Stats Terminology

descriptive statistics

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

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

discrete variable

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

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

mean, median, mode,

measures of variation

range, standard deviation, variance, inter-quartile range

standard deviation

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

resistant measures

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

left skewed

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

bell shaped

the mean would be equal to the median

right skewed

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

Approximately 68% of the data falls within

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

 3 standard deviations of the mean

parameter

a descriptive measure for a population

statistic

a descriptive measure for a sample

z-score

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

mutually exclusive events

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

independent events

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

permutation

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

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

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

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

least squares regression line

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

interpretation of slope

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

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

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

standard normal distribution

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

sampling error

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

relation between sample size and sampling error

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

Central Limit Theorem

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

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

relation between confidence and precision

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

margin of error

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

interpretation of a confidence interval

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