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Stat 212
Exam 1 (chapter 2)
29
Mathematics
Undergraduate 2
09/28/2009

Additional Mathematics Flashcards

 


 

Cards

Term
Variable
Definition
  • Any characteristic that is recorded for the subjects in a study
    • Can be Categorical
    • Or can be Quantitative
      • Discrete
      • Continuous
Term
Categorical Variable
Definition
  • Observations belongs to one of a set of categories
  • EX. Gender, Religious Affiliation etc.
Term
Quantitative Variable
Definition
  • Observations that take numerical values to represent different magnitudes of the variable
  • EX. age, number os siblings
  • Key features: Center and spread (variability)
Term
Quantitative Variable (Discrete)
Definition
  • values form set of separate numbers
  • have finite number of possible values are discrete
  • EX. number of pets in household, number of children in family
Term
Quantitative variable (Continuous)
Definition
  • values that form an interval
  • have infinite number of possible values
  • EX. Height/Weight, age, blood pressure
Term
Proportion
Definition
  • frequency (count) of observation in category divided by total number of observations.
Term
Relative frequencies
Definition
  • AKA proportions / percentages
Term
Frequency table
Definition
  • Listing of possible values for a variable
    • Counts number of observations / relative freqencies for each value
Term

Describing data using graphical summaries:

 

Distribution

Definition
  • Graph or frequency table describes distribution
  • Tells us possible value a variable takes as well as the occurrence of those values (frequency / relative frequency)
Term

Describing data using graphical summaries:

 

Pie Chart / Bar graph

Definition
  • Pie Chart:
    • Summarizing categorical variable
  • Bar Graph
    • Summarizing categorical variables
    • height of bar = frequencies
    • Pareto Charts = bar graghs arranged by tallest bar to shortest
  • This is fucking retarded
Term

Describing data using graphical summaries:

 

Dot Plot

Definition
  • Summarizing quantitative variable
  • Horizontal line with regular values of variables
    • for each observation, place dot above its value on number line
    [image]
Term

Describing data using graphical summaries:

 

Stem-and-Leaf Plot

Definition
  • separate each observation into stem (first part of the number) and a leaf (typically last digit of number)
  • This bitch:[image]
Term

Describe data using graphical summaries:

 

Histogram

Definition
  • Use bars to portray frequencies for relative frequencies of the possible outcomes of a quantitative variable
  • divide range of data into regular intervals
  • label values/end point of intervals on horizontal axis
  • draw bar over each value / interval w/ height equal to frequency (or percentage)

[image]

Term

Interpreting histogram:

 

Center

Definition
  • found by finding the median
Term

Interpreting histogram:

 

Spread

Definition
  • how much it is.... spread.
Term

Interpreting histogram:

 

Shape

Definition
  • symmetric
    • both left and right sides mirror images of each other
    • Mean and Median close together
  • Skewed to the left
    • left tail is longer than right tail
    • Mean less than median (mean to the left of median)
  • Skewed to the right
    • right tail is longer than left tail
    • Mean more than median (mean is to the right of median)

[image]

Term

Interpreting Hisogram:

 

Time Plots

Definition
  • displaying data set collected over time
  • observation on vertical scale vs. time on horizontal scale

[image]

Term
Calculating Median
Definition
  • Midpoint of observations when ordered smallest to largest
  • if # of observation is:
    • Odd, median is middle observation
    • Even, median is average of two middle ovservations
Term
Resistant
Definition
  • Numerical summary measure is resistant if extreme ovservations have litte if any influence on its value
  • Median resistant to outliers
  • Mean is not resistant to outliers
Term
Range
Definition
  • Max value - Min value
  • strongly affected by outliers
Term
Standard deviation
Definition
  • deviation from the mean
  • positive deviation if it falls above meaan
  • Negative iff it falls below mean
  • sum of deviation = 0
  • [image]
Term
Properties of standard deviation
Definition
  • s measures spread of data
  • bigger spread = larger S
  • Variance = s2
  • s is not resistant
Term
Empirical Rule
Definition
  • If distribution of data is bell-shaped then:
    • 68% of observations fall w/ 1 standard deviation of mean
    • 95% of observations fall w/i 2 standard deviation of mean
    • nearly all observations fall w/i 3 standard deviations of mean
Term
Quartiles
Definition
  • ranked data set divided into 4 equal parts
    • Median is second quartile Q2
    • 1st quartile Q1 = median of lower half of ovservations
    • 3rd quartil Q3 = upper half of the observations
Term
5 number summary
Definition
  • Minimum value
  • First Quartile
  • Median
  • Third Quartile
  • Maximum value
Term
Interquaritle range and detecting potential outliers
Definition
  • Interquartile rage (IQR) = Q3 - Q1
    • Gives spread of middle 50% of data
  • Observation is potential outlier if it's more than 1.5 x IQR below Q1 or higher than Q3
Term
Boxplots
Definition
  • Box goes from Q1 to Q3
  • line drawn inside box at median
  • Line goes from lower end of box to smallest observation that's not potential outlier and from upper end of box to largest observation that is not a potential outlier
  • Potential outliers shown separately
Term
Z-score
Definition
  • number of standard deviation that i falls from the mean
  • Observation from bell-shaped distribution is potentiall outlier if it's z-score <-3 or >+3
  • [image]
Term
Guidelines for constructing effective graphs
Definition
  • Label both axes and provide proper headings
  • vertical axis start at 0 to better compare relative size
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