for either quantitative or categorical data -there may be no mode -there may be several modes
cumulative frequency
____- a running total of frequencies through the classes of a freq. distribution -Sum of the frequencies starting at lowest interval & including frequencies within that interval. -for a class is the sum of the frequencies for that class and all previous classes.
data
____- are recorded and stored measurements analyzed by a business statistician in order to learn more about the variables being studied
outliers
____- data points that appear outside the main body of observations and many rep. phenomena that diff. from those rep. by other data points
parameter
____-a descriptive measure of a population denoted by greek letters and examples in: population mean population variance population standard deviation
differentiation
____-b/w terms parameter and statistics is only imp. in use of inferential statistics abd approximations about parameters are merely impossible bc of amount of time and money needed to take a census
ratios
____-height, weight, time, volume, kelvin temp - many data measured by values or gauges
ABSOLUTE ZERO
____-means that zero is fixed and the zero value in the data represents the absence of the characateristic being studied -value of zero cannot be assigned bc represents a fixed point which allows statisticians to create ratios w/ data
ratio data
____-measurement is the highest level of data -has same properties as interval data -BUT has an ABSOLUTE ZERO and the ratio of the two numbers is meaningful
Variance:
____Average of squared deviations of values from the mean
frequency distribution
_____ Step 1: Create an ordered array (sort data from smallest to largest). Step 2: Determine the number of classes ( k) based on the number of observations ( n) using Sturges Rule: ∗ . + = Step 3: Set class width based on minimum and maximum value in ordered array and the number of classes ( k). Class Width = ݔ − ௫ݔ k Step 4: Determine class boundaries. Step 5: Count the number of values (frequencies) in each class.
MEASURES OF VARIATION MEASURES OF SKEWNESS measures of position measures of central location
_____ Range Variance Standard Deviation Coefficient of Variation _____-shape _____- Percentiles Quartiles ______ Mean Median Mode Weighted Mean
WEIGHTED MEAN
_____ Used when values are grouped by frequency or relative importance An investor bought common stock of Microsoft Corporation on three occasions at the following prices. Example: 2012 total return percentages for several popular investments
probability rules
_____ Probability rule for an event -The probability of an event A is equal to the sum of the probabilities of the elementary events forming A. That is, if: then: A = {e1, e2, e3} P(A) = P(e1) + P(e2) + P(e3)
Sample Space 6 52
_____ (S): List of all possible outcomes All___ faces of a die: All ____ cards of a bridge deck
Parameter: Statistic
_____ A descriptive measure of a population Usually denoted with a Greek letter Population size is denoted by uppercase letter N Example: Population mean (μ) ___: A descriptive measure of a sample Usually denoted with a Roman letter Percentiles Quartiles Skewness Sample size is denoted by lower case letter n Example: Sample mean (x )
Elementary Event: Event:
_____ A single outcome of the sample space. Cannot be broken down into other events. Example: Getting a 1 on a single roll of a die _____: Two or more elementary events
inferential statistics Estimation Hypothesis Testing Regression Analysis
_____ Drawing conclusions from a sample and/or making decisions/uses statistics concerning a population from which the sample is taken b-ased only on sample data Example: The average starting salary of college graduates is $45,000. You would not ask each and every college graduate what their starting salary was, but instead would select a subset of them to draw a conclusion of the average starting salary. ___ Estimate the monthly average data usage on mobile broadband by all Smartphone users using the sample monthly average data usage. _____ Test the claim that the monthly average data usage by all Smartphone users is 10GB. _____ Examine the relationship between education and income.
