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Statistics is about relationships Mathematics Lessons for Remote Learning Strand: Probability and Statistics Target: Y7, 8, 9, 10 –NZC Level 3/4 Topic: PS Comparative Statistisical Investigations and Language Starter – Odd One Out questio n summati ve sample compara tive bivaria te relatio nship The idea here is to select the odd one . I choose __________ because _____________________ Learning THE DEEP UNDERSTANDING OF STATISTICS Being enabled to collect and use data to make sense of the world around us and to solve problems Asking Better Questions There are two ways of interpreting this heading. • A question in statistics must be answerable using the data collected and be specific enough to be repeated by someone else. In a comparative question the numerical variable, the two groups being compared, the direction of the comparison and the population must all be included. Direction means we indicate which group are heavier. • We can ask more than just a summative question about a variable. We can compare two groups with a comparative question and we can compare two numerical variable to understand more about that relationship. TASK 1 – PPD (AC) and a Comparative Question [see next resource for relationship] The context for this data is the Lake Taupo Trout Fishing Competition held in April 2011. More info about Taupo Trout Length (mm) Weight (kg) Condition Factor How Caught Species Sex 455 0.865 33.2 J Rainbow F 415 0.787 39.8 DT Rainbow F 580 2.06 38.1 FF Rainbow F 405 0.746 40.6 DT Rainbow F 500 1.965 56.8 FF Rainbow F 435 1.016 44.6 DT Rainbow M 430 0.897 40.8 DT Rainbow F 495 1.52 45.3 ST Rainbow F 425 0.986 46.4 J Rainbow F 480 1.088 35.5 ST Rainbow F 490 1.218 37.4 ST Rainbow F 460 1.036 38.5 ST Rainbow M 420 0.842 41.1 ST Rainbow F 480 1.089 35.6 ST Rainbow M 420 0.763 37.2 ST Rainbow M 505 1.261 35.4 DT Rainbow F 520 1.56 40.1 J Rainbow F 430 0.958 43.5 DT Rainbow M 555 2.316 48.9 FF Rainbow M 475 1.32 44.5 J Rainbow F 495 1.172 34.9 J Rainbow F 540 2.176 49.9 FF Rainbow F 520 1.976 50.8 DT Rainbow M 480 1.203 39.3 J Rainbow F 445 1.072 43.9 ST Rainbow F 495 1.059 31.5 DT Rainbow F 425 1.684 79.3 ST Rainbow F 430 0.979 44.5 ST Rainbow F 470 0.975 33.9 DT Rainbow F 590 2.155 37.9 FF Rainbow F 510 1.594 43.4 DT Rainbow F 440 1.025 43.5 DT Rainbow F 440 0.957 40.6 J Rainbow M 425 0.823 38.7 DT Rainbow F 450 0.89 35.3 DT Rainbow F 415 0.824 41.7 ST Rainbow F In Statistics “the eyes have it!” There are six variables heading the data columns. Three are numerical data and three are categorical data. This data was recorded by DOC rangers measuring the fish that were caught during the competition. The Length and Weight variable is easy to understand and measure. The Condition Factor is a formula using L and W and is a measure of the best or fattest fish. How Caught is by Jigging, Deep Trolling or Shallow Trolling. These fish are all Rainbow trout and the Sex variable shows if the fish is a male or a Female. Here is a link to more details and information . P – A Comparative Question. I wonder if the weight of a female hen trout is greater than the weight of male jack trout in the 2011 LTTFC data. I am interested in this because in April the trout start to head upstreasm for spawning and I would expect the hens to be generally heavier because they are full of ripe egg sacs (roe) and the make sperm sacs are much smaller and lighter.

schools.reap.org.nz Maths Lessons... · Web view430 0.897 40.8 DT Rainbow F 495 1.52 45.3 ST Rainbow F 425 0.986 46.4 J Rainbow F 480 1.088 35.5 ST Rainbow F 490 1.218 37.4 ST Rainbow

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Statistics is about relationships

Mathematics Lessons for Remote Learning

Strand: Probability and Statistics

Target: Y7, 8, 9, 10 –NZC Level 3/4

Topic: PS Comparative Statistisical Investigations and Language

Starter – Odd One Out

question

summative

sample

comparative

bivariate

relationship

The idea here is to select the odd one .

