2012

Challenge the statistics!

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

Place the graphs on a cline from least familiar to most familiar

Least familiar

Most 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

The median

Mean girls are AVERAGE

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:

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

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

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.

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

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:

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

Pack shed two

3, 3, 7, 7, 8, 8, 9

Quartile 1:

Quartile 2:

Quartile 3:

73 8

3

7

8

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

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

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

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