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Statistics from the Students Voices
Monica Dabos & Dustin Silva College of the Canyons
How not to be ignorant about the world
https://www.youtube.com/watch?v/s/Sm5xF-Uygdg&start=10
How did deaths per year from natural disasters change in the last century?
A. More than doubledB. Remained about the sameC. Decreased to less than
half
Women aged 30 spent how many years in school? (Man of the same age spent 8 years)
A. 7 yearsB. 5 yearsC. 3 years
In the last 20 years the percent of people living in extreme poverty has…?
A. Almost doubledB. Remained about
the sameC. Almost halved
We Need Statistics!!!
Shape Center
&Spread
1
3
2
Distribution
Shape Center and Spread
• Shape
• Spread
Center
Shape, Center and Spread
Math 140
• Center = • Mean, Median, Mode
• or bulk of the data
• Shape = • Unimodal, • Skewed,• Symetric
•IN CONTEXT• Spread
=• Range,
• IQR• SD
1 2
3 4
Got it ?
Lets See
I know everyone LOVES grading on a Saturday….
• Please grade the student description of a histogram
• Grade on a scale of 0-10, with 10 being the maximum point value
• On a Post It put your grade and any pros and cons about your student’s description
• Compare your responses with your group
If you have not seen the graph and/or have no idea of the topic being described, which of the
following descriptions would be the best to understand the data (topic).
Student 1
Student 2
Student 3
Student 4
Student 5
The Graph
2702402101801501209060300
16
14
12
10
8
6
4
2
0
Size (acres)
freq
uenc
y~ N
umbe
r of
Vin
eyar
ds
The histogram shows the sizes (in acres) of 49 vineyards
How would you describe a distribution?
CONCLUSION
Learn from Students VoicesLESSON ONE: Don’t let students follow a script• Students will mimic us, if we let them. • Coach students to be independent and take
risks• Guide students to success beyond the
classroom • Move away from recipes• What is our students’ greatest competition in
the workforce?
LESSON 2: Make students understand why histograms are important• Why Students struggle with histograms? • What do we want them students to learn?• Why histograms are important?
Learn from Students Voices
LESSON 3: Why do students have difficulties with histograms?• Students…
– …. Don’t understand aggregated data– ….Don’t understand what the x and y axis represent– ….Don’t emphasize context – …. Focus on statistics lingo rather than understanding what
it tells us about the data– …. Don’t connect histograms to other statistics topics
Learn from Students Voices
WHY HISTOGRAMS?
Why are histograms so important?
• They are the most widely used type of graph in media
• They are widely misused
• Three types of Lies:
Histograms area Multipurpose tool.
Need to be understood
Levels of Understanding (according to Monica Dabos)
– Level one ~ understand ~ x-axis and y-axis– Level two ~ extract info from Histogram ~ find the
median or other percentages– Level three ~ Describe in context ~ unveiling
information from our data– Level four ~ Understand variability in data– Level five ~ Which Standard deviation is larger or
smaller – Level six ~ Informal Inference– Level seven ~ sampling distribution
Proportion of hits
Figure 1From Meletiou-Mavrotheris and
Lee (2006) p. 5
Comparing Standard Deviation
A has larger standard deviation than B
B has larger standard deviation than A
Both have equal standard deviation
Both have the same rangeRelative few deviations of -2 or 2 in Graph AMajority of the deviation are -2 or 2 in Graph B
What Makes the SD Larger or Smaller?
Comparing Standard deviation
A has larger standard deviation than B
B has larger standard deviation than A
Both have equal standard deviation
One graph mirrors the otherFrequencies of each mean deviation the sameTherefore, average deviation is the same.
Comparing Standard deviation
A has larger standard deviation than B
B has larger standard deviation than A
Both have equal standard deviation
All deviations in Graph B are -2.5 or 2.5 1/3 deviations in Graph A are -2.5 or 2.5Therefore, average deviation is larger for Graph B.
Connection with Formal Inference
Null Hypothesis: Average salary for females equals average salary for malesAlternative Hypothesis: Average salary for females is not equal to average salary for males
1) Given the following graphs describe if there is a difference between male and female beginning salary. Make sure you use shape, center and spread in context to compare and contrast the beginning salaries. 2) By considering shape center and spread, do you think there is a significant difference between the beginning salaries for the two groups? Can you predict if the p-value will small or large?
T-Value = -11.97 P-Value=0.000
Gender N Mean StDev SE Meanf 216 13092 2936 200m 260 20255 9092 564
Two-sample T for Beginning Salary Gender N Mean StDev SE Meanf 216 13092 2936 200m 260 20255 9092 564 Difference = mu (f) - mu (m)Estimate for difference: -716395% CI for difference: (-8340, -5986)T-Test of difference = 0 (vs not =): T-Value = -11.97 P-Value = 0.000 DF=321
Who would like to Tango?
• Mentors• Mentees• Hub coordinators
• http://monicadabos.com/TANGOSTATED.html
TANGO STAT EDTraining a New Generation of Statistics Educators
CSICSI is a collection of yearlong activities for high school and community college faculty that will help deepen understanding of the teaching and learning of statistics. This first weekend will focus on statistical inference and will include topics such as conceptual understanding, informal inference vs. formal inference, utilizing technology, choosing the proper test, and p-value.
Keynote Speaker Friday/Saturday: Roxy Peck
Mark your calendar! Date: Saturday, October 24, 2015 8:45am to 4:00pm with an optional reception and talk at 6pm on Friday, October 23rd. Location: University Center 258College of the Canyons26455 Rockwell Canyon RoadSanta Clarita, CA 91355 Please register at: https://www.statcrunch.com/5.0/survey.php?surveyid=12267&code=WRVAL
