Statistics
the science of designing studies and analyzing the data that those studies produce. Statistics is the science of learning from data.
Population
the entire set of subjects in which we are interested in
Sample
subset of the population for whom we have data
Subject
an entity that we measure in a study
Parameter
a numerical value summarizing the population data
Statistic
a numerical value summarizing the sample data
Population Mean ( � )
an average for a full population
Sample Mean ( x-bar )
an average calculated from a sample
Population Proportion ( p )
the proportion for an entire population
Sample Proportion ( p hat )
the proportion for just a sample
Design
how to obtain the data to answer questions of interest
Description
summarizing and describing the obtained data
Inference
making decisions and predictions based on the sample data
Random Sample
a sample in which every subject has some chance of being selected for the sample
simple random sampling
a sample in which every subject has an equally likely chance of being selected for the sample
Stratified Sampling
the population is divided into non-overlapping groups ( strata ) and a simple random sample is then obtained from each group
Cluster Sampling
the population is divided into non-overlapping groups and all individuals within the randomly selected group or groups are sampled
Systematic Sampling
selecting every kth subject from the population
Convenience Sampling
sampling where the individuals are easily obtained
Variable
a characteristic or property of an individual population unit
Categorical Data
classifies subjects based on some attribute or characteristic-each observation belongs to a set of categories
Quantitative Data
takes on numeric values
Discrete Variable
(Quantitative) there is a countable number of distinct possible values that the variable can equal
Continuous Variable
(Quantitative) for any two values of that variable there are an infinite number of other possible values in between
Frequency Table
lists the number of occurrences for each category in the data
Bar Graph
a graph constructed by putting the categories on the horizontal axis and the frequency/proportion on the vertical axis
Pareto Chart
a bar graph whose bars are drawn in decreasing order of frequency/proportion
Pie Chart
a circle divided into sectors. each sector represents a category of data with the size of each sector corresponding to the proportion of responses falling in that category
Histogram
a display that is similar to a bar graph, but shows quantitative data
Stem-and-leaf plot
looks like a bar graph on its side. consists of all digits except for the final one, which is the leaf
Mode
the number in the data set that appears most often
Median
the central value of an ordered data set
Mean
the sum of all the numbers divided by the total number of numbers in the set
Mean < Median
graph is skewed left
Mean > Median
graph is skewed right
Variability
used to measure the spread or volatility contained in the data set
Range
the difference between the largest and the smallest values in the data
Variance
the average of the squared deviations from the mean, calculated using n-1 as the divisor
Standard Deviation
positive square root of the varience
Population Standard Deviation ( ? )
( SIGMA ) the standard deviation for an entire population
Sample Standard Deviation ( s )
the standard deviation for a sample population
Empirical Rule
if a distribution is bell-shaped, we can approximate the percentage of data that lie within 1, 2, or 3 standard deviations from the mean using this rule ( 1 = 68% , 2 = 95%, 3 = almost all of the data )
Quartiles
specific percentiles that split the data into quarters ( 3 of them)
First Quartile ( Q1)
a value such that 25% of the data values are smaller that Q1 and 75% are larger
Second Quartile ( Q2)
a value such that 50% of the data values are smaller than Q2 and 50% are larger ( median)
Third Quartile ( Q3)
a value such that 75% of the data values are smaller than Q3 and 25% are larger
Outliers
extreme observations in the data that often occur because of error in the measurement of the variable, during data entry, or from errors in sampling
Interquartile Range (IQR)
the difference between the third and first quartile and represents the range covered by the middle 50% of the data ( Q3-Q1) values outside of ( Q1-1.5
IQR) and (Q3+1.5
IQR) are outliers
5-number summary
the five values that split the data into quarters ( minimum, Q1, Q2 (median), Q3, maximum)
Boxplot
graphical representation of the five number summary
Distribution for Boxplots
median left of center of box and/or the right line is much longer than the left line = skewed right
median right of center of box and/or the left line is much longer than the right line=skewed left
Z-Score
measures the position a value has in the data set, relative to the mean ( measured in standard deviations)
Response Variable
a variable that can be explained by, or is determined by, another variable (y-axis)
Explanatory Variable
explains, or affects, the response variable ( x-axis)
Association
exists between two variables if a particular value for one variable is more likely to occur with certain values of the other variable
Lurking Variable
a variable that is related to the response or explanatory variable ( or both), but is not the variable being studied
Contingency Table ( 2-way table)
a table that relates two categorical variables. each box inside the table is referred to as a cell
Conditional Proportion
the proportion for a value of a variable, given a specific value of the other variable
Relative Risk
conditional proportion for one group/ conditional proportion for another group
Scatterplot
a graphical display for two quantitative variables
Positive Association
exists between two variables if as x increases, y also increases
Negative Association
exists between two variables if as x increases, y actually decreases
No Association
as x increases, there is no definite shift in the values of y
Linear Correlation
exists when the data tend to follow a straight line path. if as x increases, y also increases it is a positive correlation; or if as x increases, y decreases it is a negative correlation
No Correlation
as x increases there is no definite shift in the values of y ( no linear relationship between x and y )
Regression Line
predicts the value for the response variable ( y) as a straight-line function of the value of the explanatory variable (x)
Residual
the difference between the actual value and the predicted value of y ( y-y(hat))
Extrapolation
using the regression line to predict the costs for other properties ( observations that have similar x values as our data)