Qualitative
_____(categorical)Labels or names to identify categories of like items (classifications) Examples: Gender Political Party Eye Color
descriptive statistics
_____-Organizing, summarizing, and presenting data in an informative way -majority of stat. data Collect data Survey, Observation, Experiments Present data Charts and graphs Characterize data
classical approach...population....sample... without..using...sorting..Cumulative Frequency...Cumulative Relative Frequency....line charts...scatter diagrams
_____-based on equally likely events Number of outcomes with A/ Number of outcomes in sample space ____All likely voters in the next election Grade point averages of all the students at USD All sales receipts for November ___ 1000 voters selected at random for interview Grade point averages of 100 USD students Every 100th receipt from November selected for audit Visual (charts and graphs) provides insight into characteristics of a data set____ using mathematics. 19 Numerical (statistics or tables) provides insight into characteristics of a data set ____ mathematics ____Shows range (min to max) Provides some signals about variability within the range May help identify outliers (unusual observations) If the data set is large, sorting is less useful ____: A summary of a set of data that displays the number of observations with values less than or equal to the upper limit of each of its classes. _____: A summary of a set of data that displays the proportion of observations with values less than or equal to the upper limit of each of its classes. ___: Show values of one variable vs. time _____Plots two quantitative variables against one another
Union of Two Events
_____: Event that occurs when either A or B or both occur (denoted "A or B"). -For example, randomly choose a card from a deck of 52 playing cards. If Q is the event that we draw a queen and R is the event that we draw a red card, what is Q and R? It is the possibility of getting both a queen and a red card (_2__ ways).
Outcome results
_____: The result of a single trial of a probability experiment or random process. There may be just a few outcomes (____), or many possible outcomes. Usually, we know all possible outcomes of the experiment or process...
continuous data
_____Data whose possible values are uncountable and which may take on any value in an interval The most common type of continuous variable is a measuring variable. Amount of soda in a Coke bottle (ml) Speed of a car (mph)
complement rule
_____Since A and A' makes up the entire sample space P(A) + P(A') = 1 The probability of A' is found by P(A' )=1-P(A)
Quantitative dicrete continuous
______(numerical) subdivided into --__________ Examples: Number of Siblings Customers per hour (Counted items) ____ Examples: GPA Weight (Measured characteristics
uncertainty Random Experiment
_______ Managers often base their decisions on an analysis of uncertainties such as the following: What is the likelihood a new assembly method will increase productivity? What are the odds that a new investment will be profitable? ______: An observational process that leads to one of several possible outcomes. What are the chances that sales will decrease if we increase prices? Examples: Tossing Coins Rolling Dice Drawing Cards Bidding Contracts Selecting Investments
Data Warehousing
_______-Organizations obtain large amounts of data on a daily basis by means of magnetic card readers, bar code scanners, point of sale terminals, and touch screen monitors. Wal-Mart captures data on 20-30 million transactions per day. Visa processes 6,800 payment transactions per second. Capturing, storing, and maintaining the data is a significant undertaking.
coefficient of variation
________Relative to the amount invested in a stock, the coefficient of variation reveals the risk of a stock in terms of the size of the standard deviation relative to the size of the mean (in percentage)
coefficient of variation
__________ Compares the variation between two data sets with different means and different standard deviations and measures the variation in relative terms. CV): Measures relative variation =Always in percentage (%) -Measures the size of the standard deviation -relative to the size of the mean -Provides a proportionate measure of variation Sample Example: A standard deviation of 10 may be perceived as large when the mean value is 100, but only moderately large when the mean value is 500.
relative frequency classical subjective
___________-There is a 2 percent chance of twins in a randomly- chosen birth. ____There is a 50 % probability of heads on a coin flip. ____there is a 5% chance that England will adopt the euro currency by 2017
frequency polygon def
____like a histogram,graphical display of class freq. but instead of using rectangles plotted as a dot at class midpoint and dots are connected by series of line segments
DATA
____or Facts and figures collected, analyzed, and summarized for presentation and interpretation. To provide input to survey/study To measure performance of service or production process To evaluate conformance to standards To assist in formulating alternative courses of action To satisfy curiosity
relative frequency
____the proportion of total frequency in any given class interval in a frequency distrib. is individual class frequency divided by the total frequency Percentage or proportion of the whole number of data.
