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AP STATISTICS
Chapter 1 – Exploring Data
Exploring the Basics
Day 4
A. Section 1.2
Name _______________________
Date __________
Period _____
Describing Distributions with Numbers - Continued
Key Vocabulary: measures of center (mean, median, mode, mid-range)
resistant measure (of center), five-number summary, box-and-whisker plot,
quartiles (first – Q1 and third – Q3), interquartile range (IQR = Q3 – Q1),
outlier criterion (>Q3+1.5IQR, <Q1-1.5IQR), modified box plot,
measures of spread and variability (range, variance, standard deviation, IQR, etc.),
degrees of freedom,
linear transformation (xnew = a+bxold),
comparing distributions, back-to-back stemplots, parallel box plots
B. Ages of presidents at inauguration data:
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Enter data in list 1, check accuracy, sort ascending, make split stem plot
median, mode, mid-range as measures of center – define and find
calculate mean with calculator, introduce formula, yellow packet
resistant measure – define and show how median is and mean is not
show median and mean relationship for symmetric and skew distributions – when to use each
five number summary (min, Q1, med, Q3, max), box-and-whisker, etc.
measures of spread – define and find, introduce formula for s.d., yellow packet
linear transformation – ages to dog years – explore and conclude
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61
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68
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64
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56
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1
xi  x 2

n 1
s measures spread about mean and should only be used when mean is measure of center
s = 0 only when there is no spread; otherwise s > 0 and larger s means more spread
s, like x , is not resistant to large values and skewness of distributions
1
xi  x 2
s is the square root of the variance: s x2 

n 1
Properties of the Standard Deviation : s x 
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2.
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C. Comparing distributions, back-to-back stem plots, parallel box plots:
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Hammerin’ Hank Aaron versus Barry “roid” Bonds
Data on for Barry on page 38 and for Hank on page 40
Compare by making back-to-back stem plots and parallel box plots
Find five number summaries by hand from stem plots and confirm from calculator
D. Calculate variance and standard deviation (by hand) for this data set:
1, 3, 5, 7, 9
E. Investigate effect of adding 27 to the data above on mean and standard deviation
F. Homework: Follow the directions for each question. Highest quality work expected!!!
1. Exercise 1.36 SSHA Scores on page 47: understanding comparing distributions
2. Exercise 1.55 on page 63: understanding linear transformations: xnew = a+bxold
3. Exercise 1.57 Better Corn on page 63: understanding summary statistics comparisons
G. Prepare for Quiz