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115 Cards in this Set
- Front
- Back
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What is statistics
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branch of math that transfors data into useful information for decision making
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Why do we study statistics?
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present and describe data
draw conclusions about lg. pop make reliable forcasts improve process |
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What is inferential statistics?
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branch of stats that use sample data to draw conclusions about an entire population
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What is a variable?
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characteristic of an item or individual
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What are operational definitions?
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universally accepted meanings that are clear to all associated with analysis
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What is a sample?
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portion of a population selected for analysis
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What is a parameter?
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numerical measure that describes a characteristic of a population
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What is a statistic?
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numerical measure that describes a characteristic of a population
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Name two data sources
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Primary (data used by primary data collector) and Secondary (non-data collector using statistics)
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Four Sources of Data
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Data dist. by organ or indiv.
Designed experiment Survey Observational Study |
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What is a categorical variable?
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"qualitative" values that can only be placed into categories such as "yes" and "no" or days of the week
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What are the types of variables?
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Categorical and Numerical (numerical then divided into discrete and continuous)
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What is a numerical variable?
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"quantative" has value that represents quantaties (subdivided into discrete or continuous)
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What is a discrete variable?
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numerical values that arise from a counting process
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What is a continuous variable?
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produces numerical responses that arise from a measuring process (no two cont. variables will be identical)
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What are the types of scales?
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Nominal
Ordinal Interval Ratio |
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What is a nominal variable?
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Classifies data into distinct categories in which no ranking is implied (weakest form)
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What is an ordinal scale?
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classifies data into distinct categories in which ranking is implied (excellent, very good, fair, poor) weak form
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What is a ratio scale?
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ordered scale in which the difference btwn measurements involves a true zero point (age, weight, salary)
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What is an interval scale?
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ordered scale in which the diffs btwn msuremnts is a meaningful quantity but does not involve true zero point
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What is a pie chart
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circle broken up into slices that represent categories; size varies according to %
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What is a summary table?
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indicates freq amt of % of items in set of categories so diffs can be seen btwn cat. (cat/freq, amt. or % in diff col.)
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What is a bar chart?
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shows category and length of which rep. the amt, freq. or % of values falling into category
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When do you use a bar chart?
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if comparison of categories is most impt.
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When do you use a pie chart?
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when observing the portion of the whole that is in a particular category is most impt
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What is the Pareto Principle?
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Exists when maj. of items in set of data occur in small # of cat. & few remaining items are spread out over lg # of cat.
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What is a Pareto Diagram?
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Categorized responses are plotted in descending order according to freq. and are combined with a sum % line on same chart (prioritizing improvements)
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What is an ordered array?
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sequence of data, in rank order, from smlest to lgest
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What is a stem and leaf display?
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organizes data into grps ("stems") so values in each grp (leaves) branch out to the right on each row
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What is a frequency distribution?
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summary table in which data are arranged into numerically ordered class grpings (draw conclusions about maj char.)
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What are class groupings?
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must establish appropriate # and suitable width & boundaries to avoid overlap
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What are class boundaries?
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place each value in one and only one class
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What is class midpoint?
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center of each class (halfway btwn lower boundary and upper boundar of class)
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What is the width of class interval?
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Width=range/#of desired class groupings
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What is the range?
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highest value - lowest value= range
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What is relative frequency distribution?
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dividing freq. in each class of freq. dist. by the total # of values
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What is percentage distribution?
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multiply each relative freq. by 100%
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What is cumulative % distribution?
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provides way of presenting info. about the % of items that are less than a certain value
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What is a histogram?
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bar chart for grped numerical data in which freq. or % of ech grp of num. data are represntd as indiv vertical bars (no gaps)
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When do you use histogram, polygons and/or cumulative % polygons?
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when analyzing a single numerical value
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What is a cumulative percentage polygon?
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"Ogive" displays the variable of interest along the X axis & the cumulative % along theY axis
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What is a contingency table?
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presents results of two categorical variables
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What are the cells in a contingency table?
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values located at the intersection of the rows/columns
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What is a side by side bar chart?
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useful way to visually display the result of cross-classification data
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When do you use scatter plots and time series plots?
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when analyzing two numerical values
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What is a scatter plot?
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examines possible relationships btwn two num. variables
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What is a time series plot?
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Studies patterns in the values of a numerical variable over time
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What kinds of charts obscure data in Excel?
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doughnut, radar, surface, bubble, cone and pyramid
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What are guidelines for developing good graphs?
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do not distort data; title; no cartjunk; two dimensional; scale on vertical axis should start at 0; simplest possible
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What is central tendency?
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extent to which all data values group around a typical or central value
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What is a variation?
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amt of dispersion or scattering of values away from a central value
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What is a shape?
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pattern of distribution of values from the lowest to highest values
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What are the 3 measures of central tendency?
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mean, median, mode
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What is the arithmetic mean "mean"
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most common measure of central tendency "balance point"
Mean = sum of values / # of values |
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What is the summation notation?
