Formula Quiz 1
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| individual | an object described by a set of data
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| variable | a characteristic of an individual
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| quantitative variable | a variable that takes on a numerical value that can be measured
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| quantitative data | values of quantitative variables
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| categorical/qualitative variable | a variable that places an individual into a category
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| distribution | indicates what values a variable takes on and the frequency at which it takes these values
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| graphs of qual. | pie chart, bar chart
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| bar chart | qual.
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| pie chart | qual.
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| graphs of quan. | dotplot, histogram, stemplot
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| dotplot | quan.
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| historgram | quan.
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| stemplot | quan.
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| outlier | an individual observation that falls outside the overaell pattern of the graph
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| relative frequency histogram | has the same shape as a histogram with the exception that the vertical axis measures relative frequencies instead of frequencies
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| key features of a histogram | the center (mean, median), the spread (range), the shape
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| shapes of a graph. | symmetric, skewed left, skewed right
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| measures of center | sample mean, mode, median
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| sample mean | arithmetic average or arkithmetic mean
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| mode | element or elements that occur most often
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| median | "the middle number"/average of two middle numbers
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| median position formula | (n+1)/2 (n=number of numbers in the data set)
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| mean=median when... | distribution is perfectly symmetric
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| when it is skewed right | the mean is dragged to the right
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| when it is skewed left | the median is dragged to the left
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| measures of spread | range, iqr, five number summary, the variance and the sample standard deviation
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| range | largest #- smallest #
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| iqr | IQR= Q3-Q1
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| five number summary | min. q1 med q3 max
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| variance | sum of (xi-the mean)squared divded by n-1
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| standard deviation (equation) | square root of variance...sum of (xi-average)square/n-1
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| standard deviation (definition) | the st. dev. is a set of numbers that emasures how numbers are spread out from the mean
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| xi-xbar | a deviation of xi from the mean
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| the sum of all the deviations of the mean | always equals 0
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| st. dev. is .... to outliers | nonresistant (is affected by)
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| n-1 is.. | degrees of freedom
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| a datapoint is an outlier if... | it lies mroe than one a half iqr ranges before q1 or above q3
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| boxplot | is a graph which displays five num summary of a set of data
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| modified boxplot | a graph that displays the fiver numeb summary of a data set (tests for outliers)
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| side-by-side boxplots | can be used to compare the distributions of to data sets
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| within one standard deviation of the mean | 68% of the data will fall
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| two sample standard deviations from the mean | about 95% of the data will fall
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| three devations fromt he mean | about 99.7% of the data wqill fall
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| z-score | meansures how far these points lie from the mean (using standard devations as the unit)
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| equation for z-score | x-xbar/s
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| sample mean of a z-score is | 0
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| the sample dev of a zcore is | 1
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| cumulative frequency | is the nunber of observations less than or equal to a given number
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| cumulative relative frequency | cumulative frequency divded by the toal number ofobservations
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| empirical distribution function | is a graph of the cumulative relative frquency vs. the raw data in the sample
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| a density curve | a curve that always lies on or above the horizontal axis and has area exactly of 1 underneath
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| median of a density curve | is the point that divides the area under the curve in half
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| mean of a density curve | the point at which the curve would balance if it was made of a solid material
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| the standard normal distribution is..(mean/st. dev.) | a normal distribution with mean 0 and standard deviation 1
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| conversation formula is used | to convert normal distribiton values to standard normal distribution values
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| conversation formula (actual form) | z= (x-mu)/s
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| what does a z-score measure | the number of standard deviations between anobservation x and the mean mu of the data set
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| normal quantile plot | graphs raw data (horizontal) versus their z-score (y-axis)
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| a data set is approximately normal when its | quantile plot is approximately linear
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| independent variable x is | the explanatory varaible
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| dependent variable y | response variable
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| directions of scatterplots | positive association, negative association or neither
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| scatterplots are analyzed according to: | direction, form, strength of relationship, and outliers
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| correlation coefficient measures | the direction and strength of the linear relationship between two quantitative variables
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| formula for r | r= one over n minus 1 times the sum of the (xi-x) divided by sx and (yi-y) divided by sy
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| the correclation coefficient r is always a number between | -1 and 1
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| if r is positive then | x and y have a posistive association
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| if r=1 then | x and y have a perfect positive correlation
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| if r is negatrive then | x and y have a negative association
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| if r=-1 then | x and y have a perfect negative correlation
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| least squares regression lineis the equation.. | of the line that makes the sum of the squares fof the residuals as small as possible
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| equation for the LSQR | yhat=bnaught+b1x
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| bnaught is.. | y intercept
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| b1 is... | the slope of the line
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| equation for b1 | r(sy/sx)
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| equation for bnaught | ybar-b1xbar
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| ybar | the mean of the y coordinates
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| x bar is | the mean of the x coordinates
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| the difference between y and yhat is called | an error or a residual
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| residual is | the observed value of y mins the predicted value of y (y-yhat)
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| the point xbar, ybar... | is a point on every regression line
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| rsquared is | called the coefficient of determination
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| rsquared measures | the variation in y that is explained by y's linear association with x
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| a residual plot graphs.. | the residuals on the vertical axis and either the explanatory, response or preodicted response values on the horizontal
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| residuals from a LSQR always | have a mean of 0
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| the horizxontal axis of a residual plot | corresponds to the regresson line
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| an observation is influential if | removing it would markedly change the position fot her egression line
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Created by:
lilee256
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