Question Answer
Compare a 'population' to a 'sample'. Pop = set of all measurements of interestSample = subset of the population
Compare a 'parameter' to a 'statistic'. Parameter = a # deduced from the populationStatistic = a # taken from the sample data
What is the problem with populations/parameters? Or, why do we use samples/statistics more frequently? Populations and parameters are very difficult to gather. Stats gives us an accurate account of the larger groups information.
Define 'mean'. The sum of the observations divided by the # of observations. (average)
Define 'median'. The value in the middle of the data set when they are organized lowest to highest. This is averaged when there are two numbers. (middle)
Define 'mode'. The value that occurs with the greatest frequency.
Define and calculate a 'percentile'. Def – The pth percentile is a value where p percent of all observations are less than or equal to this value. i = (p/100)n, where n is the number of values. 'i' is the i'th number in the ordered list of data. note: the 50th percentile is also the median.
Calculate the 'quartiles'. Q1 :: i=(25/100)n , Q2 :: i=(50/100)n , Q3 :: i=(75/100)n
Calculate 'range'. largest value – smallest value = range
Calculate 'Interquartile Range (IQR)'. IQR = [Q1 – Q3] , Q1 :: i=(25/100)n , Q3 :: i=(75/100)n
Define the 'variance' and calculate sample variance. The measure of variability around the mean. Sample variance (denoted as s^2) = (sum of all squared deviations)/(n – 1) where "deviations" is (x'i – mean)
Define and calculate the 'standard deviation'. The standard deviation is the positive square root of the variance.
Calculate the 'coefficient of variation'. ((standard deviation / mean) x 100)%
Define and calculate the 'z-score'. aka 'the standardized value'. The number of standard deviations the value is away from the mean. (x'i – mean)/(sample standard deviation)
Define 'Chebyshev's Theorem'. At least (1 – 1/z^2) of the data values must be within z standard deviations of the mean, where z is any value greater than 1.
Define 'empirical rule'. *only used when symmetrical, bell-curve distribution* 68% of data is within 1 standard deviation, 95% is within 2 sd, and almost all is within 3 sd.
Explain how to detect an outlier. An outlier has a z-score of 3 or more (it is 3 or more standard deviations away from the mean).
Draw a Tree Diagram.
Combinations nCr
Define 'Intersection'. The points belonging to A and B.
Define 'mutually exclusive'. Neither A nor B have any similar points.