The art and science of collecting, analyzing, presenting, and interpreting data.

In business, it gives managers a better understanding of business enviroment, enabling them to make more informed and better desicions. 

Data

Data Set

The facts and figures that are collected, analyzed and summarized for presentation and interpretation.

all the data collected in particular study

The set of measurements for a particular element

# is equal to # of elements

The number of measurments obtained for each element is queal to the number of varibles. 

total # of data items= # of observations multiplied by the # of variables. 

determines the amount of information contained in the data and indicates the data summarization and statistical analysis that are more appropriate.

Nominal

Ordinal

Interval

Ratio

data are labels or names

can be numeric or nonnumeric

The data have the properties fo nomral data and cab be orderedin some meaningful way. RANKED

Ex. Survey: Excellent, Good, Poor

The data have the properties of interval data and contain an absolute zero value resutling in meaningful ratios.

Ex. Distance, Height, Weight, and Time

It indicates how much or how many

it can be discrete or continuous.

Qualitative variable is limited in terms of statistical analysis because its nominal. Its hard to do arthematic on the data.

Quantitative variables you are able to find the mean, median, mode, etc. as well as add, divide, mulitply, etc. 

Data that is collected over a period of time or series of time periods...

ex. Weather throughout the Year in San Diego

 When a Statistical Study is Experimental.. the researchers...

make no attempt to control the independent variable.

ex. survey for a restruant. 

The set of all elements of interest in a particular study.

• improper sampling

• inappropriate analysis of the data

• Development of misleading graphs

• use of inappropriate summary statistics
• biased interpreation of the statisical results
• multiple tests until a desired result is obtained

arithmetic average or average value of a variable

** Most important measure of location**

add up the numbers and divide by the total number of participants. The data can be skewed with an outlier. 

The middle value when the data is sorted in ascending order.

To compute the median, sort the data in ascending order:

if n is odd, the median is the middle number

if n is even, the median is the average of the two middle numbers

The value occurs at the greatest frequency.

** There is NO MODE if no number is repeated**

*There can also be MULTIPLE MODES**

(ex. 1,2,2,3,3,5) mode- 2&3

symmetrical

(1)mean (2)median (3)bellshape curve

Mode

ex. distribution of soft drinks.

Want to know which soft drink is purchased most frequently.. Coke Classic

the p^th percentile is a value that at least p percent of the observations are ≤to this value and at least (1-p) percent of the observations are ≥ to this value

ex. 67 percentile

67 percent fall below this percentile while 33 percent are above this percentile. 

1. sort data in ascending order (small to large)

2. compute an index- i

i= (p/100)n

*p= percentile of interest, n=# of observations/times, i= the item which is in the P percetile

3. (a) if i is not an interger, round up.the next interger greater than i denotes the position of the p^th percentile. 

(b) if i is an interger, the p^th percentile is the average of the values in positions i and i+1

Q_{1= first quartile, or 25th percentile}

Q_{2= second quartile, or 50th percentile (median)}

Q_{3= third quartile, or 75th percentile}

IQR=Q₃-Q₁

Its the range for the middle 50% of the data.

It overcomes the dependency on extreme values

measure of variabiltiy that utizles all the data.

its the difference between the value of each observation (x_i) and the mean

often reffered to as the standardized value. it is a number of standard deviations an observation is away from the mean. it tells you the location.

normal

exception: can sometimes be used in similar distributions

(1)If Z score is positive, its ______ the mean

(2)If Z score is negative, its ______ the mean

(1) above

(2) below

µ±1σ(_{STD DEV)}≈68%

µ±2σ(_{STD DEV)}≈95%

µ±3σ(_{STD DEV)}≈99.7%

1. Smallest Value

2. First Quartile (Q₁)

3. Median (Q₂)

4. Third Quartile (Q₃)

5. Largest Value

If the Correlation Coefficient is _________, the variables go in the same direction.  

/

If the Correlation Coefficient is _____________, the variables go in the opposite direction. 

\

positive

negative

What is the experimental outcome when you...

Toss a Coin

Select a part for inspection

conduct a sales call

roll a die

play a football game

heads/tails

defective/nondefective

purchase/ no purchase

1,2,3,4,5,6

win, lose, tie

its a numerical measure of the likelhood that an event will occur

on any single repeitition of an experiment, how many possible experimental outcomes will occur?

(in reference to probability)

if an experiment can be described as a sequence of k steps with n₁ possibile outcomes on the first step, n₂ possible outcomes on the second stpeh, and so on, then the total number of experimental outcomes is given by (n₁)(n₂)...(n_k).

ex. tossing 2 coins. what are the possible outcomes?

n1=2; n2=2, so (2)(2)=4.

in a combination

0! = ?

1

5! is equal to..

(5)(4)(3)(2)(1)= 120

DOES

The three approaches most frequently used to assign probabilties are:

1. Classical

2. Relative Frequency

3. subjective methods

top 2 are the best approaches*

classical

1

n

is used in the ________method

n being the experimental outcomes

classical

relative frequency 

subjective method. 

*its arbitrary, its a feeling, there isnt hard data, its pretty common espeically when data is hard to obtain. 

For an experiment to be assigned probabilties it must:

(2 things)

1. the outcome must be between 0 and 1.

2. the sum of the probabilties for all the experimental outcomes must equal 1. 

what is an event?

(probability, ch.4)

is a collection of sample points or experimental outcomes.

What is the probability of an event?

It is equal to the sum of the probabilities of the sample points in the event. 

Given an event A, What is the complement A?

its the event consisting of all sample points that are not in A. The completment of A is denoted by A^c

P(A)+ P(A^c)=

1

The _________ of A and B is the event containing all sample points belonging to A or B or both. It is denoted by ________.

union

A υ B

Given two events, A and B, the _____________ of A and B is the event containing the sample points belonging to both A and B.  Its denoted by ________

intersection

A ∩ B

What is the Addition law?

it is used to compute the probability of the union of two events.

P(AUB)= P(A)+P(B)-P(A∩B)

What are Mutually Exclusive Events?

Two events are said to be Mutually Exclusive if the events have no sample points in common. 

What is the Addition Law for Mutually Exclusive Events?

P(AUB)= P(A)+P(B)

P(A∩B)= 0 when A & B are ___________.

mututally exclusive (disjoint)

P(A|B) reads:

The probability of A given B

What is Conditional Probability?

The probabulity of an event given that another event already occurred.

The conditional probability of A given B is P(A|B)= P(A∩B)/P(B)

What is Joint Probability?

THe probability of two events both occurring; that is, the probability of the intersection of two events.

What is Marginal Probability?

The values in the margins of a joint probability table that provide the probabilities of each event separately. 

What are independent events?

two events A and B where P(A|B)=P(A)

or P(B|A)=P(B);

that is, the events have no influence on each other. 

What is the Multiplication Law?

A probability law used to compute the probabilty of the intersection of two events.

For Dependent events: P(A∩B)= P(B)P(A|B) or  P(A∩B)= P(A)P(B|A).

For Independent events:P(A∩B)= P(A)P(B)