Managerial Statistics
Terms
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- operational definition of variables
- specifies just how a variable is measured or counted
- processes
- systematic, repetitive actions whose purpose is to create something of value
- rework
- undoing and redoing actions taken previously
- scrap
- complete adandonment of a partly completed task
- sampling
- a plausible approach to data gathering any time potentially valuable data are to be gathered by complete data would be impossible or uneconomical to gather
- experimentation
- an approach to data gathering that is a key component of the drive to improve quality of products and processes
- frequency table
- a table that specifies the distribution of the data of the frequencies in which all the various values occur
- relative frequency
- the frequency of a value divided by the total number of measurements
- qualitative data
- Data that counts the numbers or percentage in a particular category that have an attribute or characteristic. (e.g. eye color, brand preference, quality errors)
- bar chart
- A method of displaying counts of attribute data. - use rectangles to porray the data
- quantitative data
- Numerical data that measures some variable of interest - often a measurement on a continuous scale where magnitude is significant information. (e.g. amount of an additive in a process, rotational speed of a drill bit, expenditures on advertising)
- grouped data
- combining of values from a variable that has many possible values
- classes
- choice of groups
- histograms
- often used with grouped data, these charts are always used with quantitative data - rectangles are diretly adjacent
- skewed
- data on a chart with a long tail in one direction or the other
- outliers
- data values that lie far above or below the preponderance of the data
- bimodal
- two distinct peaks in a distribution separated by a pronounced valley
- stem-and-leaf diagram
- A method for displaying data that both shows the data set and a kind of histogram of the data.
- time series plot / sequence plot
- a graph of the data values of a quantitative variable versus time or collection order
- seasonality
- a reaoccuring pattern in the data
- trend
- a gradual increase or decrease in the in the data over time
- two-way frequency table / cross-tabulation
- an appropriate tabular summary for 2 qualitative variables
- stacked bar chart / 100% stacked bar chart
- useful graphical displays for 2 qualitative variables
- scatterplot
- the best tool for visualizing the relationship between 2 quantitative variables
- mode
- the value or category with th highest frequency in the data - most commonly used with qualitative data
- average
- mode, median,or mean
- median
- the middle value of a set of data when the data is arranged from lowest to highest.
- mean
- the sum of the measurements taken on that variable divided by the number of measurements - only meaningful for quantitative data
- trimmed means
- a process that eliminates the outliers when determining the mean
- measures of location / measures of central tendancy
- mode, median, mean, trimmed means - indicate the center or general location of data values
- range
- the difference between the largest and smallest values - the simplest measure of variability
- mean absolute deviation
- the simplest measure of the magnitudes of the deviations - the average of the absolute values of the deviations
- variance / mean squared error
- the average squared devation - the sum of the squared deviations divided by (n-1)
- standard deviation
- the positive square root of the variance
- interquartile range
- 25th and 75th percentiles - the values that mark the bottom 1/4 and top 1/4 of the data
- e-notation
- exponents used in computer outputs
- pareto chart
- A bar chart that ranks the categories from highest to lowest
- means chart / x-bar chart
- a plot of times versus means of observations taken at those times
- statistical control
- the state of a process that is operating consistently, wherein the means will vary randomly, but won't show any systematic changes
- r chart
- a result of when data is taken over time and the range is plotted against time - shows that a problem is developing over time
- s chart
- a plot of standard deviations against time - a useful quality control tool in assessing whether there has been a change in variability
- cusum chart
- a chart that keeps track of the cumulative sum of a series of measurements
- random variable
- a quantitative result from a random experiment that is subject to random variability. it is determined by specifying its possible values and the probability associated with each value.
- discrete
- variables whose possible values are distinct and seperate, like 0, or 1, or 2, or 3.
- continuous
- variables whose possible values form a whole interval or range
- probability distribution
- this for a discrete random variable Y assigns a probability to each value y of the random variable Y. Can be expressed as a formula, graph, or a table.