nonmetric data
___are most limited data in terms of types of statistical analysis that can be used with them -lowest level -nominal and ordinal -qualitative data -can use in nonparametric stats
pie chart
___circular depiction of data where area of whole pie represents 100% of the data and slices of the pie respresents a percentage of the sublevels
stem and leaf plot stem leaf
___numbers are divided into two parts: stem and leaf - ___(listed individually)=leftmost digits of numbers -___= rightmost digits
cross tabulation
___process for producing a two dimensional table that displays the frequency counts for two variables simultaneously
MEDIAN
___the middle value of ascending data Not affected by extreme values (outliers) ex.only if sensitive to outliers!!! examples... - Personal income Ages House prices Medical results Grades
ogive
__a cumulative freq. polygon construction begins by labeling x-axis w/ class endpoints and y-axis with frequencies. -most useful by researchers to det. running totals
mean
__is affected by every observation's value -is pulled toward extreme values
contingency table
__referred in excel as pivot table
probability statements
__to estimate the level of confidence in the result of a process
line chart
a chart that uses points connected by a line to illustrate values in a worksheet
standard deviation
coefficient of variation VS __________ Some financial investors use the coefficient of variation or the standard deviation or both as measures of risk.
subjective approach...complemet ...union of two events ....4,26,2...........intersection of events .......PROB RULES
ex of _______ Probability based on individual's past experience, personal opinion, analysis of situation When there are no precise mathematics and no large number of historical trials available Examples When you wake up in the morning, look out the window and figure that because there are no clouds it won't rain today, so don't take your umbrella with you What is the probability that the price of Apple stock will rise within the next 30 days? ____ Event consisting of all sample points that are "not in A". ____Event that occurs when either A or B or both occur (denoted "A or B") It is the possibility of drawing either a queen (____ ways) or a red card (____ ways) or both (____ ways). ________Event that occurs when both A and B occur (denoted "A and B"). ______ The probability of an event A is equal to the sum of the probabilities of the elementary events forming A. That is, if: then: Probability rule for an event 38 A = {e1, e2, e3} P(A) = P(e1) + P(e2) + P(e3)
examples of classical approach..... exhaustive, ....cond.prob......rel. freq.........larger...accurate...rel. freq approach
ex of ________ Lottery Casino Gambling Teaching Probability Beads in an Bowl Decks of Cards Coin Tosses P(A| B) = P(A and B)/P(B) . The probability of one event, given that another event has occurred B is the event known to have occurred and A is the uncertain event whose probability you seek, given that B has occurred_______ :_____ Assigning probabilities based on experimentation or historical data. P(E)= . NUMBER OF TIMES E OCCURS/ n The ______ the number of observations used to calculate the probability, the more_____ it is Applications limited to situations where there are a large number of identical trials.______
heads or tails 1,2,3,4,5,6 right or wrong win or lose red, green,yellow
experiment. outcomes -flip a coin once...................................... _____________ -roll a single die ..................................... _____________ -guess T/F question................................ _____________ -presidential election.............................____________ -color of approaching traffic light...................______________
Line charts scatter diagram
graphing quantitative data ___: Show values of one variable vs. time ____Plots two quantitative variables against one another.
large numbers relative frequency
law of_____ For a very large number of toss, we believe that approximately half of the outcomes would be heads ____: assigning probabilities based on experimentation or historical data..P(e)=number of times e occurs/n The larger the number of observations used to calculate the probability the more accurate it is ex. records show it has rained in SD 9 of the 300 weekends P(rain in San Diego on a weekend) =9/300 = 0.03
quartiles
the numbers that separate the set into four equal parts
C
which of the following is an outcome ____ A. Choosing two business cards from a jar B. Selecting a card from a deck of cards C. Getting a '6' on a roll of a die D. None of the above
