Download Displaying Distributions With Graphs (Part I)

Chapter 1 Notes
Individuals(Observational Units): The objects described by the set of data. They can
be people but they can also be just about anything.
Variables: Any characteristic of an individual.
Distribution: Describes the different values of a variable and the frequency (may be
relative frequency) the variable takes on each value
Categorical Variable: Places individuals into category based on things such as
race, gender, etc.
Bar Graph
Pie/Circle Graph
Quantitative Variable: Takes on numerical values about the individual such as
height, weight, I.Q. score, etc.
Histogram
skewed right
Stem-Plots
1 01
2 235
3 4568
4 467
515
symmetric
Box-Plots
skewed left
Shape:
Symmetric: values are balanced
3 Key Features
Of A Distribution
Skewed: One end of the distribution stretches out further
than the other
Center: Describes middle of distribution (mean or median)
Spread: Variation in the data (Range, Standard Deviation, or IQR)
Other Feature
Of A Distribution
Outliers: A value not part of overall pattern
Modes: Peak(s) or Cluster(s)of a distribution


Mean x  Average of the values for the variable
Median: The midpoint of the value for the variable
First Quartile(Q1): The midpoint for the lower half of the data
Third Quartile(Q3): The midpoint for the upper half of the data
Five Number Summary:
Min
Q1
Median
Q3
Max
Range: Distance between the minimum vale and the maximum value
Interquartile Range: Distance between the Q3 and Q1
Outlier: Any value outside Q1  1.5  IQR , Q3  1.5  IQR 

or  x
Standard Deviation S x
 The average distance the value of the variable is
from the mean.

Variance: S x
2
or  x

2
Resistant Measure: A value that is relatively unaffected by changing a small proportion
of the total number of values
Density Curve
1. Has an area of exactly 1 underneath it.
2. Describes overall pattern underneath it.
mean > median
mean = median
mean < median
The median of a density curve is the equal areas point and the mean of a density curve is
the point at which the curve would balance.
Standard z-score: z 
x

. This value tells you how many standard deviations your
value is from the mean.
68-95-99.7 rule:
99.7%
95%
68%