STATS POSTERS

Level 2

(Don’t print this page.)

GarethBell.com

Thoughts from the Author

• Made in 2025 for teaching Level 2 Stats.
• I like to have all the answers as concisely as possible on the wall for each assessment, so students can refer to them in assessments. i.e. Networks and Probability each have three topics, three questions, and I’ve made three posters.
• I usually colour this class pink in my planner, �hence a pink colour scheme.
• There are a couple of math songs (PPDAC, Mean Median Mode). The audio tracks are from youtube audio library.
• Images from nounproject.com
• Other free resources on Garethbell.com

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Envisaged Wall Layout

• Printed A3, Landscape, Colour. �Don’t laminate, these standards get thrown out in a few years.

NETWORKS

Achievement Standard 91260 (2.5)�2 Credits

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Traversability – All Edges Once

> 2 Odd Nodes = Not Traversable

2 Odd Nodes = Semi Traversable �Must start and finish at an odd node.�aka Eulerian Path.

All Even Nodes = Fully Traversable �Can start anywhere. Will finish same place.�aka Eulerian Circuit.

Minimum Spanning Trees – All Nodes

Minimum Spanning Tree: Lowest weight tree connecting all nodes.�

Kruskal’s Algorithm:

1. Find the shortest edge.
2. Find the next shortest edge �that does not create a circuit.
3. Repeat step 2 until all �nodes are connected.
4. Show the total weight �of the MST at the end.

5

4

3

7

5

4

3

7

5

4

3

7

Weight

3

Weight

3

4

Weight

3

4

5

Total: 12m

=

Number of Edges in MST = Nodes - 1

Shortest Path – Tree Diagram

How: Construct a tree diagram.

Example: Shortest Path A-B (km)

A

B

C

D

6

1

1

6

3

Total = 6km

Total = 7km

Total = 5km

A

B

C

D

6

1

1

6

3

Answer: Shortest Path A-B = 5km

Between two nodes

Shortest Path – Dijkstra

Example: Shortest Path A-B (km)

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Start from the origin. �

1. Find cheapest cost to all nearby nodes, and write them in.�
2. If there are two ways to get to one node, write in the lesser, and cross out the other.�
• Repeat.

A

B

C

D

6

1

1

6

3

A

B

C

D

6

1

1

6

3

A

B

C

D

6

1

1

3

3

3

4

A

B

C

D

1

1

3

3

4

5

6

6

6

Answer: A-C-D-B = 5km

Networks Requirements

GRAPHING

Achievement Standard 91257 (2.2)�4 Credits

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2.2 Graphing

Parabola (U) �y = x^2�y = a(x + b)² + c

�

Cubic (N) �y = x^3�y = a(x + b)³ + c

^�

Absolute Value (V) �y = |x|�y = a|x + b| + c

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Exponential�y = a^x�y = a^{(x + b)} + c

�

Hyperbola�y = . a . + c� (x + b) .

^�

a 🡪 scale factor

b 🡪 left shift

c 🡪 up shift

Key words

• Symmetry: reflection
• Vertex: turning point
• Restricted domain: � These x-values
• Asymptote: �no touch line

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PARABOLA

Features:

• a 🡪 scale factor
• b 🡪 left shift
• c 🡪 up shift
• Domain and Range

y = a(x + b)² + c

Properties:

• Continuous smooth curve
• Has a Vertex (min or max)
• Line of Symmetry through vertex

�

CUBIC

Features:

• a 🡪 scale factor
• b 🡪 left shift
• c 🡪 up shift
• Domain and Range

y = a(x + b)³ + c

Properties:

• Continuous smooth curve
• Point of Inflection (not vertex)
• Rotational Symmetry about �Point of Inflection�

ABSOLUTE VALUE

Features:

• a 🡪 scale factor
• b 🡪 left shift
• c 🡪 up shift
• Domain and Range

y = a|x + b| + c

Properties:

• Straight, not curved
• Line of Symmetry through vertex

�

HYPERBOLA

Features:

