Making the call Year 10
Some activities to immerse students in
ideas about sample, population,
sampling variability and how to make a
“claim” when comparing two groups
Aim of the workshop
To present some classroom activities to immerse
students in ideas about:
 sample, population, and the link between sample
and population
 the need to sample
 sampling variability
 shift and overlap when comparing two groups
 formulating guidelines for making a claim when
comparing two groups
Population ideas
Karekare College
 Students selected from 2009 C@S
 School is fictional
 616 students (389 female, 227 males)
 13 variables from C@S survey
 Each card represents a student
 Card colour indicates gender
Karekare College Data
Ethnicity
Transport to
school
Age
Time to school
Year level
Height
Way of carrying
school bag
School bag weight
Popliteal length
Fitness level
Index finger length
Ring finger length
Summary question
(give out strips)
What are typical popliteal lengths of students
at Karekare College?

How would you go about answering a question
like this? (think like a student – Marina & Pip stories: the need to
sample)
Plots using data cards
Summary question
What are typical popliteal lengths of students
at Karekare College?

How would you go about answering a question
like this? (think like a student – the need to sample)
What would the population distribution look like?

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In pairs, take a sample of about 30 students
Plot your sample (box and dot plot)
Compare your plots

What do you notice?
Summary question
What are typical popliteal lengths of students at
Karekare College?




How would you go about answering a question
like this? (think like a student)
What would the population distribution look like?
In pairs take a sample of about 30 students
Plot your sample (box and dot plot)


Get students to describe their sample distribution
Compare your plots – what do you notice?
Location of centres, spread, shape, . . .
Comparison questions


At Karekare College, do boys tend to be taller
than the girls?
At Karekare College, who tends to take a longer
time to get to school; students who walk or
students who travel by bus?
Comparison questions
For each question, ask students to:
 Predict and draw the population
distributions for the variable in the
question.


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Show one population distribution relative to
the other.
Give a rough indication of the range of values
expected.
Collect and plot samples / data.
Comparison questions



Hand out students’ box plots for height and
travel times
Luxury of 18 samples for each question
Box plots drawn without whiskers
B
G
Exploring the plots
Take each question in turn
 For each pair of plots (sample):

Which group tends to have the bigger
values?


Consider shift and overlap
Sort the plots wrt shift and overlap
B
G
Exploring the plots: for example
Heights plots
B
G
In this plot:
Shift is small, boys values shifted slightly further up the scale
– boys’ median is higher than girls’
Lots of overlap
Suggestive message: back in the two populations
boys tend to be taller than girls
Exploring the plots: for example
Heights plots
B
G
In this plot:
Shift is large, girls value shifted further up the scale
– girls’ median higher than boys
Little overlap
Suggestive message: back in the two populations girls
tend to be taller than boys
Exploring the plots
Take each question in turn (start with BW: ‘time to school’)
 For each pair of plots (sample):

Which group tends to have the bigger values?


Consider shift and overlap
Sort the plots wrt shift and overlap
B
G
What do you notice over all
samples? – BG: heights of boys & girls

Sometimes it’s the boys’ box shifted
further up the scale and sometimes it’s
the girls’.

Sometimes the boys’ median is higher,
sometimes the girls’ median is higher,
sometimes they are the same.
Small shift

In all samples, large overlap of boxes
What do you notice over all
samples? – BG: heights of boys & girls

Suggestive message is not consistent

Not prepared to make the call which group tends
to have the larger values back in the two populations
What do you notice over all
samples? – BW: time to school

In all samples the bus box is shifted much
further up the scale

The bus median is always much higher than the
walk median
Large shift

Sometimes the boxes overlap, sometimes
they do not, when they overlap it is only by a
small amount
Small or no overlap
What do you notice over all
samples? – BW: time to school

Suggestive message is consistent

Make the call that students who travel by bus tend to take a
longer time to get to school than those who walk back in the two
populations.
Formulating guidelines


Small shift and large overlap –
not prepared to make a call, (‘too
close to call’)
Large shift and small or no overlap
– make the call
How large does the shift
have to be to make the call?
Formulating guidelines
At least one group’s median
has to be outside the box of the other group.
Formulating guidelines
Make the call when
At least one group’s median is outside
the box of the other group.
otherwise,
it’s too close to call.
Formulating guidelines
Make the call when
At least one group’s median is outside
the box of the other group.
otherwise,
it’s too close to call.
Before we carry on:
Please paper-clip your height strips and
time strips back together
Visualising the suggested
message
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Show animations
Raise hands to indicate which median is
higher.
E.g.
boys higher – boys up the scale: right hand;
girls higher – boys down the scale: left hand
Examples: Iron data

3 examples
Wrap Up
Presented some classroom activities to immerse
students in ideas about:
 the link between sample and population
 the need to sample
 sampling variability
 shift and overlap when comparing two groups
 formulating guidelines for making a claim when
comparing two groups
Thank you!