I choose __________ because _____________________

Learning

THE DEEP UNDERSTANDING OF STATISTICSBeing enabled to collect and use data to make sense of the world around us and to solve problems

Asking Better Questions

There are two ways of interpreting this heading.

• A question in statistics must be answerable using the data collected and be specific enough to be repeated by someone else. In a comparative question the numerical variable, the two groups being compared, the direction of the comparison and the population must all be included. Direction means we indicate which group are heavier.

• We can ask more than just a summative question about a variable. We can compare two groups with a comparative question and we can compare two numerical variable to understand more about that relationship.

TASK 1 – PPD (AC) and a Comparative Question [see next resource for relationship]

The context for this data is the Lake Taupo Trout Fishing Competition held in April 2011. More info about Taupo Trout

There are six variables heading the data columns. Three are numerical data and three are categorical data. This data was recorded by DOC rangers measuring the fish that were caught during the competition. The Length and Weight variable is easy to understand and measure. The Condition Factor is a formula using L and W and is a measure of the best or fattest fish. How Caught is by Jigging, Deep Trolling or Shallow Trolling. These fish are all Rainbow trout and the Sex variable shows if the fish is a male or a Female.

Here is a link to more details and information.

P – A Comparative Question.

I wonder if the weight of a female hen trout is greater than the weight of male jack trout in the 2011 LTTFC data. I am interested in this because in April the trout start to head upstreasm for spawning and I would expect the hens to be generally heavier because they are full of ripe egg sacs (roe) and the make sperm sacs are much smaller and lighter.

P – Plan

I will randomly select 49 trout from the population of about 1000 trout that were caught that year. I will create dot plots and box and whisker graphs for both M and F and compare. I will use the online Jake Wills NZGRAPHER for analysis.

D - Data

Shown elsewhere on this page. All randomly selected.

Condition Factor Calculator.

http://superfly.co.nz/pro_reports/condition_factor.htm

Length (mm)

Weight (kg)

