AP Statistics Standards
I.
Exploring Data:
Describing patterns and departures from patterns
(20% –30%)
- A.
Constructing and interpreting graphical displays of distributions of
univariate data (dotplot, stemplot, histogram, cumulative frequency
plot)
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Center and spread
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Clusters and gaps
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Outliers and other unusual features
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Shape
B. Summarizing distributions of
univariate data
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Measuring center:
median, mean
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Measuring spread: range, interquartile
range, standard deviation
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Measuring position: quartiles,
percentiles, standardized scores (z-scores)
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Using boxplots
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The effect of changing units on summary
measures
C. Comparing distributions of univariate data
(dotplots, back-to-back stemplots, parallel boxplots)
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Comparing center and spread: within
group, between group variation
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Comparing clusters and gaps
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Comparing outliers and other unusual
features
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Comparing shapes
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Objectives |
| Essential Question:
How many numbers are needed to
describe a complex event or object? |
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State the difference between categorical and
quantitative variables and give examples of each.
- Define distribution and state two key pieces
of information require to produce a distribution.
The pattern of variation of a
single variable
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Quantitative data (numbers)
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How often various values are
expected
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State the 3 key ways a distribution can be
described.
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Central tendency or center
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Spread
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Shape
Homefun: Read section 1.1 and
1.2, work exercises 1.3(p.9), 1.5, 1.7(pp.16, 17)
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Activities |
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- Lesson 1
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Class Start
Up
Distribute & discuss
syllabi . |
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- Warm Up: Have each person
describe themselves with 2 words and 2 numbers. Object: Complex
objects and phenomenon are frequently described with a few
numbers. How these numbers are produced is critical.
The Key Elements
- Design--the systematic way in which
the data is collected
Analysis--the
systematic use of graphical
and mathematical tools to describe and evaluate the data
- Conclusions--the
systematic manner in which
inferences are drawn from the data
- Key Concept:
What is a distribution?
- Purpose:
Lay the foundation for describing a set of
data.
Interactive Discussion:
Objectives
Resources/Materials:
Picture of histogram with various sized increments to
illustrate the key weakness of histograms. |
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| Essential Question:
When using a number to describe a
complex event or object is
there a difference between using a single number and using a
single data point? |
Ch1.2 Describing Distributions
- Name and define the 3 key measure of central tendency.
- Mean - numerical average
- Median - midpoint, 50% above, 50% below
- Mode - most common data point or highest peak
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Given a set of data determine the
mean, median and mode.
- Define and ID outliers.
- Data point not in distribution
- Gaps
- State which measure of central tendency is
generally most influenced by outliers.
- Using the Mr. Rogers Rat Tail Rule, state
whether a distribution is skewed left or right, high or low.
- Give examples of data which would tend to be
symmetrical and data which would be skewed left or right.
- Easy Test
- Hard Test
- Normal Test
- Incomes
Homefun: read 1.2, 1.15, 1.17, 1.19 p.
27-28
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- Lesson 2
- Key Concept: Central
tendency and shape of a distribution.
- Purpose: Lay the
foundation for describing a set of data.
Interactive Discussion:
Objective
| Conclusions unduly
influenced by a single data point are statistically
indefensible! |
Individual
Work: Find the mean, median, and mode in simulated sets of data with
both odd and even numbers of data points.
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The Mr. Rogers Rat Tail Rule--FAQ
Skewed distributions often look like a rat with a long tail.
The tail points in the direction of skew.
What gets skewed? The mean gets skewed or moved in the
direction the rat tail points.
Why does skew matter? For a skewed distribution, the
mean is less representative of the bulk of the data points.
What gets skewed very little? The median. It will be
more representative of the bulk of the data points than the
mean. |
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Stats
Investigation:
Investigation School Evaluation - time approx 3 class periods
(individual work) |
| Purpose:
Determine if it is reasonable
for 50% of all schools receiving a school report card to be scored below average.
Instructions:
Perform the simulation of school ratings using the Excel Spread
Sheet provided.
Questions /Conclusions:
(see Excel spread sheet.)
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| Essential Question:
Is there a difference between
looking at numbers and looking at plots or graphs of numbers? |
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Make dot plots.
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Make histograms using the TI-83 calculator and in Minitab.