- probability histogram
- graph of a probability distribution
- cumulative distribution function
- for a discrete random variable Y is a function that specifies the probability that Y<=y for all values of y.
- expected value
- of a discrete random variable Y with probability distribution Py(y) is the probability-weighted average of its possible values
- Expected value of Y - E(Y)
- a porbability-weighted average, a summary figure that takes into account that relative probabilities of different values of Y - or a long run average of Y
- variance of a discrete random variable
- the probability-weighted average of squared deviations from the mean (expected value)
- pie charts
- A method of displaying proportions of attribute data that fell in various exhaustive catagories.
- sttribute (nominal) data
- A type of qualitative data where the only measure is that the item has the attribute or does not. (e.g. marital status, yes/no responses, brand preference (like/dislike))
- bar charts
- A method of displaying counts of attribute data.
- Box plot
- A graphical depiction of a data set that uses a box to show the 1st and 3rd quartiles and whiskers to show the minimum and maximum values. Asterisks are used to show outliers - anamoly values determined to be outside of reasonable minimum and maximum.
- maximum
- the largest value in data set
- minimum
- the smallest value in a data set
- Ranked (oridnal) data
- A type of qualitative data in which the measure goes beyond attribute data and actually ranks how much of the attribute the item has. (e.g. Bond ratings Aaa, Aa, A, Baa; brand preference (ranked best to worst))
- stratification
- A method to "break down" a larger data set into a set of smaller data sets by some factor.
- regression analysis
- past dara on the relevant variables (independant variables) are used to develop and evaluate a prediction equation (dependant variables)
- dependant variable
- the variable that is being predicted by regression analysis
- independant variable
- the variable that is being used to make the prediction in regression analysis
- prediction v. explanation
- reference to future values v. reference to current or past events
- unit of association
- an entity that relates two variables
- simple linear regression
- there is a single independent variable, and the equation for predicting a dependant variable y is a linear function of a given independant variable x
- intercept
- the constant term that is the predicted value of y when x=( ).
- slope
- The predicted change in y when there is a one-unit change in x
- linearity assumption
- the slope of the equation does not change as x changes
- smoothers
- have been developed to sketch a curve through data without necessarily assumingany particular model
- least-square method
- used to minimize the the total squared prediction error.
- NORMAL DISTRIBUTION
- THE MOST COMMONLY USED SYMETRIC BELL-SHAPED DISTRIBUTION CURVE
- DSTRIBUTION
- THE PATTERN FORMED AS YOU COLLECT MORE DATA AND THE PICTURE BECOMES MORE REFINED
- PARAMETERS
- DETERMINED QUANTITIES THAT SPECIFY DIFFERENT FEATURES OF THE DISTRIBUTION
- COEFFICIENT OF VARIATION
- THE COMMON EXPRESSION OF STANDARD DEVIATION AS A PROPORTION OR PERCENTAGE OF THE MEAN
- SAMPLE VARIANCE
- THE SQUARE OF THE STANDARD DEVIATION
- STANDARD NORMAL DISTRIBUTION
- HAS A MEAN OF ZERO AND A STANDARD DEVIATION OF ONE
- CHI-SQUARE DISTRIBUTION
- TELLS THE PROBABILITY OF THE SAMPLE RESULT (THE ACTUAL NUMBERS) HAVING ARISEN PURELY BY CHANCE
- DEGREE OF FREEDOM
- THE NUMBERS WILL IDENTIFY A ROW OF THE CHI-SQUARE TABLE
- CHITEST
- A STATISTICAL FUNCTION THAT SHOWS THE PROBABILITY THAT THE DIFFERENCES BETWEEN WHAT WE OBSERVE AND WHAT WE WOULD EXPECT ARE DUE TO CHANCE - GIVES US THE EXACT PROBABILITY, WHICH WE CAN THEN USE TO JUDGE WHETHER THE DIFFERENCES ARE REAL OR NOT
- STANDARD ERROR OF PROPORTIONS
- STANDARD DEVIATION OF A PROPORTION