2012 challenge the statistics!. overview examine rationale for developing statistical and graphing...
TRANSCRIPT
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2012
Challenge the statistics!
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Overview
• Examine rationale for developing statistical and graphing skills in a workplace context
• Explore statistical techniques
• Explore a learning sequence for use with graphs
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There are three kinds of lies:
lies, damned lies, and statistics
Mark Twain
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Getting to know graphs
Place the graphs on a cline from least familiar to most familiar
Least familiar
Most familiar
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A shift in thinking...
Number Statistics
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Critical Numeracy
Four aspects of critical numeracy:
• The ability to critique or make critical interpretations of mathematical information
• The ability to unpack, interpret and decode mathematical situations
• The ability to use mathematics in a self-reflective way
• The ability to use mathematics to operate more powerfully in the world
Stoessiger, 2002
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Understanding statistics
• Statistics help us to explain things
• They provide agreed methods of presenting information
Therefore statistics sit well inside the literacy/numeracy framework
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What do we want?
We want employees to engage autonomously in critical analysis of statistical information – particularly in the workplace.
This means supporting employees to:
• Initiate quality questions
• Identify limitations/strengths
• Reflect on the information
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Statistical awareness
Question:
Estimate how many people will there be in Auckland in 70 years time if the population grows by 5% per year?
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70 / 5 = 14
Therefore the population will double every 14 years.
Question: How many times will the population double in 70 years?
70 /14 = 5
1.5 million x 2 x 2 x 2 x 2 x 2 =
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48 million!!!
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Measures of centre
The mean
The median
Mean girls are AVERAGE
The middle of the road
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Finding the ‘mean’
Darrel records the time it takes him to travel to work every day for six days. He records the following times in minutes:
Add all numbers and divide by how many there are.
(17 + 19 + 21 + 22 + 22 + 27) = 128
17, 19, 21, 22, 22, 27
6
Mean: 21.3 minutes
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Finding the ‘median’
17, 19, 21, 22, 22, 27,
The ‘median’ is the middle number in the series.
Median = 21.5
Total amount of data points, plus one, divided by 2.
6 + 1 2
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Activity
In your groups – describe the difference between the two packing sheds using statistical methods
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Measures of spread
• Range
• Interquartile range
• Standard deviation
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Finding the range
The range is found by subtracting the minimum value from the maximum value.
So... max – min = range
For example, our data from pack shed one is:
4, 5, 5, 6, 6, 7, 9
Range = 9 – 4 = 5
94
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Interquartile range
Question:How many cuts does it take to divide one plank of timber into quarters?
Three
To find the Interquartile range – you identify where the three cuts are made to your data.
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Pack shed one:
4, 5, 5, 6, 6, 7, 9
7 + 1 2
= 4
3 + 1 2
= 2
5 6 7
Q 1: 5
1 2 3 41 2
1 2
Q 2: 6Q 3: 7
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Pack shed two
3, 3, 7, 7, 8, 8, 9
Quartile 1:
Quartile 2:
Quartile 3:
73 8
3
7
8
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Interquartile range
1 2 3 4 5 6 7 8 9 10
Pack shed one: 4, 5, 5, 6, 6, 7, 9
Q 1: 5Q 2: 6Q 3: 7
Pack shed two:3, 3, 7, 7, 8, 8, 9
Q1: 3Q2: 7Q3: 8
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Interquartile range
1 2 3 4 5 6 7 8 9 10
Pack shed one: 4, 5, 5, 6, 6, 7, 9
Q 1: 5Q 2: 6Q 3: 7
Pack shed two:3, 3, 7, 7, 8, 8, 9
Q1: 3Q2: 7Q3: 8
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Interquartile range
1 2 3 4 5 6 7 8 9 10
Pack shed one: 4, 5, 5, 6, 6, 7, 9
Q 1: 5Q 2: 6Q 3: 7
Pack shed two:3, 3, 7, 7, 8, 8, 9
Q1: 3Q2: 7Q3: 8
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Critical analysis
Generating questions
• I wonder why...?
• What if ...?
• Has the sample size differed between the graphs?
• Is the sample large enough?
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Teaching sequence
The Learning Progressions provide a learning sequence for instruction on graphs.
Learners will:
1. Describe the features of a graph
2. Analyse the data (ask critical questions)
3. Draw reasonable conclusions based on the data
4. Generate (or manipulate) a graph based on workplace data
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Instructional strategies
Modelling• The tutor selects a graph and models verbally how it can be critiqued.
Questioning• Present learner with a range of questions that encourages them to explore
the graph – What type of graph is being used (and why?)
– What does this graph represent?
– What unit of measures are used?
– What does the graph not show?
Discussion• Interactive conversation in which tutor and learner become joint constructors
of learning
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Activity
1. Design a learning plan for a workplace graph
2. Discuss with others
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Summary
• Examine rationale for developing statistical and graphing skills in a workplace context
• Understand how graphs represent data
• Explore statistical techniques
• Explore a learning sequence for use with graphs