Vocab
Census = collection of data from all members of a population
Sample = selection of data from some members of a population
Range = highest less lowest value
Median = put the data in order and the median is the middle value, or add the 2 middles values together and divide by two
Mode = the most common value
Mean = add all the values up and divide by the number of values
Discrete Data is counted (whole numbers)
Continuous Data is measured (decimals too)
Distribution = the way data is spread out
peak, rounding, skewed,

Above is a sample of 9 males and 9 females, below there is 1000 people in the sample.
This is an example of the "too close to call" situation - the small sample gave us the impression that girls had a longer arm span than boys.
We used the DBM/OVS to see that it was less than a thrid - so too close to call.
You can take more samples - of 18 - and see sampling variability in action!

Thrusday the 31st of May; Cleaning Data; Bias; working on practise internal in the book.

Cleaning Data = remove or fix obvious input errors
- eg a person being 165m tall. It must be 165cm! - fix it!
- eg a person being "very tall" when all the other pieces of data is in cm - remove it!
5 Key statistics: highest; UQ Upper Quartile; median; LQ Lower Quartile; lowest
IQR = Inter Quartile Range = UQ - LQ (Middle 50%)
If you calculate the mean (add them all up and divide by the number of pieces of data)
and compare the mean to the median think about skew. http://www.studyit.org.nz/subjects/maths/math1/10/

Use http://www.scholarnet.co.nz/member/courses/smol/view.php?r=196&id=950 Choosing a sample: You are GIVEN the sample - does it represent the population? Comments about "a larger sample will give a more accurate result" are true but will not give you excellence. If I was given a different sample, the results would be different.

Choosing a random sample helps to remove bias. Was the sample you were given chosen randomly?

Bias occurs when a sample does not accurately represent the group from which it is taken. Do you think the sample you were given represents the population?

Tricky - we have been working with a sample of a sample! The census at school data base is made up of self selected students - collected via the internet.

The Bias is that students who attend schools without plenty of access to computers did not ever have the chance to fill it in.

The Bias is also the fact that people were not randomly chosen.

Statistical investigation

Plan and conduct investigations using the statistical enquiry cycle:

identifying and communicating features in context differences within and between distributions, using multiple displays

making informal inferences about populations from sample data

Monday 28th May
Started a Practise assessment from the green book, page 51
Students wrote their own questions and started to do the data analysis.
We discussed the fact you choose a continuous variable, and use a category to compare it with.
You CAN NOT compare two continuous variables, you would look at their relationship, and this is a different internal.
You must write your own question to have a chance of getting excellence.

Wednesday the 23rd of May.
Algebra questions from the algebra solving practise test in the green book.
Page 38 of the green book - Vocab for Stats - fill it in.
Used the chapter "Statistical Methods" starting on page 261.
Used the index of the text book.
Also at home students can and should use: http://www.nzmaths.co.nz/glossary http://nzmaths.co.nz/nzc-glossary-mathematics-terms

Statistical inference

Statistical inference is the part of statistics concerned with drawing conclusions about a population based on sample data.

Multivariate data

Data that consists of measurements of three or more attributes or variables for each individual or object in a sample (for example age, height and gender). This contrasts with univariate data where measurements are made of only one attribute, and bivariate data where measurements are made of two attributes.

The boxes below have a median "to the left" so the call could be made with the 3/4 - 1/2 rule is some cases.
Check out the "How to make the call" document

Each student came up with four comparison questions. Yeah Right ;-)

Page 40 to 46 of the green workbook.

Here are some acceptable comparative questions.

The population is the 2009 census at school database.

You are looking at a sample from that population.

This internal requires you to statistically analyse the sample and then use those statistics to make an inference (educated guess) about the population.

Choose a continuous variable and a variable to compare it with. Eg height and gender; bag weight and “bag carry”.

1. What are the similarities and differences of year 11 male and female heights in the 2009 census at school database?

2. Do year 11 males tend to be taller than year 11 females in the 2009 census at school database?

How does the height of year 11 males compare with year 11 females in the 2009 census at school database?

3. Do year 11 males tend to have a longer popliteal length than year 11 females in the 2009 census at school database?

How does the popliteal lengthof year 11 males compare with year 11 females in the 2009 census at school database?

4. Do year 11 males tend to carry heavier bags than year 11 females in the 2009 census at school database?

How does the bag weightof year 11 males compare with year 11 females in the 2009 census at school database?

5. Do year 11 students who carry their bag with two straps tend to carry heavier bags than those who carry their bag with one strap in the 2009 census at school database?

How does the bag weightof year 11 students who carry their bags with one strap compare with those thay carry their bag with two straps in the 2009 census at school database?

6. Does the time taken to get to school by bus tend to be longer than the time taken to walk to school for year 11 students in the 2009 census at school database?

How does the time taken to get to schoolof year 11 students that travel by bus compare with year 11 students that walk to school in the 2009 census at school database?

What did students learn:

Use the word "tend" because this implies you are comparing averages.

The word tend is excellent for the conclusion and acceptable for the question.