• a 🡪 scale factor
• b 🡪 left shift
• c 🡪 up shift
• Domain and Range

. a . �(x + b)

Properties:

• Two separate smooth curves
• Horizontal and Vertical Asymptotes�
• Two Axis of Symmetry

�

+ c

y =

EXPONENTIAL

Features:

• a 🡪 scale factor/base
• b 🡪 left shift
• c 🡪 up shift
• Domain and Range

y = a^{(x + b)} + c

Properties:

• Continuous smooth curve
• Horizontal Asymptote
• Untransformed, goes through �(0,1), and (1, “a”)

�

Graphing Self-Checklist

17

INFERENCE

Achievement Standard 91264 (2.9)

4 Credits

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Mean Median Mode song

Mean is the average, add and divide them

Median is the middle, mode is most common

Range is the big one, minus the small one

This works for a sample, or the population

PROBLEM

Example:

I wonder if the median travel time (minutes) for students who catch the bus is longer than the median travel time (minutes) for students who walk, for ALL high school students in NZ, for data from Census at School in 2015.

20

Comparison Questions must have:

1. Two Categorical variables �(2 groups)
2. Numerical variable (Measurement or Count)
3. The word “median”
4. Direction
5. Population (e.g. use the word ALL to describe it)

PLAN

1) Simple random sample: �Everybody has same chance.

2) Stratified sample: Break population into Strata (groups) based on a characteristic. Sample each.

3) Cluster sample: Randomly �chosen clusters only sampled.

4) Systematic random sampling: �Sample every nth person on a list. (like a comb)

Bigger Sample sizes are more accurate (e.g. >= 30)

Biased samples are bad.

Representative samples are good

DATA

Creating a comparison �graph in NZGrapher

1. Select/Upload your data
2. Get the right sample size
3. Make a dot plot with your number and category variables
4. Add summaries, box plots �and confidence intervals

ANALYSIS

23

Main features to analyse and compare for your sample.

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1. Shape�
2. Centre�
3. Spread�

Merit: justify your statements using numbers and context

Excellence: include the story behind your statements including research

Normal

Left-skewed

Right-Skewed

Bimodal

Mode

Median�(Middle)

Mean�(Average)

Outlier 🡪

🡨 IQR 🡪

CONCLUSION

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• The Confidence Intervals overlap, so we can’t confidently say �the median amount of chairs wrecked by cats is more than dogs.
• A sample size of only 20 means the confidence intervals are large, �and the sample isn’t very representative.
• Other Factors: E.g. Dogs often live outside, so can’t wreck couches.

1. Interpret the confidence intervals
2. Answer the original investigation question
3. Discuss Sampling variability

Example:

The confidence intervals don’t overlap, �so we can confidently make the call that:

The median travel time (minutes) for students who catch the bus is longer than the median travel time (minutes) for students who walk, for ALL high school students in NZ, for data from Census at School in 2015.

If I took a different sample, there would be different randomly chosen data, so would have slightly different statistics and confidence intervals.

CONCLUSION

• The Confidence Intervals overlap, so we can’t confidently say �the median amount of chairs wrecked by cats is more than dogs.
• A sample size of only 20 means the confidence intervals are large, �and the sample isn’t very representative.
• Other Factors: E.g. Dogs often live outside, so can’t wreck couches.

Number of couches wrecked

Sample Size: �20 of each

Dogs

Cats

EXPERIMENTS

Achievement Standard 91265 (2.10)� 3 Credits

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​

PPDAC

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Problem Plan Data, Analysis Conclusion

This is the cycle that we’re using

The way to find, your enquiry solution

Is Problem Plan Data, Analysis Conclusion

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Controlled Experiments

A controlled experiment is where one or more factors are intentionally changed (independent / explanatory variable), ��Other(s) are kept constant (controlled variable), ��to find the outcome of a dependent / response variable.

