Transcript Chapter 1 Notes

Organizing Data
AP Stats Chapter 1
Organizing Data

Categorical
Dotplot (also used for quantitative)
 Bar graph
 Pie chart
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Quantitative
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Stemplots
 Unreasonable
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with large data sets
Histogram
 Frequency/relative
frequency
Describing Distributions
Remember “SECS-C”
 S – Shape
 E – Extreme Values (outliers)
 C – Center
 S – Spread
 C – Context
 **Make meaningful descriptions and
comparisons. Don’t just list numbers.**
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Shape
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Symmetric
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Values smaller and larger than the midpoint
are mirror images.
Skewed
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The tail on one end is much longer than the
other tail.
Example: Symmetric
Examples: Skewed
Ways to Measure Center
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Mean
x =
x1 + x2 + . . . . + xn
n
 xi
x =
n
The mean is not a resistant measure of
center. (sensitive to outliers)
 Used mostly with symmetric distributions.
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Ways to measure center
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Median
Midpoint of a distribution
 Median is a resistant measure of center
 Used with symmetric or skewed distributions.
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Ways to Measure Spread
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1) Range
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Highest value – lowest value
Problem: could be based on outliers
2) Quartiles (for use with median)
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pth percentile – value such that p percent of the
observations fall at or below it
Q1 (quartile 1): 25th percentile
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Median of the first half of the data
Q3 (quartile 3): 75th percentile
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Median of the second half of the data
Ways to Measure Spread
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5 Number Summary
Minimum, Q1, median, Q3, maximum
 The 5-number summary for a distribution can
be illustrated in a boxplot.
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1.5 x IQR Rule for Outliers
IQR = Q3 – Q1 (Interquartile Range)
 Rule: If an observation falls more than 1.5
x IQR above Q3 or below Q1, then we
consider it an outlier.
 The 5 Number Summary can be used for
distributions which are skewed, or which
have strong outliers.
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Ways to Measure Spread
Standard deviation (for use with the mean)
 Std Dev tells you, on average, how far
each observation is from the mean.

variance: s2 =
std dev: s =
 (xi - x)2
n-1
 (xi - x)2
n-1
Properties of Standard Deviation
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s gets larger as the data become more
spread out.
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Only use mean and std dev for reasonably
symmetric distributions which are free of
outliers.
Linear Transformation of Data
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Xnew = a + bx
The shape of the distribution does not change.
Multiplying each observation by a positive
number, b, multiplies both measures of center
and measures of spread by b.
Adding the same number, a, to each observation
adds a to measures of center and to quartiles,
but does not change measures of spread.