Do ------ tend to be ------ than -------- in the population.

The above question could be answered yes or no, so it not the best comparative question.

How does the ------- compare with the-------- in the population.

Next year there is an internal much the same as this one, except you are not given the sample, you take a sample. This video is for next years internal, but some of it may apply to this years internal. http://www.youtube.com/watch?v=-upOeF8MMuM&sns=em

This Video Shows how easy it is to draw box and whisker graphs in geogebra

## MV Stats Internal

## Thursday 7th June: Write your investigative question

## Monday 11th June: Draw your stem and leaf, dot plot and box and whisker

## Tuesday 12th June: Write up your comparisons of the sample statistics, and your inference about the population.

## http://2012maths.wikispaces.com/11Maths+MV+Stats+Inference

## Complete pages 231 to 246 in your Learning Workbook,

## Bring it to class and use classtime also.

## ======================================================================

The Standard: http://www.nzqa.govt.nz/nqfdocs/ncea-resource/achievements/2011/as91035.pdf

Key Tips: http://www.studyit.org.nz/subjects/maths/math1/10/keytips/

Nayland: http://maths.nayland.school.nz/Year_11/AS1.10_Multivar_data/AS1.10_home.htm

Describing Features: http://maths.nayland.school.nz/Year_11/AS1.10_Multivar_data/12_Describing_Data_Features.htm

Inference: http://maths.nayland.school.nz/Year_11/AS1.10_Multivar_data/14_Population_Inference.htm

## ==========================================================

VocabCensus = collection of data from all members of a population

Sample = selection of data from some members of a population

Range = highest less lowest value

Median = put the data in order and the median is the middle value, or add the 2 middles values together and divide by two

Mode = the most common value

Mean = add all the values up and divide by the number of values

Discrete Data is counted (whole numbers)

Continuous Data is measured (decimals too)

Distribution = the way data is spread out

peak, rounding, skewed,

## ==========================================================

Level 6: http://www.nzmaths.co.nz/elaborations-level-six-statistics-0?parent_node=The above link has this document on it

Good links from past teaching of similar topics (For Ms Allan)

http://2011maths.wikispaces.com/NCEA+Level+1+MV+Statistics

http://2012maths.wikispaces.com/12MAI+Inference

## ===================================================================================

Lesson Log - What links were used and what we did in class. Remember we are doing algebra every day too!## =======================================================================

8th June - study period## =======================================================================

7th June - write your question for the internal on Monday and Tuesday the 11th and 12th of June.## =======================================================================

6th June - Practise writing comparative statements; Headings; Inferences; Using a small sample from:Used: http://www.censusatschool.org.nz/2010/data-viewer/ (Just 9 of each)

Above is a sample of 9 males and 9 females, below there is 1000 people in the sample.

This is an example of the "too close to call" situation - the small sample gave us the impression that girls had a longer arm span than boys.

We used the DBM/OVS to see that it was less than a thrid - so too close to call.

You can take more samples - of 18 - and see sampling variability in action!

## =======================================================================

5th June - Polish the practise internal - make a good copy - make it fit the excellence criteria of the marking schedule!## ===================================================================================

Thrusday the 31st of May; Cleaning Data; Bias; working on practise internal in the book.Cleaning Data = remove or fix obvious input errors

- eg a person being 165m tall. It must be 165cm! - fix it!

- eg a person being "very tall" when all the other pieces of data is in cm - remove it!

5 Key statistics: highest; UQ Upper Quartile; median; LQ Lower Quartile; lowest

IQR = Inter Quartile Range = UQ - LQ (Middle 50%)

If you calculate the mean (add them all up and divide by the number of pieces of data)

and compare the mean to the median think about skew.

http://www.studyit.org.nz/subjects/maths/math1/10/

Use http://www.scholarnet.co.nz/member/courses/smol/view.php?r=196&id=950

Choosing a sample: You are GIVEN the sample - does it represent the population?Comments about "a larger sample will give a more accurate result" are true but will not give you excellence.If I was given a different sample, the results would be different.Biasoccurs when a sample does not accurately represent the group from which it is taken. Do you think the sample you were given represents the population?Statistical investigation- Plan and conduct investigations using the statistical enquiry cycle:
- identifying and communicating features in context differences within and between distributions, using multiple displays
- making informal inferences about populations from sample data
- justifying findings, using displays and measures.

http://nzcurriculum.tki.org.nz/Curriculum-documents/The-New-Zealand-Curriculum/Learning-areas/Mathematics-and-statistics/Mathematics-and-statistics-curriculum-achievement-objectives#6Assessment Resources: Below are the two practise assessments that have been downloaded from this link:

http://ncea.tki.org.nz/Resources-for-aligned-standards/Mathematics-and-statistics/Level-1-Mathematics-and-statistics

Use the marking schedule as a guide for the structure of sentences.## =======================================================================

Wednesday the 30th of May; This wiki was covered; we discussed all the links; working on practise internal in the book.## =======================================================================

Tuesday the 29th May--------------------------------------------------------------------------------------------------------When doing your dot plot and box plot- place the scale in the MIDDLE of the page- put the "boys" above the scale and the "girls" below the scale--------------------------------------------------------------------------------------------------------The best question starts with How Does....and has the word "compare"How does the ------- compare with the-------- in the population.--------------------------------------------------------------------------------------------------------Data Analysis: stem and leaf, box and whisker, dot plotDescribe what you SEE in the SAMPLE data.Make an INFERENCE: What you SAMPLE tells you about the POPULATION.Use headings:Describing my sample:Making an inference:## 11Maths MV Stats Inference

## =======================================================================

Monday 28th MayStarted a Practise assessment from the green book, page 51

Students wrote their own questions and started to do the data analysis.

