Welcome To Mrs. Tibbetts’ Class
Room: 2210Class: AP Statistics
Course Description ~ The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in
Chapter 1 Introduction
Statistics is the science of data, “Great Statisticians are masters at the
art of examining data!”
Individuals ~ are the the objects described by a set of data (people but
also animals and things)
Variable is ANY characteristic of an individual (Can be quantitative or categorical)
When given New Set Of Data
Introduction Continued…
Categorical variables describe individuals into categories and
quantitative variables into numerical values for which we can do arithmetic
Row of data will often be seen called a CASE
Distribution “Pattern of variation of a variable,” specifically addressing
WHAT values the variable takes & HOW often it takes these values
Exploratory data analysis, examining data in order to describe their
main features. Every problem will have background information, however the emphasis is on examining data!!
1. Begin by examining each variable by itself, Then move on to study relationships among the variables
Chapter 1 Section 1
The purpose of a graph is to help us UNDERSTAND the data. Always ask yourself “What do I see?”
Look for an overall pattern and also for striking deviations from that pattern
Displaying Categorical Variables Displaying Quantitative Variables
Bar Graphs Dot Plots
Pie Charts Stem Plots
Histograms
Relative Cumulative Frequency Graphs “O – JIVE”
Chapter 1 Section 1
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Displaying Categorical Variables
Bar graphs and pie charts help an audience grasp the distribution
quickly
Bar Graph ~
Label axes, title graph Scale the axes
Leave space between bars
Chapter 1 Section 1
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Displaying Categorical Variables Continued…
The distribution of a categorical variable lists the categories and gives
either COUNT or the PERCENT of individuals who fall in each category
Pie Charts
Label each part of chart key, title of chart Shows percentages
Chapter 1 Section 1
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Chapter 1 Section 1
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Displaying Quantitative Variables
Advantages of dot-plots and stem-plots: easy to construct, display the
actual data values
Disadvantages of dot-plots and stem-plots: cumbersome and
time-consuming with large data set
Dot-Plots
Label axes, title graph
Chapter 1 Section 1
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Displaying Quantitative Variables Continued..
Stem Plots (aka Stem and leaf plot)
Determine stem (all but the rightmost digit) and leaf (rightmost digit) example: 50, 5 is stem and 0 is leaf
Write stems vertically increasing order from top to bottom, draw a vertical line to the right of the stems, write each leaf to the right of its stem (You can avoid this step if you sort your data in your
calculator in ascending order before constructing plot).
Rewrite stems again, rearranging the leaves in increasing order Title graph, add key describing what stems and leaves represent
Chapter 1 Section 1
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Displaying Quantitative Variables Continued..
Stem-Plot!!
Chapter 1 Section 1
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Displaying Quantitative Variables Continued…
Histograms
Divide data into classes of equal width, count observations in each individual class (5 classes is a good minimum)
Label axes, title graph
Draw bar to represent the count (histogram), percent(relative frequency histogram), or cumulative relative frequency (O-JIVE)in each class
Chapter 1 Section 1
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Displaying Quantitative Variables Continued…
Relative Cumulative Frequency Graph “O-JIVE” Step 1:
Decide on class intervals and make a frequency table, just as in making a histogram. Add three columns to your frequency table: relative
frequency, cumulative frequency, and relative cumulative frequency. To get the values in the “relative frequency” column, divide the count in
each class interval by total frequency. Multiply by 100 to covert to percentage.
To fill in the “cumulative frequency” column, add the counts in the frequency column that fall in or below the current class interval
For the “relative cumulative frequency’ column, divide the entries in the cumulative frequency column by total frequency (total number of
individuals)
Step 2 : Label and scale axes, as well as title graph
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Chapter 1 Section 1
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Time Plots: Displays change over time
Mark time on the horizontal axis
Mark the variable of interest on the vertical axis
Look for trends (a long-term upward or downward movement over time) and seasonal variation (pattern that repeats itself at regular time intervals)
The figure below shows a clear trend of increasing price. In addition to
Chapter 1 Section 1
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When talking about the overall pattern of a distribution, remember
“C.C.S.S.O” , Must ALWAYS include the following Context ~ who, what, and why????
Center ~Mean or Median
Spread ~ how spread out is the data
Shape ~ distributions come in a limitless variety of shapes, but certain shapes arise often enough to have their own names.
Bell-Shaped…
Symmetric (is not always bell-shaped)- one half is roughly a mirror
image of the other
Skewed right ~ the right side of the distribution extends much farther out than the left side
Skewed left ~ the left side of the distribution extends much farther out than the right side
Uniform ~ the variables have approximately equally likely outcomes
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Also, peaks or clusters that indicate the data fall into natural subgroups.
Also, Granularity – values occur only at fixed intervals ( such as multiples of 5 or 10)
pth percentile ~ percent of the observations that fall at or below.
