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TRANSCRIPT
Session 110
Strategic Use of Technology Tools in High School Statistics
● Take the survey at http://tinyurl.com/CMCN-Session110 to provide the following data: name, height, arm span, eye color, gender, teaching level, and email (so we can send you links to all digital resources).
● Place a sticky dot on the dot plot (height) and another on the scatter plot (arm span vs. height).
Agenda● Univariate Statistics
○ Median-based (median, IQR, box plots, histograms)○ Mean-based (mean, standard deviation, normal curve)
● Bivariate Statistics○ Numerical (line of best fit, residuals, LSRL)○ Categorical (two-way tables, association)
● Probability (simulations)
● Digital tools: TinkerPlots, spreadsheets, Desmos, Fathom
@SFUSDMath @CAMathCouncil#cmcmath
Univariate Statistics: Median-based
● Determining median and quartiles
● Making a box plot○ Quartiles: include or exclude median?○ Whiskers: entire range or last data point within 1.5 • IQR?
● Box plots and histograms using TinkerPlots (data)
● Relating histograms and box plots (demo)
Univariate Statistics: Mean-based
● Calculating standard deviation with a Google spreadsheet
● Sketching a normal curve
● Plotting a normal curve in Fathom
● Transforming a normal curve in Desmos
● Area under a normal curve
Normal Curve: The Empirical Rule
Univariate StatisticsRepresenting Data ● dot plots
● histograms● box plots
Introduced: Grade 6Reviewed: Algebra 1
Measures of Center ● median● mean
Introduced: Grade 6Reviewed: Grade 7, Algebra 1
Measures of Spread ● range● interquartile range● mean absolute deviation
-----------------------------------------● standard deviation
Introduced: Grade 6Reviewed: Grade 7, Algebra 1
--------------------------------------------------Reviewed: Algebra 1
Comparing Groups ● informal inferences Introduced: Grade 7Reviewed: Algebra 1
Normal Curve ● normal distributions● population percentages● margin of error● inferences
Introduced: Algebra 2
Bivariate Statistics: Numerical
● From univariate to bivariate representations in TinkerPlots
● Line of best fit (spaghetti method)
● Linear regression using Desmos
● Least Squares demo
● Least squares in Fathom
Bivariate Statistics: Categorical
● Two-way tables○ gender vs. teaching level○ gender vs. eye color
● Determining association
● Two-way tables using Titanic data in TinkerPlots
Fill in the counts in the two-way table.
Calculate row percents or column percents.
Middle School High School Other Level Total
Female 20 34 2 56
Male 7 26 1 34
Other Gender 1 0 0 1
Total 28 60 3 91
Gender vs. teaching level
Row Percentages
Percent of each gender that is a particular teaching level. Total of each gender is denominator.
Middle School High School Other Level Total
Female 36% 61% 4% 100%
Male 21% 76% 3% 100%
Other Gender 100% 0 0 100%
Total 31% 66% 3% 100%
Column Percentages
Percent of each teaching level that is female or male.Total of each teaching level is denominator.
Middle School High School Other Level Total
Female 71% 57% 67% 62%
Male 25% 43% 33% 37%
Other Gender 4% 0 0 1%
Total 100% 100% 100% 100%
Fill in the counts in the two-way table.
Calculate row percents or column percents.
Blue Brown Hazel Other Color Total
Female 12 29 10 5 56
Male 14 13 6 1 34
Other Gender 1 0 0 0 1
Total 27 42 16 6 91
Gender vs. eye color
Row Percentages
Percent of each gender that has particular eye color. Total of each gender is denominator.
Blue Brown Hazel Other Color Total
Female 21% 52% 18% 9% 100%
Male 41% 38% 18% 3% 100%
Other Gender 100% 0 0 0 100%
Total 30% 46% 18% 6% 100%
Bivariate Statistics
Representing Data ● two-way tables● scatter plots
Introduced: Grade 8Reviewed: Algebra 1
Linear Models ● line of best fit● interpreting slope
---------------------------------------● residual plots● correlation coefficient
Introduced: Grade 8Reviewed: Algebra 1-------------------------------------------------------------Introduced: Algebra 1
ProbabilityProbability Models ● random sampling
● sample space● relative frequencies
Introduced: Grade 7Reviewed: Geometry
Compound Events ● lists, tables, tree diagrams● simulations
------------------------------------------------------● weighted tree diagrams, area
models
Introduced: Grade 7Reviewed: Geometry------------------------------------------------Introduced: Geometry
Conditional Probability ● independence of events● conditional probabilities● addition and multiplication rules (+)● expected value (+)
Introduced: Geometry
From 6–8 Statistics and Probability Progression (page 7):It must be understood that the connection between relative frequency and probability goes two ways. If you know the structure of the generating mechanism (e.g., a bag with known numbers of red and white chips), you can anticipate the relative frequencies of a series of random selections (with replacement) from the bag. If you do not know the structure (e.g., the bag has unknown numbers of red and white chips), you can approximate it by making a series of random selections and recording the relative frequencies. This simple idea, obvious to the experienced, is essential and not obvious at all to the novice. The first type of situation, in which the structure is known, leads to “probability”; the second, in which the structure is unknown, leads to “statistics.”
Digital ToolsTinkerPlots (http://www.tinkerplots.com)Fathom (http://fathom.concord.org)Desmos (http://www.desmos.com)Tuva Labs (https://tuvalabs.com)Relating Histograms and Box Plots DemoLeast Squares DemoTransforming a Normal Curve DemoToday’s Workshop DataGoogle spreadsheets (standard deviation example)
Thank you!Elizabeth DeCarliHS Math Content [email protected]
Andres MartiHS Math Content [email protected]
www.sfusdmath.org
@SFUSDMath @CAMathCouncil#cmcmath
