Transcript YMS 1.1 - Mt. Lebanon School District

Chapter 1 – Exploring Data
YMS - 1.1
Displaying Distributions with
Graphs
xii-7
Consider This….
Data beat anecdotes - seatbelts
Lurking variables – Simpson’s Paradox
Origin of data – Ann Landers
Variation
3 W’s – Who, What, Why?
xii-7
Vocabulary
Data

Numbers with a context
Individuals
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Objects described by a set of data
Variable
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Characteristic of an individual
Categorical Variable – places individual into one of
several groups or categories
Quantitative Variable – take values for which
arithmetic operations make sense
p7 #1.1 – 1.4
xii-7
Case

Row of data (all variables of an individual)
Distribution
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Pattern of variation of a variable
What values the variable takes and how often
Exploratory Data Analysis
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xii-7
Statistical tools and ideas that help you
examine data in order to describe their main
features
Count
Percent
Outlier
Overall Pattern of a Distribution (SOCS)
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8-17
Shape. Outlier. Center. Spread.
Write 2-3 sentences in context with
appropriate measures.
Types of Graphs
1. Bar Graph
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Leave a space between the bars
Label the category names at equally spaced
intervals beneath the horizontal axis
2. Pie Chart
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Must add up to 100%
Let the computer create it
3. Dotplot
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8-17
Mark a dot above number on horizontal axis
corresponding to each data value
4. Stemplot
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Stems and leaves are arranged in increasing
order
Include legend
Split stems if necessary (0-4 and 5-9)
Round or truncate when necessary
p15 Technology Toolbox
Greed
8-17
The Game of Greed
Everyone stands.
A pair of dice will be thrown by a classmate. After each
toss you have the option to sit and keep the score (the
total on the dice) or stand and continue onto the next
round.
The game is over when everyone has decided to sit OR
when a two is thrown (not snake eyes - just the number
2). If you're standing when a 2 is thrown, your score for
the round is zero.
A game consists of 5 rounds. At the end of the game, add
your 5 scores to get your total.
HW: p16 #1.8 & 1.9
Activity: Legendary WS
More Vocab
Symmetric

If the right and left sides of a distribution are
mirror images of each other
Right/Left Skewed

Values are stretched to the right/left
Percentile

18-34
The value such that p percent of the
observations fall at or below it
More Graphs
5. Time plots
Plots each observation against the time at
which it is measured
Trend - a long-term upward or downward
movement over time
Seasonal Variation - a pattern that repeats
itself at regular time intervals
18-34
6. Histogram
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Graphs the distribution of one quantitative
variable
Precise intervals
Intervals must be kept at same width
Can use percentages instead of counts
p22 #1.12 – calculator – zoom stat
p27 #1.16 – reading a histogram
18-34
7. O-Jive aka Relative Cumulative
Frequency Graph
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Make table with class, frequency, relative
frequency, cumulative frequency, and
relative cumulative frequency
Plot a point corresponding to the relative
cumulative frequency in each class
interval at the left endpoint of the next
class interval
p31 #1.19
18-34
HW: #1.20, 1.26 & 1.28
Meet in the lab 557 tomorrow.
YMS - 1.2
Describing Distributions with
Numbers
Measures of Center
Mean

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Add all values and divide by the number of
observations
Not a resistant measure of center
Median
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Midpoint of a distribution; 50th percentile
All values must be arranged in increasing order
before finding median
Median is a resistant measure
Mean vs. Median
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When to use
In skewed distributions
#1.34-1.35 on p41
37-47
Boxplots and Vocab
Range

Difference between largest and smallest value of a
distribution
Quartiles
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25th and 75th percentiles
Interquartile Range
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The distance between the first and third quartiles
Modified Boxplots
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37-47
Shows the outliers
Always use this one!
Outliers
1.5 x IQR Rule
1 3 3 5 7 10 11 11 11 15 25
#1.36 on p47
#1.39 on p48
37-47
Measures of Spread
Standard Deviation
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How far are the observations from their mean
The larger the standard deviation, the wider the
distribution
Is the square root of the variance
Is not a resistant measure
Variance

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Average of the square of the deviations of the
observations from their mean
Has a different unit of measurement than standard
deviation
#1.40 and #1.43 on p52
49-53
Degrees of Freedom = n -1
What measures to use

Mean and Standard Deviation
Reasonably symmetric distributions that are free of
outliers

5-number summary
Skewed distributions or ones with strong outliers
Would you rather have a 10% raise or a
$1000 raise?
49-53
Effect of a Linear Transformation
xnew = a + bx
Fathom First Day
Multiplying by constant b
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Multiplies both measures of center and
spread by constant b.
Adding the same number a
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Adds a to measures of center and to quartiles
Does not change measures of spread
Transformations do not change the shape
of a distribution
53-66
Comparing Distributions
Use back to back stemplots or boxplots
Easy to do in Fathom!
Example 1.17 on p57
53-66