• Any characteristic that is recorded for the subjects in a study
  • Can be Categorical
  • Or can be Quantitative
    • Discrete
    • Continuous

• Observations belongs to one of a set of categories
• EX. Gender, Religious Affiliation etc.

• Observations that take numerical values to represent different magnitudes of the variable
• EX. age, number os siblings
• Key features: Center and spread (variability)

• 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

• values that form an interval
• have infinite number of possible values
• EX. Height/Weight, age, blood pressure

• frequency (count) of observation in category divided by total number of observations.

• AKA proportions / percentages

• Listing of possible values for a variable
  
  • Counts number of observations / relative freqencies for each value

Describing data using graphical summaries:

Distribution

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

Describing data using graphical summaries:

Pie Chart / Bar graph

• 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

Describing data using graphical summaries:

Dot Plot

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

Describing data using graphical summaries:

Stem-and-Leaf Plot

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

Describe data using graphical summaries:

Histogram

• 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]

Interpreting histogram:

Center

• found by finding the median

Interpreting histogram:

Spread

• how much it is.... spread.

Interpreting histogram:

Shape

• 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]

Interpreting Hisogram:

Time Plots

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

[image]

• 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

• 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

• Max value - Min value
• strongly affected by outliers

• deviation from the mean
• positive deviation if it falls above meaan
• Negative iff it falls below mean
• sum of deviation = 0
• [image]

• s measures spread of data
• bigger spread = larger S
• Variance = s²
• s is not resistant

• 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

• 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

• Minimum value
• First Quartile
• Median
• Third Quartile
• Maximum value

• 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

• 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

• 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]

• Label both axes and provide proper headings
• vertical axis start at 0 to better compare relative size