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all n values added together
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What is the summation of the square?
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in stats the squared values of variables are often summed
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What is the square of the sum?
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the summation notation then squared
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What is the sample mean?
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Sum of values divided by the # of values
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What does n equal?
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number of values or sample size
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What is an outlier?
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extreme value
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What is the median?
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middle value in a set of data (if odd number is middle number is set....if even is average of two middle values)
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What is the mode?
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the most frequently occuring value in a set of data
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What is the middle quartile?
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the median
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What are the rules for calculating quartiles?
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whole number = ranked value
fract. 1/2 = avg. of corresp. ranked values if not whole or fract 1/2 then result is rounded to nearest integar and select that ranked value |
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What is the geometric mean?
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measures rate of change of variable over time
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What does variation measure?
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spread or dispersion of values in a data set
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What is the range?
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measure of variation; diff btwn lgest and smallest values
"simplest umerical descriptive measure of variation in data set |
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What are the two most common measures of variation?
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variance and standard deviation
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What is a shape of data set?
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repreesnts pattern of all values from lowest to highest
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What is the range?
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midspread "middle fifty" Q3-Q1 (cannot be affected by extreme values)
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What is resistant measures?
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summary meausres such as median, Q1, Q3, and interquartile range which cannot be influenced by extreme measures
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What do variance and standard deviation measure?
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the "average" scatter around the mean - how larger values fluctuate above and smaller values distribute below
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What is the sum of squares (SS)?
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squares the difference btwn each value and the mean and then sums these squared differences
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What is the sample variance?
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sum of the squared differences around the mean divided by the sample size minus one
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What is the sample standard deviation?
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square root of the sum of the squared differences around the mean divided by the sample size minus one
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What is the coefficient of variation?
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relative measure of variation always expressed as a % rather than in terms of units of the particular data **measures scatter relative to the mean**
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What is considered an outlier in Z-scores?
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anything above 3.0 or below -3.0
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What is the shape?
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pattern of dist. of data values throughout entire range of all variables
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What are the types of distribution?
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symmetrical and skewed (values not symmetrical around the mean)
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What does left skewed mean?
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mean < median: negative
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What does right skewed mean?
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mean > median: positive
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What does symmetrical mean?
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mean = median: symmetrical
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What are parameters?
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summary measures for a population
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What are population parameters?
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population mean
population variance population standard deviation |
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What is a population mean?
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sum of values in the population divided by the size N
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What is the general addition rule?
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The probability of A or B is equal to the probability of A plus the probability of B minus the probability of A and B
P(AorB)=P(A)+P(B)-P(AandB) |
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What does collectively exhaustive mean?
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when one of the events in a set of events must occur
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What is mutually exclusive?
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when both events cannot occur simultaneously
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What is joint probability?
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the probability of an occurrence involving two or more events
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What is marginal probability?
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"simple probability" because it enables you to compute the total # of successes from the appropriate margins of the contingency table
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What is simple probability?
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probability of occurrence of a simple event P(A)
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What is a contingency table?
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way to present a sample space
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What is a sample space?
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collection of all possible events
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What is a complement of event A "A"?
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All parts that are not part of event A
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What is a joint event?
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an event that has two or more characteristics
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What is a simple event?
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a single characteristic
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What is an event?
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each possible outcome of a variable
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What is subjective probability?
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differs from person to person (useful in making decisions when you cannot use a priori or empirical classical)
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What is the probability of occurrence?
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the # of ways in which events occur / the total # of possible outcomes
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What is empirical classical probability?
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outcomes are based on observed data, not on prior knowledge of a process
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What is a priori classical probability?
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the probability of success is based on prior knowledge of the process involved
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What are three approaches to the subject of probability?
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a priori classical probability
empirical classical probability subjective probability |
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What is an impossible event?
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event that has no chance of occurring....probability of 0
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What is a probability?
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numeric value representing the chance, likelihood or possibility a particular event will occur
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What is the empirical rule?
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68% of values are within 1 standard deviation from mean; 95% are within 2 sd of the mean and 99.7% are within 3
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What is chebyshev rule?
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states that for any data set, regardless of shape, the % values that are found within a distance of K standard deviations from the mean must be at least (1-1/K squared) x100%
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What is a five number summary?
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X smallest, Q1, median, Q3, X largest
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What is a box and whisker plot?
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graphical representation of the data based on the five number summary
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What is covariance?
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measures strength of the linear relationship between 2 numerical variables (X & Y)
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What is the coefficient of correlation?
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measures the relative strength of a linear relationship between two numerical variables
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What is Bayes' theorem?
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used to revise previously calculated probabilities based on new info.
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What is conditional probability?
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probability of Event A given info about the occurrence of another Event B
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What is a decision tree?
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alternative to contingency table
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What is statistical independence?
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when outcome of one event does NOT affect theprobability of occurrence of another event
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What is the general multiplication rule?
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Probability of A & B is equal to the probabilityof A given B times the probability of B
P(A&B)=P(A\B)P(B) |
