" There are three kinds oflies; lies, damned lies, and statistics."

Benjamin Disraeli, 1804-1881

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.

1.1 DISPLAYING DISTRIBUTIONS WITHGRAPHS (Pages 4 -24)

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 one-variable data.

• Areas of bars represent percent (particularly important if horizontal number intervals are not equal in length.)
• Horizontal intervals have form [a,b). That is, a value at the right end point of an interval is considered to be in the rectangle to its right. (Important to know if histogram is to be interpreted correctly.)
• Histogram shows distribution of the values of a quantitative variable. Choice of length of horizontal interval makes a difference in how histogram "looks."
• A bar chart, which resembles a histogram, compares sizes of different items and is frequently used to display frequencies related to categorical variables.

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 (Stem-Leaf plot): Effective for small data sets.Phrases such as split stems and back-to-back 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: 2|3 means 23

2|345
3|06

We could "spread out" the data by splitting stems.

2|34
2|5
3|0
3|6

Extremely important for success of the Advanced PlacementStatistics Examination:
If you are given a numerical data set, always (I repeat,always) display the shape of the distribution.
Using the TI-83, this can be done very easily with a histogram or aboxplot.