CBAD 291 Unit 1

disadvantages of mode

no mode because of repeat values, 2 modes because more than one value repeats, used less frequent than mean or median bc of disadvantages

Interval simple

numerical data-data that is natural measured (by default) in numbers -no meaningful zero point

Qualitative

object or individual observed is recorded as non numeric characteristic -often summarized in charts & bar graphs

Independence

occurrence of one event has no effect on the probability of the occurrence of another event (A and B occur at different times)

Mutually exclusive

occurrence of one event means that none of the other events can occur at the same time

Combination Formula

order of selected objects is not important, number of combinations is always less than the number of permutations -R object combinations, set of objects

outcome

particular result of an experiment

Empirical Probability

probability of an event happening is the fraction of the time similar events happened in the past

Joint Probability

probability that measures the likelihood two or more events will happen concurrently

experiment

process that leads to the occurrence of one and only one of several possible results

sample

proportion, or part, of the population of interest -Used when you can only survey a limited number of population to obtain reasonable estimates of population parameters

Tree Diagrams

summarizes all probabilities based on the contingency table

median

the midpoint of the values after they have been ordered from the minimum to the maximum values

Statisitcs

the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions

the mode

the value of the observation that appears most frequently -can determine for nominal, ordinal, interval, ratio

Special Rule of Multiplication

two events A & B are independent

3 reasons for studying statistics

1. Data is collected everywhere and require statistical knowledge to make the information useful 2. Statistical techniques are used to make professional and personal decisions 3. No matter what career, you will need a knowledge of statistics to understand the world and to be conversant in your career More effective in personal & professional decisions

Contingency table

a table used to classify sample observations according to two or more identifiable categories or classes

parameter

any measurable characteristic of a population

Collectively exhaustive

at least one of the events must occur when an experiment is conducted, every possible outcome -mutually exclusive & sum of probability is 1

sample mean

average of sample

Examples of Quantitative

balancing check account, number of people employed at company, battery life in years

Population

entire set of individuals or objects of interest or the measurement obtained from all individuals or objects of interest

Special Rule of Addition

events must be mutually exclusive

Chebyshev's Theorem

for any set of observations (sample or population), the proportion of the values that lie within k standard deviations of the mean is at least 1-1/k^2, where k is any value greater than 1

Why do we need levels of measurement?

Level of measurement impacts which statistical tests you can & can't use

Tasks in statistics

-Collecting & processing information to create a conversation -Stimulate additional questions -Provide basis for making decisions

Which of the three measures of location would be used as the location set of data?

-If symmetrical, mean is usually reported -Long tail to the right, positively skewed-depends -Long tail to the left, negatively skewed-depends

Example of nominal

-M&M classified by color (any color can be listed first)

What IS statistics?

-Set of knowledge and skills used to organize, summarize and analyze data -Results of statistical analysis used to help us make decisions -ex. 2.3% interest rate, next year, higher or lower?

Example of qualitative

-brand -maritial status -hair color -gender -preference

Population mean

-considers data of all people involved =sum of all the values in the population/number of values in population

Probability

-decimal or percent -a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur -1 certain to happen -0 not going to happen

arithmetic mean (normal mean)

-most widely used & reported -data measured at the interval or ratio level -all values are included in computing the mean -only ONE mean in set of data

major properties of median

-not affected by extremely large or small values -it can be computed for ordinal level data or higher

Law of Large Numbers

-over a large number of trials, the empirical probability of an event will approach its true probability -basis of empirical approach -More observations, more accurate estimate of probability

Measures of location/averages

-pinpoint center of distribution of data

The empirical rule (normal rule)

68%-1 standard deviation +/- 95%-2 standard deviation +/- 99.7%-3 standard deviations +/-

What ARE statistics

A number used to communicate a piece of information ex. inflation rate is 2.3%

Subject Probability

The likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available

Inferential statistics

The methods used to estimate a property of a population on the basis of a sample ("random sample") -Widely applied to learn something about a population in business, agriculture, politics, and government

Ratio level data

based on a scale with a known unit of measurement and meaningful interpretation of zero on the scale -has characteristics of interval level but 0 point and ratio between two numbers are both meaningful

Classical probability

based on the assumption that the outcomes of an experiment are equally likely

Example of ordinal

businesses make decisions about where to locate their facilities based on factors like labor costs, business tax, quality of life, etc.

Continuous

can assume any value within a specific range -result from measuring

Discrete

can assume only certain values & there are gaps between the values -1, 2, 3-cannot be decimals -result from counting

Quantitative

can be reported numerically -either discrete or continuous

Ordinal simple

categorical in nature, inherent rank & order, each option has a different value -categories but have rankings

Nominal simple

characteristics or groups with no inherent order or ranking -most basic level of measurement

event

collection of one or more outcomes of an experiment

standard deviation

commonly used as a measure to compare the spread in two or more sets of observations -amounts are clustered more closely to the mean, the mean for the set is a more reliable measure

Inferential statistics simple

computing change that something will occur in the future

General Rule of Multiplication

conditional probability is required to compute the joint probability of two events that are not independent expressed as -P(A|B)-not independent

Interval & ratio are both

continuous

weighted mean

convenient way to compute the arithmetic mean when there are several observations of the same value

Nominal

data recorded are represented as labels or names, have no order & can only be classified and counted -any value can be reported first -often converted to percentages

Ordinal Level

data recorded is based on a relative ranking or rating of items based on a defined attribute or qualitative variable. Variables based on this level of measurement are only ranked or counted -ranked from best to worst, cannot distinguish magnitude of difference between responses like "good" or "poor"

Example of interval level

high temperatures can be easily ranked highest to lowest, but we can also determine the interval or distance between them Uses a constant degree of measure: 1 degree

Levels of Measurement

how data should be summarized and presented & type of statistical analysis that can be performed 1. nominal 2 ordinal 3. interval 4. ratio

Multiplication Formula

if there are m ways of doing one thing and n ways of doing another thing, there are m x n ways of doing both

or =

inclusive

Interval Level

interval or the distance between values is meaningful. The interval level of measurement is based on a scale with a known unit of measurement (includes all characteristics of ordinal level) -constant degree of measure -cannot make statements like "size 16 is twice as large as size 8" -distance between numbers makes sense, but ratios do not

statistic

mean of a sample or any other measure based on sample data is called a

average

measure of location that shows the central value of the data

Descriptive statistics

methods of organizing, summarizing, and presenting data in an informative (or meaningful) way -Ex. Predictions of how money will be spent on average

Ratio Data simple

most sophisticated level of measurement -Numerical & ordered with equal distance between points- can be measured -0 point always reflects meaningful zero point

General Rule of Addition

used to compute the probability of two events that are not mutually exclusive

Complement Rule

used to determine the probability of an event occurring by subtracting the probability of the event not occurring

Permutation Formula

used to find the number of possible arrangements when there is a single group of objects

Mean weakness

uses every single value of sample or population, if one or two are very small compared to the majority of the data, this might not be an appropriate average to represent data

dispersion

variation or spread

example of ratio level

wages, units of productions, weight, changes in stock prices -father earns twice as much as son

Sum of deviations of each value from the mean =

zero