Download Q 2 - National Centre of Literacy and Numeracy for Adults

Challenge the statistics!
2012
Overview
•
Examine rationale for developing statistical and
graphing skills in a workplace context
•
Explore statistical techniques
•
Explore a learning sequence for use with
graphs
There are three kinds of lies:
lies, damned lies, and statistics
Mark Twain
Getting to know graphs
Most familiar
Place the graphs on a cline from
least familiar to most familiar
Least familiar
A shift in thinking...
Number
Statistics
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
Understanding
statistics
•
Statistics help us to explain things
•
They provide agreed methods of presenting information
Therefore statistics sit well inside the
literacy/numeracy framework
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
Statistical awareness
Question:
Estimate how many people will there be in Auckland in 70 years time if the
population grows by 5% per year?
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 =
48 million!!!
Measures of centre
The mean
Mean girls are
AVERAGE
The median
The middle of the road
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:
17, 19, 21, 22, 22, 27
Add all numbers and divide by how many there are.
(17 + 19 + 21 + 22 + 22 + 27) = 128
6
Mean: 21.3 minutes
Finding the ‘median’
The ‘median’ is the middle number in the series.
17, 19, 21, 22, 22, 27,
Total amount of data points,
plus one, divided by 2.
Median = 21.5
6+1
2
Activity
In your groups – describe the difference between the two
packing sheds using statistical methods
Measures of spread
• Range
• Interquartile range
• Standard deviation
Finding the range
The range is found by subtracting the minimum value from the maximum value.
max – min = range
So...
For example, our data from pack shed one is:
4
4, 5, 5, 6, 6,
9 7, 9
Range = 9 – 4 = 5
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.
Pack shed one:
1 2
4, 55, 5, 66, 6, 7
7, 9
1 2 3 4
Q 1: 5
Q 2: 6
Q 3: 7
7+1 =4
2
3+1 =2
2
Pack shed two
3, 33, 7, 7
7, 8, 88, 9
Quartile 1: 3
Quartile 2: 7
Quartile 3: 8
Interquartile range
Pack shed one:
4, 5, 5, 6, 6, 7, 9
Pack shed two:
3, 3, 7, 7, 8, 8, 9
Q 1: 5
Q 2: 6
Q 3: 7
Q1: 3
Q2: 7
Q3: 8
1
2
3
4
5
6
7
8
9
10
Interquartile range
Pack shed one:
4, 5, 5, 6, 6, 7, 9
Pack shed two:
3, 3, 7, 7, 8, 8, 9
Q 1: 5
Q 2: 6
Q 3: 7
Q1: 3
Q2: 7
Q3: 8
1
2
3
4
5
6
7
8
9
10
Interquartile range
Pack shed one:
4, 5, 5, 6, 6, 7, 9
Pack shed two:
3, 3, 7, 7, 8, 8, 9
Q 1: 5
Q 2: 6
Q 3: 7
Q1: 3
Q2: 7
Q3: 8
1
2
3
4
5
6
7
8
9
10
Critical analysis
Generating questions
•
I wonder why...?
•
What if ...?
•
Has the sample size differed between the graphs?
•
Is the sample large enough?
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
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
Activity
1. Design a learning plan for a workplace graph
2. Discuss with others
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