The photographs below show ten brilliant AdvancedPlacement Statistics students at Cate School. For each photo,identify by choosing (A), (B), or (C) that which is beingdemonstrated.
(A) Adistribution that is skewed to the left.
(B) A distribution that is skewed to the left.
(C) A symmetric distribution.






OVERVIEW: Statistics is the science of gaininginformation from numerical data. Statistical tools, such as graphing,can be helpful in examining data in order to describe their mainfeatures. The shape of data is important. Graphs present a good wayto demonstrate shape.
Individuals: Objects being described by data set.
Variable: Characteristic of an individual.
Categorical: Values are labels, such as "male"and "female."
Numerical: Values are numerical, such as "salary in dollars"and "weight in pounds."
Distribution of a variable: Tells what values variableassumes and how often it takes these values.
Dotplot: Simple plot that allows one to visualize arelatively small data set. (Not really convenient if data set islarge.)
Histogram: Common distribution graph for onevariable data.
Outlier: An observation that falls outside the overallpattern of a data set.
Key words in describing the overall pattern of a distribution:Center, Spread, Shape.
Symmetric distribution: right and left sidesapproximately mirror images of each other.
Skewed to the right: Right side of distribution extends muchfarther out than the left. The distribution "points" to the right.The mean is greater than the median.
Skewed to the left: Distribution "points" to the left. Themean is less than the median.
Symmetric
Skewed right
Skewed left
X
Y
Z Z
X X X
Y Y Y
Z Z Z
X X X X X
Y Y Y Y Y Y Y
Z Z Z Z Z Z Z Z
Stemplot (StemLeaf plot): Effective for small data sets.Phrases such as split stems and backtoback stemplotsare important. One has lots of leeway in constructing stemplots. Akey to reading the plot should always be provided so that areader can correctly interpret the data displayed.
Example of splitting stems: Consider the data set {23,24, 25,30,36}
Key: 23 means 232345
306We could "spread out" the data by splitting stems.
234
25
30
36
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