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Convert distribution data into a cumulative frequency plot.
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State the key weakness of histograms.
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- Lesson 3
- Key Concept: Central
tendency, spread, and shape of a distribution must be visualized
in order to analyze them.
- Purpose: Lay the
foundation for describing a set of data.
Interactive Discussion:
Objectives
Individual
Work: Given a set of data, make a dot plot
on paper, make a histogram using the TI-83, and make a frequency
plot on paper
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| Essential Question:
Can the type of plot influence the
conclusions drawn and if so how can this be prevented? |
Stem and Leaf Plots
- Draw and interpret stem and leaf plots
including back to back stem and leaf plots (p.
19).
- Draw and interpret back to back
stem and leaf plots .
- State why a time plot should always
be used in an analysis of data.
Homefun: prob. 1.20
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Lesson 4
Key Concept: All data
varies with time. Stem and Leaf Plot
Purpose: Understand the
reasons all data should be plotted against time.
Interactive Discussion:
Objectives
- What can a stem and leaf plot
reveal ?
- What variable is virtually everything
dependent on?
Seat Work: Draw stem and leaf plots both on
paper and a histogram with a TI-83 calculators using using baseball
data for Babe Ruth vs Roger Maris p. 37, prob 1.27.
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| Essential Question:
Is there a difference between skew
and outliers? |
Box and Whiskers Plots
- Calculate quartiles, Q1 and Q3.
- Interpret 5 number summaries.
- Find the IQR or interquartile range
for a data set.
- Draw a box and whiskers plot.
- State the Mr. Rogers Rat Whisker
Rule for determining skew using a box and whiskers plot.
- State the % of the data expected in
each whisker and in the box for a box and whiskers plot.
Homefun: prob. 1.49, 1.52:
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- Lesson 5
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- Key Concept: Using box
and whiskers plots to describe distributions
- Purpose: Box and whiskers
plots are an outstanding tool for communicating information
about data in a straight forward manner
Interactive Discussion:
Objectives
Individual Work: Draw
box and whiskers plots both on paper and with TI-83 calculators using
simulated data.
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| Essential Question:
Why are outliers important? |
Modified Box and Whiskers Plot
- Identify outliers using a modified
box and whiskers plot.
- Whisker's End = 1st data pt within 1.5 IQR of
box edge
- Outlier = data pt beyond the whisker's end
- Create box and whisker plots on
the TI-83.
- Create and interpret parallel box and whisker plots on
the TI-83 and in Minitab.
Homefun: prob. 1.55, 1.59:
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- Lesson 6
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- Key Concept: ID outliers
using modified B&W plots
- Purpose: The modified box
and whiskers plots are an outstanding tool for identifying
outliers.
Interactive Discussion:
Objectives
Which type of plot(s) is(are) best at
identifying outliers in a consistent manner?
- Which type of plot(s)
is(are) best at identifying clusters?
- Which type of plot(s)
is(are) best at identifying multiple-modes?
- Which type of plot(s)
is(are) best at identifying gaps?
Individual Work: Draw modified box and whiskers
plots both on paper and with TI-83 calculators using simulated data.
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| Essential Question:
Ideally, how many data points in a
set of data are needed to characterize spread? |
Standard Deviation
- Calculate range.
- Write the formula for standard
deviation from memory and explain its meaning.
- State how standard deviation and
variance are related.
- Calculate standard deviations by
hand and with a calculator
- Note the difference between S and
sigma.
- Be as one with the 3 points about
standard deviation in the magic box on page 49.
- State why the standard deviation
is a better indicator of spread than range.
- State an approximate relationship
between range and standard deviation.
(The range is roughly = 6 sigma.)
Homefun: work exercises
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- Lesson 7
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- Key Concept: Measuring
spread - Range, standard deviation, and IQR
- Purpose: Understand the
pros and cons of various spread measuring techniques.
- Quantities represented as Greek
alphabet symbols are considered true (known by
Zesus).
- Quantities represented in our
normal alphabet (known by mere mortals) are
estimates of the ones represented as Greek alphabet symbols.
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Interactive Discussion:
Objectives
Seat Work: Calculate ranges, standard
deviations, and variances both on paper and with TI-83 calculators using
simulated data.
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