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39 Cards in this Set
 Front
 Back
Individual

the objects described by a set of data.


variable

any characteristic of an individual


categorical variable

places an individual into one of several groups or categories


quantitative variable

takes numerical values for which arithmetic operations such as adding or subtracting make sense


distribution

tells us what values it takes and how often it takes these values


rules for a histogram

1. The bars of a histogram should cover the entire range of values of a variable. When the possible values of a variable have gaps between them, extend the bases of the bars to meet halfway between the two adjacent possible values


describing overall pattern

shape, center, spread and check for outliers


how to make a stemplot

1. separate each observation into stem/leaf 2. Write the stems in a vertical column with smallest at top 3. Write each leaf in the row to the right of its stem in increasing order out 4. For double stems, 04 goes on the upper stem and 59 goes on the lower stem


mean

average (x1+x2+x3….)/n


resistant measure

because the mean cannot resist the influence of extreme observations, it is not a resistant measure. Outliers may pull the mean toward its long tail and skew the mean. The median is resistant. Standard deviation is not resistant either.


median

midpoint


how to find the median

1. Arrange all observations in order of size, from smallest to largest 2. If the number of observations, n, is odd, the median is the center. Find the location by counting (n+1)/2. If n is even, average the two center observations


relationship between the mean and the median graphically

in a symmetric distribution, they are close together. If the distribution is exactly symmetric, the mean and median are exactly the same. In a skewed distribution, the mean is farther out n the long tail than the median


How to measure spread:

look at the spread of the middle half of the data where there are not outliers, that is look at the quartiles


first quartile

lies one quarter of the way up the list


third quartile

larger than 75% of the observations


how to make a boxplot

take the 5 number summary. Draw horizontal lines at the 3rd quartile, the median and the first quartile. Then draw vertical lines to the maximum and minimum.


variance

(s squared) of a set of observations is an average of the squares of the deviations of the observations from their mean


standard deviation

(s) measures spread by looking at how far the observations are from their mean


density curve rules

1. Always on or above the horizontal axis 2. Has area exactly 1 underneath it… describes the overall pattern of a distribution. The area under the curve and above any range of values is the proportion of all observations that fall in that range


median on a density curve

equal areas point with half the area under the curve to the left and the remaining to the right


mean on a density curve

the point at which the curve would balance if it was made of solid material. The mean and median of a symmetric density curve are equal


mu

the notation for the mean of an idealized distribution


Normal distributions

normal curves that are symmetric, singlepeaked, and bellshaped.


689599.7 rule

68% of the observations fall within 1 standard deviation on either side of the mean, 95% of the observations fall within 2 standard deviations on either side of the mean, 99.7% of the observations fall within 3 standard deviations on either side of the mean


standardized value

z= (xmu)/alpha also known as Z score


z score

tells us how many standard deviations the original observation falls away from the mean and in which direction. Observations larger than the mean are positive when standardized and vice versa


the standard normal distribution

N(0,1) with mean 0 and standard deviation 1. If a variable x has any Normal distribution N(mu, alpha) with mean mu and standard deviation alpha, then the standardized variable is Z


response variable

measures an outcome of a study aka dependent variables


explanatory variable

explains or influences changes in a response variable also known as independent variables


scatterplot

shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each indvidual in the data appears as the point in the plot fixed by the values of both variables for that individual. Always plot the explanatory variable, if there is one, on the horizontal axis of a scatterplot. Explanatory variable = x and response variable = y.


how to examine a scatterplot

chech for overall pattern, striking deviation, direction, strength, outlier


positive association

above average values of one tend to accompany aboveaverage values of the other, and belowaverage values also tend to occur together


negative association

above average values of one tend to accompany belowaverage values of the other, and vice versa


strength of a stemplot

determined by how closely the points follow a clear form


correlation

r measures the direction and strength of the linear relationship between two quantitative variables ( you are trying to evaluate how closely points lie to a straight line)


how to assess correlation

1. positive r denotes positive correlation and negative r shows negative correlation. 2. Correlation is always between 1 and 1. Values of r near 0 indicate a weak linear relationship. The strength of the linear relationships increases as r moves toward 1 or 1. 1 or 1 only occur in the case of a perfect linear relationship. 3. Does not describe curved relationships 4. Not resistant


If X~N(6, 2)and a sample of n=4 is taken, then x bar is distributed

N(6,1) (standard deviation/root n)


If X~N (6,2) and a sample of n=4 is taken, (x6)/2 is distributed

N(0,1) equal to Z
