Stats

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homogenous populations

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contain one type of object

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population size denoted by

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N.

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sample

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any subset of a population- denoted by n.

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random sample

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all samples of the same size have the same chance of being picked ex: names in a hat

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representative sample

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sample's interests are similar to those of the whole population

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parameter

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a fixed, usually unknown numerical feature of a population ex: uconn student body (N= 30,000) numerical features would be % female, avg. gpa, % out of state, etc.

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statistic

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numerical quantity from sample data, value varies from sample to sample

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experimental unit

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an individual member of a population/sample from which data is collected ex: population- all hybrid cars in U.S., experimental unit- individual hybrid car

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discrete variables

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values are distinct, with minimum distance between them

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continuous variables

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can be any value in one or more intervals-

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descriptive statistics

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the display and summary of data using graphs

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inferential statistics

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uses sample data to calculate estimates and draw conclusions about the population

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data set

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a collection of all the values of a variable obtained from the members of a sample or population

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cross-sectional data

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data obtained from different members of a population or sample at the SAME POINT in time

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time series data

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data collected from a single member of a population at different points in time

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class frequency

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the number of population members in that class

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relative frequency

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the fraction of population members in a class

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percent frequency

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the percentage of population members in that class

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skewed right graph

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peak is on the left

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skewed left

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peak is on the right

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symmetric graph

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bar data is symmetric

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mean

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sum of all values in the sample or population/the number of values. For a sample, the mean is denoted by "x bar". For a population, the mean is denoted by the greek letter mu.

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finding the median when n is odd

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(n+1)/2

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finding the median when n is even (median also known as 50th percentile or Q2)

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median is the average of (n/2) and (n/2) +1

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first quartile of data (Q1)

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25% of the values are below Q1 and 75% are above - find the median of the bottom half of the data

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third quartile (Q3)

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75% of the values are below Q3 and 25% are above - find the median of the top half of the data

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inter quartile range

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Q3 minus Q1 - measures how spread out the middle 50% of the data is

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5 number summary

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min, q1, q2, q3 and max

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review percentiles

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on notes

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distribution/density curve

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the smooth curve that develops due to continuous data becoming increasingly large

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range of data

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max - min

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variance

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denoted by the greek symbol sigma

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standard deviation

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positive square root of the variance

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z score

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z score of x is the number of standard deviations x is from the mean

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chebyshev's theorem

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used when the shape of a distribution is unknown, or is known but not bell-shaped or symmetric. tells us what the minimum fraction of data is within "k" standard deviations of the mean, for any value k > 1