We discussed the fact you choose a continuous variable, and use a category to compare it with.

You CAN NOT compare two continuous variables, you would look at their relationship, and this is a different internal.

You must write your own question to have a chance of getting excellence.

## =======================================================================

Friday 25th May = No Maths - Cycled Out## =======================================================================

Thursday 24th of MayAlgebra - Factorizing

## =======================================================================

Wednesday the 23rd of May.Algebra questions from the algebra solving practise test in the green book.

Page 38 of the green book - Vocab for Stats - fill it in.

Used the chapter "Statistical Methods" starting on page 261.

Used the index of the text book.

Also at home students can and should use:

http://www.nzmaths.co.nz/glossary

http://nzmaths.co.nz/nzc-glossary-mathematics-terms

## Statistical inference

Statistical inference is the part of statistics concerned with drawing conclusions about a population based on sample data.## Multivariate data

Data that consists of measurements of three or more attributes or variables for each individual or object in a sample (for example age, height and gender). This contrasts with univariate data where measurements are made of only one attribute, and bivariate data where measurements are made of two attributes.## =======================================================================

22nd May Algebra Lesson then MV Data -and we went over yesterdays lesson again...

## =======================================================================

21st May: We measured all the students in this class and made an inference about year 11 students at Pakuranga College.## ===================================================================================

18th May Linkhttp://www.censusatschool.org.nz/2009/informal-inference/WPRH/

http://www.censusatschool.org.nz/2009/informal-inference/WPRH/Animations/Boxplots%20with%20memory%20vs%20sample%20size.pdf

## ===================================================================================

Links used in lesson on the 16th of May 2012http://www.censusatschool.org.nz/2008/informal-inference/wild_informal_inference_handout1.pdf

http://www.censusatschool.org.nz/2008/informal-inference/bars.html

The boxes below have a median "to the left" so the call could be made with the 3/4 - 1/2 rule is some cases.

Check out the "How to make the call" document

## ===================================================================================

Link used in the lesson on the 14th of May 2012http://www.censusatschool.org.nz/2005/box-whisker/?s=05-14-33837697

## ===================================================================================

15th May## Each student came up with four comparison questions. Yeah Right ;-)

## Page 40 to 46 of the green workbook.

## Here are some acceptable comparative questions.

## The population is the 2009 census at school database.

## You are looking at a sample from that population.

## This internal requires you to statistically analyse the sample and then use those statistics to make an inference (educated guess) about the population.

## Choose a continuous variable and a variable to compare it with. Eg height and gender; bag weight and “bag carry”.

## 1. What are the similarities and differences of year 11 male and female heights in the 2009 census at school database?

## 2. Do year 11 males tend to be taller than year 11 females in the 2009 census at school database?

## How does the height of year 11 males compare with year 11 females in the 2009 census at school database?

## 3. Do year 11 males tend to have a longer popliteal length than year 11 females in the 2009 census at school database?

## How does the popliteal length of year 11 males compare with year 11 females in the 2009 census at school database?

## 4. Do year 11 males tend to carry heavier bags than year 11 females in the 2009 census at school database?

## How does the bag weight of year 11 males compare with year 11 females in the 2009 census at school database?

## 5. Do year 11 students who carry their bag with two straps tend to carry heavier bags than those who carry their bag with one strap in the 2009 census at school database?

## How does the bag weight of year 11 students who carry their bags with one strap compare with those thay carry their bag with two straps in the 2009 census at school database?

## 6. Does the time taken to get to school by bus tend to be longer than the time taken to walk to school for year 11 students in the 2009 census at school database?

## How does the time taken to get to school of year 11 students that travel by bus compare with year 11 students that walk to school in the 2009 census at school database?

## What did students learn:

## Use the word "tend" because this implies you are comparing averages.

The word tend is excellent for the conclusion and acceptable for the question.Do ------ tend to be ------ than -------- in the population.The above question could be answered yes or no, so it not the best comparative question.## =======================================================================

The best question starts with How Does....How does the ------- compare with the-------- in the population.Next year there is an internal much the same as this one, except you are not given the sample, you take a sample.This video is for next years internal, but some of it may apply to this years internal.http://www.youtube.com/watch?v=-upOeF8MMuM&sns=em

This Video Shows how easy it is to draw box and whisker graphs in geogebra