Meet the Kiwis…. Population of kiwis… Codes… Species Region GS-Great Spotted, NIBr-NorthIsland...
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Transcript of Meet the Kiwis…. Population of kiwis… Codes… Species Region GS-Great Spotted, NIBr-NorthIsland...
Meet the Kiwis…
Population of kiwis…
Species
Weight (kg) Height (cm)
Region/gender
Codes…
Species Region• GS-Great Spotted, • NIBr-NorthIsland
Brown, • Tok-Southern Tokoeka
• NWN-North West Nelson, • CW-Central Westland, • EC-Eastern Canterbury• StI-Stewart Island, • NF-North Fiordland, • SF-South Fiordland• N-Northland, • E-East North Island, • W-West North Island
Kiwi Kapers 1
Take a handful of data cards and sort them
Write some “I notice…” statements
Look at what other people have done
Problem
I wonder what the median weight of New Zealand kiwis is?
I wonder what the median weight of New Zealand kiwis is?
What do you think the typical weight will be?
Why? Sketch the shape of the distribution
of weights of New Zealand kiwis.
Plan
What variable are we going to use to answer our question?
How are we going to gather our data? Everyone? Sample?
Simple random sample of 15 kiwis please.
Data
SRS of 15 kiwis Make sure you don’t sample the
same kiwi more than once
Analysis
Plot dot plot on axes Add box plot above Note the 5 point summary
{Minimum, lower quartile, median, upper quartile, maximum}
Analysis
Repeat three more times to complete 4 sets of 15 samples
Write (at least) three “I notice…” statements about your samples Look at shape and spread – what do you notice? Similarities? Differences? – between your sets of
samples… Make sure your statements include context
Would I be able to tell that you were looking at the weight of Kiwis?
Conclusion
Use sample median to provide a point estimate of the population parameter
From my sample data I estimate that the median weight for all New Zealand kiwis is….
Conclusion
But they’re all different!
Who is right?
From my sample data I estimate that the median weight for all Stage 1 statistics students is….
Kiwi Kapers 1
Activity recaps…
•Language needed (eg population, sample, variables, etc)
•PPDAC cycle
•Question types
•Posing good investigative questions
•Sampling issues
•dot plot box plot
•Describing distributions HANDOUT
Kiwi data cards
Kiwi Kapers 1 lessons
Kiwi Kapers 1
What do you think the population distribution will look like?
*most values are between ___ & ___
* the largest value is about ___
* the smallest value is about ___
* the middle is around ___
HANDOUT
Kiwi data cards
Kiwi Kapers 1 lessons
Kiwi Kapers 1
Movies – one sample - summaryBox plot with memory…
n = 30
Sketch what you think the box plots with memory would look like for
n = 10n = 100n = 1000
..\..\Pip\Animations_WILD\boxes_1samp_mem_30.pdf
Movies – one sample - summary
Box plot with memory…
We want to plant a reflex…
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 10
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 10
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 30
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 30
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 100
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 100
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 300
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 300
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 1000
Movies – one sample - comparisonBox plots with memory…
Could you make a call back in the population?
n = 1000
Sample size vs making the call…
If the samples are larger, the difference between the two groups doesn’t have to be as big to make the call that there is a difference between them BACK IN THE POPULATION
HANDOUT
Guidelines for “How to make the call”
L6 Guide – incorporates aspects of both spread and sample size
We want to plant a reflex…
Kiwi Kapers 2Explores what sample size we want to take to be reasonably sure that the inference(s) we make are representative of the population.
I wonder what are typical weights of kiwis?
What is a sensible and reliable sample size to use for making inference about a population HANDOUT
Kiwi Kapers 2 lessons
Kiwi Kapers 2 Fathom lessons
Go play on Fathom…
… head down to the computer lab with your Kiwi Kapers 2 student fathom document…
TASK 1 – reflection
What appears to be the effect of increasing the sample size on:
(i) the median from sample to sample?
(ii) the IQR from sample to sample?
(iii) the range from sample to sample?
TASK 2 – reflection
What is a sensible and reliable sample size to use to make inferences about a population?
Samples of 30 or 50 are okSamples of 15 are too variableSamples of 100, while even better, are not so much better that we need to spend the extra time and energy (and $) collecting 100 kiwis when 30 or 50 will do
We want the smallest sample that should give us a reliable estimate of the population
Kiwi Kapers 3
Develops students’ understanding of the L7 guide & informal interval estimates
Under deve
lopment
Kiwi Kapers 3Under development
Kiwi population
weight
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Kiw ipop Dot Plot
1.5 2.0 2.5 3.0 3.5 4.0 4.5
weight
Kiw ipop Box Plot
Kiwi Kapers 3Under development
Sample medians
n = 30
sample_median
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Measures from Sample of Kiw ipop (n=30) Dot Plot
sample_median
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Measures from Sample of Kiw ipop (n=30) Box Plot
Kiwi Kapers 3Under development
Sample medians
n = 400
sample_median
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Measures from Sample of Kiw ipop (n=400) Dot Plot
1.5 2.0 2.5 3.0 3.5 4.0 4.5
sample_median
Measures from Sample of Kiw ipop (n=400) Box Plot
Kiwi Kapers 3Under development
Together
population
n=30
n=400
… ideas of how to put an interval estimate around our point estimate
… is one IQR enough?
… impact of sample size?
2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
Lead into L7 guideline for informal interval estimate
They cover the true population median approximately 9 out of 10 samples taken (shown with simulations)
Lead into L7 guideline for informal interval estimate
Making the call at L7
Unit plan still under development…
And heading towards the assessment…