meet the kiwis…

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 1Take a handful of data cards and sort themWrite some “I notice…” statementsLook 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 1Activity 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 cardsKiwi Kapers 1 lessons

Kiwi Kapers 1What 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 cardsKiwi 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 - summaryBox 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 lessonsKiwi Kapers 2 Fathom lessons

Go play on Fathom…

… head down to the computer lab with your Kiwi Kapers 2 student fathom document…

TASK 1 – reflectionWhat 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 – reflectionWhat 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 3Develops students’ understanding of the L7 guide & informal interval estimates

Under development

Kiwi Kapers 3Under development

Kiwi population

weight1.5 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 4.5weight

Kiw ipop Box Plot

Kiwi Kapers 3Under development

Sample mediansn = 30

sample_median1.5 2.0 2.5 3.0 3.5 4.0 4.5

Measures from Sample of Kiw ipop (n=30) Dot Plot

sample_median1.5 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 mediansn = 400

sample_median1.5 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 4.5sample_median

Measures f rom 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…