Business Analytics 2600 Final Exam Review

coefficient of variavtion

(standard deviation/mean) x 100%

if A and B are independent events, P(A)=.2, P(B)=.7, determine P(AUB)

.2+.7-(.2*.7)=.76

0!

1

continuous probability distributions

1. Normal distribution 2. Exponential distribution

discret probability distributions

1. binomial distributions 2. poisson distribution

If n=15 and p=.4, then the standard deviation of the binomial distribution is______

1.897

a normal population has 99.73 percent of the population measurements within ________ standard deviation(s) of the mean

3

third quartile

75th percentile

intersections

A and B are elementary events that belong to both A and B; written as A upside down U B

union

A and B are elementary events that belong to either A or B or both

tree diagram

A diagram used to show the total number of possible outcomes

scatter plot

A graph with points plotted to show a possible relationship between two sets of data

stem and leaf plot

A system used to condense a set of data where the greatest place value of the data forms the stem and the next greatest place value forms the leaves

box-and-whisker plots

A way of graphically depicting groups of numerical data through their quartiles

let A, B, and C be events and assume the following probabilities: P(A)=0.2, P(B)=0.3, P(C)=0.5, P(A and B)=0.06, P(A and C)=0, P(B and C)=0.5; which two of the three events are mutually exclusive?

A, C

which if the following is not a discrete random variable? a: the number of times a light changes red in a 10-min cycle b: the number of minutes to run 1 mile c: the number of defects in a sample selected from a population of 100 products d: the number of criminals found in a five-mile radius of a neighborhood

B

mail survey

Inexpensive, Low response rates (20-30 percent), Requires multiple mailings

percent frequency

Multiply relative frequency by 100

multiplication rule if A and B are independent

P(A and B) = P(A)P(B)

the addition rule (not mutually exclusive)

P(AUB)=P(A)+P(B)-P(A upside down U B)

five number summary

Q1-25% Q2-50% Q3-75% Max Min

interquartile range (IQR)

Q3-Q1

qualitative

the possible measurements fall into several categories; categorical

quantitative

the possible measurements of the values of a variable are numbers that represent quantities

conditional probability

the probability of an event A, given that the event B has occurred, is called the conditional probability of A given B; P(A|B)=A(A upside U B)/P(B)

random variables

the quantitative value that represents the outcomes from an experiment

standard deviation

the square root of the population variance

probability of an event

the sum of the probabilities of the sample space outcomes

skewed left

the tail to the left of the peak is longer than the tail to the right of the peak

skewed right

the tail to the right of the peak is longer than the tail to the left of the peak

the addition rule (mutually exclusive)

then the probability that A or B (the union of A and B) will occur is: P(AUB)=P(A)+P(B)

x, n, p, q

x: number of success n: number of trials p: p(successes) q: p(failure): 1-p

x, u , e

x: take any values x=0,1,2,3 u: mean of expected number of occurrences of a specific interval e: 2.71828

z-score<0

x<mean

z-score=0

x=mean

z-score>0

x>mean

histogram

a bar graph depicting a frequency distribution

pie chart

a circle divided into slices where the size of each slice represents its relative frequency or percent frequency

discrete probability distribution

a discrete random variable is a table, graph, or formula that gives the probability associated with each possible value that the variable can assume

ogive

a graph that represents the cumulative frequencies for the classes in a frequency distribution

dot plots

a graph where dots that represent the value of data are plotted above a number line

frequency distributions

a list of data classes with the count of values that belong to each class

ordinal

a qualitative variable for which there is a meaningful ordering, or ranking, of the categories (ex:teaching effectiveness)

nominative

a qualitative variable for which there is no meaningful ordering, or ranking, of the categories (ex: gender, color, car color)

population

a set of all elements about which we wish to draw conclusions

event

a set of sample space outcomes

sample

a subset of the elements of a population

frequency distribution

a table that summarizes the number of items in each of several non-overlapping classes

random variable

a variable whose value is a numerical value that is determined by the outcome of the experiment (discrete and continuous)

bar chart

a vertical or horizontal rectangle represents the frequency for each category; only for categorical

multiple choice questions

allow more than two responses, usually analyzed with averages

sample space

an experiment is the set of all possible outcomes

variable

any characteristics of an element

web surveys

cheaper still, same problems as mail surveys

dichotomous questions

clearly stated, easy to answer, easy to analyze, limited information

event A(upside down U)B is the shaded region

common share; =0

non-probability sampling

convenience, voluntary, and judgement sampling

cross-sectional data

data collected at the same or approximately the same point in time

time series data

data collected over different time periods

used in survey research

dichotomous, open-ended, multiple choice

contingency table

displays counts and, sometimes, percentages of individuals falling into named categories on two or more variables; categorizes the individuals on all variables at once, to reveal possible patterns in one variable that may be contingent on the category of the other

cluster sampling

divide population into clusters and then randomly select clusters to sample

stratified random sampling

divide population into non-overlapping groups (strata) then select a random sample from each strata

complement

event a is the set of all samples space outcomes not in A

data

facts and figures from which conclusions can be drawn

first quatile

first 25%

z-scores

for any x in a population or sample, the associated z score is x-mean/standard deviation; the number of standard deviations that x is from the mean

empirical rule

if a population has mean u and standard deviation o and is described by a normal curve (68.26,95.44, 99.73)

phone survey

inexpensive, low response rate

the ________ of two events A and B is the vent that consists of the samples space outcomes belonging to both event A and event B

intersection

ratio

interval plus... measurements are on a numerical scale with a meaningful zero point; values can be compared by their intervals and ratios; such anything related to money (Ex: earnings, profits, loss)

expected value of a discrete random variable

is the average value for the random variable over many repeats of the experiment

chebyshev's theorem

let u and o be a population's mean and standard deviation, then for any value k>1

probability

likelihood that a particular event will occur

systematic sampling

list population, select random starting point, sample each nth element

continuous random variable

may assume any numerical value in an interval or collection of intervals

outliers

measurements that are very different from other measurements; lie beyond the limits of the box-and-whiskers plot

if a population distribution is skewed to the right, then, given a random samples from that population, one would expect that the

median would be less than the mean

second quartile

median; 50th percentile

the measurement in a sample or a population that occurs most frequently is the

mode

personal interviews

more expensive, more control, higher response rates

open ended questions

most honest and complete information, cannot be readily summarized

if two events are independent, we can _____ their probabilities to determine the intersection probability

multiply

sample size

number of elements, n

interval

ordinal plus... measurements are on a numerical scale with an arbitrary zero point (ex: temperature0

event AUB is shaded

p(A)+P(B)-(A upside down U B)

u

population mean

discrete random variable

possible values can be counted or listed

nominative and ordinal

qualitative/categorical; names/labels

interval and ratio

quantitative; how many/how much numerical

symmetrical

right and left tails of the histogram appear to be mirror images of each other

xbar

sample mean

judgment sampling

samples in which a person who is extremely knowledgeable about the population selects population elements he or she feels are most representative

voluntary sampling

samples in which participants self-select

probability sampling

sampling where we know the chance that each element in the population will be included in the sample

convenience sampling

sampling where we select elements because they are convenient to sample

relative frequency

summarizes the proportion of items in each class; frequency number of each class/data size (total)

variance

the average of all squared deviations of all population measurements from the population mean

data set

the data that are collected for a particular study

multiplication rule

the joint probability that A and B will occur is P(A upside down B)=P(A)*P(B|A)