Stats Terminology

descriptive statistics

consists of organizing and summarizing data and describes data through numerical summaries, tables, and graphs.

inferential statistics

uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result

population

the entire group of people/objects to be studied

sample

a subset of the population being studied

simple random sampling

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a sample completed in a way that every sample of size n has an equal chance of being selected

discrete variable

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one that takes on a finite or countably infinite values:  no decimal/fractions, Ex. number of siblings, number of dual credits taken, etc.

continuous variable

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takes on an infinite values - decimals/fractions Ex.  time, temperature, height, weight, etc.  

Distribution Shapes

bell-shaped, uniform, right-skewed, left-skewed

Measures of Center

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mean, median, mode,

measures of variation

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range, standard deviation, variance, inter-quartile range

standard deviation

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descriptive measure that describes the overall spread of a data set from the mean 

resistant measures

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descriptive measures that are not impacted by extremes, Ex. median, mode, inter-quartile range

left skewed

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the mean would be less than the median (extreme values impact the mean)

bell shaped

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the mean would be equal to the median

right skewed

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the mean would be greater than the median (extreme values impact the mean)

Approximately 68% of the data falls within

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1 standard deviation of the mean

Approximately 95% of the data falls within

 2 standard deviations of the mean

Approximately 99.7% of the data falls within

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 3 standard deviations of the mean

parameter

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a descriptive measure for a population

statistic

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a descriptive measure for a sample

z-score

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tells you the number of standard deviations an observation is from the mean of the data set.

mutually exclusive events

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two or more events that do not have any outcomes in common or they cannot happen at the same time.  

independent events

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Events A and B are independent if P(A) = P(A/B) or P(B) = P(B/A) 

permutation

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An ordered arrangement in which r objects are chosen from n distinct (different) objects so that r < n and repetition is not allowed:  Use  nPr

combination

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A collection, without regard to order, in which r objects are chosen from n distinct objects with r < n and without repetition:  Use  nCr

empirical rule for binomial experiments - unusual events

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np(1-p) > 10,   Unusual if it falls outside of the 2 standard deviation range

linear correlation coefficient  - r

measure of the strength and direction of the linear relation between two quantitative variables - the closer the value r is to 1 the stronger the positive/negative linear correlation

**coefficient of determination** - r^2

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the percent of variation in the y variable that can be explained by the variation in the x variable

least squares regression line

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the line that minimizes the sum of the squared errors (or residuals). 

interpretation of slope

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As the x variable changes by 1 unit the y variable changes by the value of the slope in your equation.

\n  **interpretation of y-intercept**

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the value of y when x = 0. To interpret you must have x values close to zero and it needs to make sense for the problem 

normally distributed variable

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bell shaped - centered at the mean within + and - 3 standard deviations 

standard normal distribution

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the z distribution - centered at 0, bell shaped, the mean is 0 and standard deviation 1

sampling error

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the error resulting from using a sample to estimate a population characteristic.

relation between sample size and sampling error

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As the sample size increases, the precision increases (the width of the C. I. decreases) 

Central Limit Theorem

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if X is not normally distributed then the Central Limit Theorem states x-bar will be normally distributed if the sample size n 30. 

point estimate

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the value of a statistic used to estimate a parameter - x bar, p hat

relation between confidence and precision

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As the confidence level increases the precision decreases (the width of the C.I. interval is increases)

margin of error

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the distance from the point estimate to the end of the confidence interval 

interpretation of a confidence interval

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We are _______% confident that the population mean/proportion (describe the variable)  is between __________ and __________.