28

Sources of Variation

1. Measurement Variation �– Unreliable measuring.
2. Occasion to Occasion variation �– Different results each time.
3. Individual to Individual Variation – Different answers for each person. AKA Real/Natural
4. Sampling Variation �– Different samples have different results.
5. Induced Variation �– Variation induced/caused by other factors.

I can’t read �the ruler

This is my �personal best

I can throw �further than you

This sample is �stronger than �that one

I’ll give you �$20 if you win

Paired Experiment Arrow Graph

1. Import Data�

2) Paired Experiment type�

3) Select numerical variables�

4) Add Arrows & Summaries�

5) Title, then screenshot

Paired vs Independent - Notes

A Paired Experiment

• Consider the change �in data.
• First find the differences, then calculate the average of the differences.

e.g. How much shorter do Aiden, Oliver and Riley throw the ball before and after 10 press ups?

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An Independent Experiment

• Multiple independent sets of data being compared.
• Find the averages, �and then calculate the difference of the averages.

e.g. How much less do three year 12s throw the ball compared �to three year 9s?

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Placebo, Blind and Double-Blind

Placebo Effect: When giving a placebo / �dummy treatment, affects or motivates the participant’s outcome.

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Blind Experiments: Some information is withheld from participants but not the experimenter. �

Double-Blind Experiments: Both participants and experimenters have limited information while the experiment is being carried out. So that neither the experimenter and participant aren’t biased

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Types of Probability

Theoretical Probability �Where outcomes are equally likely�

Experimental Probability �From trials. a.k.a. �Long-run Relative Frequency

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Conditional Probability: P(event) given that �another event has �occurred.

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P(event) = number of occurances number of trials

e.g. Probability I get a ‘Kamar’ today

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P(event) = number of occurrences� total possible outcomes

e.g. Probability it is a Saturday

�

e.g. Probability I get a ‘Kamar‘�given that it is a Saturday

Normal Distribution - Casio CFX 9860G

1. “STAT” mode:
2. F5 (DISTributions)
3. F1 (NORMal Distribution)
4. F2 (Ncd) for Normal Density �or InvN for Inverse Normal
5. Data: Variable (not List)
6. Set lower and upper values of range.
• Use 99999 for ∞ and -99999 for -∞
7. Set std deviation (σ) and mean (µ)
• Use 1 and 0 for Std Normal Distribution
8. Press Execute

Normal C.D

Data :Variable

Lower :12

Upper :99999

σ :2

μ :10

Execute .

Normal C.D

p =0.15865525

z:Low=1

z:Up =99999

​

​

p = 15.9%

PROBABILITY

Achievement Standard 91267 (2.12)�4 Credits

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Probability Trees

In my class 10/19 are girls. Of the boys 1/3 prefer cats. �And Half the girls prefer cats.

1. P(Boy and Likes cats?)�
2. P(Boy)
3. P(Boy or Likes cats)?�
4. P(Boy Given That � they like cats?)

³/₁₉ + ⁶/₁₉ = ⁹/₁₉

⁹/₁₉ × ¹/₃ = ³/₁₉

⁹/₁₉

¹⁰/₁₉

¹/₃

²/₃

¹/₂

¹/₂

Boy

Girl

Cat

Dog

Cat

Dog

³/₁₉ + ⁶/_{19 +} ⁵/₁₉ = ¹⁴/₁₉

⁹/₁₉ × ¹/₃

= ³/₁₉

⁹/₁₉ × ²/₃

= ⁶/₁₉

¹⁰/₁₉ × ¹/₂

= ⁵/₁₉

¹⁰/₁₉ × ¹/₂

= ⁵/₁₉

³/₁₉ ÷ (³/₁₉ + ⁵/₁₉) = ³/₈

In a Normal Distribution…

μ = mean

σ = std dev

Two Way Tables - And, Or, Condition

1. P(Boy and Likes cats?)���
2. P(Boy or Likes cats)?���
3. P(Boy Given That �they like cats?)

P(Boy & Cats) = ³/₁₉

P(Boy or Cats) = ¹⁵/₁₉

P(Boy | Cats) = ³/₈