Condition Factor

How Caught

Species

Sex

455

0.865

33.2

J

Rainbow

F

415

0.787

39.8

DT

Rainbow

F

580

2.06

38.1

FF

Rainbow

F

405

0.746

40.6

DT

Rainbow

F

500

1.965

56.8

FF

Rainbow

F

435

1.016

44.6

DT

Rainbow

M

430

0.897

40.8

DT

Rainbow

F

495

1.52

45.3

ST

Rainbow

F

425

0.986

46.4

J

Rainbow

F

480

1.088

35.5

ST

Rainbow

F

490

1.218

37.4

ST

Rainbow

F

460

1.036

38.5

ST

Rainbow

M

420

0.842

41.1

ST

Rainbow

F

480

1.089

35.6

ST

Rainbow

M

420

0.763

37.2

ST

Rainbow

M

505

1.261

35.4

DT

Rainbow

F

520

1.56

40.1

J

Rainbow

F

430

0.958

43.5

DT

Rainbow

M

555

2.316

48.9

FF

Rainbow

M

475

1.32

44.5

J

Rainbow

F

495

1.172

34.9

J

Rainbow

F

540

2.176

49.9

FF

Rainbow

F

520

1.976

50.8

DT

Rainbow

M

480

1.203

39.3

J

Rainbow

F

445

1.072

43.9

ST

Rainbow

F

495

1.059

31.5

DT

Rainbow

F

425

1.684

79.3

ST

Rainbow

F

430

0.979

44.5

ST

Rainbow

F

470

0.975

33.9

DT

Rainbow

F

590

2.155

37.9

FF

Rainbow

F

510

1.594

43.4

DT

Rainbow

F

440

1.025

43.5

DT

Rainbow

F

440

0.957

40.6

J

Rainbow

M

425

0.823

38.7

DT

Rainbow

F

450

0.89

35.3

DT

Rainbow

F

415

0.824

41.7

ST

Rainbow

F

480

0.92

30.1

J

Rainbow

F

415

0.715

36.1

DT

Rainbow

F

435

1.053

46.2

J

Rainbow

F

515

1.533

40.5

J

Rainbow

F

480

1.355

44.3

J

Rainbow

F

470

1.097

38.2

DT

Rainbow

F

430

0.806

36.6

DT

Rainbow

F

460

1.16

43.1

J

Rainbow

F

430

0.961

43.7

J

Rainbow

F

455

1.197

45.9

DT

Rainbow

F

625

2.688

39.8

FF

Rainbow

F

505

1.561

43.8

DT

Rainbow

M

475

1.018

34.3

DT

Rainbow

F

TASK 1 – PPD (AC) and a Comparative Question

Your task is to write a different comparative question. The plan and the data can be different. The orginal data from which you can select a new or different sample is here http://schools.reap.org.nz/advisor/Trout.html.

TASK 2 – The Analysis and Conclusions (or Findings).

A - Analysis

• I notice that there are many more female trout than male trout in this sample.

• The 40 female trout are bunched between 0.8 and 1.6 kg. It is harder to see the bunch for the male trout but there is a group between 0.9 and 1.1kg. This suggests the bump or shape of these distributions could be similar.

• The middle 50% of the female trout is between 0.9 and 1.4kg and for the male trout between about 0.95 and 1.6kg and are pretty similar despite the small sample of males and more spread or variation that will result.

• The medians for both groups are about the same near 1.1kg.

• There is no odd or unusual data. The heaviest fish are both males and females and about 2.2kg.

The two box and whisker graphs are very similar and show the typical female and typical male trout of very much the same size. [Here I have discussed the sample size, shape, middle 50%, spread and unusual data. I have stated what I am talking about, where it is and what it means for each.]

C - Conclusion

The small number of males in this sample introduces greater variation for this group and less reliability of any decision.

The analysis of this sample shows that the female trout are not heavier and I would expect this to be the case back in the population and indeed in the entire lake from which the fish were caught.

It is probably a good idea to select samples with similar sized groups to ensure the variation in both groups is about the same. This would give me more confidence of a reliable result.

TASK 2 – Do the Analysis and Conclusion or answer for your own question from TASK 1.

Use the online Jake Wills NZGRAPHER for analysis. Save your random sample of fish in a .csv file for importing on line. [Note csv means “comma separated values” and looks like “455,0.865,33.2,J,Rainbow,F,” and in binary the “455,” looks like ‘00000100000001010000010100101100” which is actually more like what is sent over the WWW. This all happens very quickly, is invisible and is a very efficient way to send data.]

Places to find other data

The Census at Schools website has a data analyser and huge amounts of data taken form surveys done with thousands of school children of all ages. You can inspect this data and perhaps find an interesting aspect to investigate.

https://new.censusatschool.org.nz/explore/

Jake Wills has done an amzing job with an on line grapher that will work on any device with internet browser software.

https://grapher.nz/

iNZight Software from Auckland University

https://www.stat.auckland.ac.nz/~wild/iNZight/

The Eyes Have it Talk by Dr Chris Wild

https://www.stat.auckland.ac.nz/~wild/talks/09.USCOTS.html

Journalling

Today I learned ________________________________________________________________

And I would like to know about ___________________________________________________

Comments

Make any comment you feel like making here.

Math Language: List all the math words you can find in this document and write what you think it means beside the word. Eg subtraction means to take away or to find the difference. Keeping a list of these words is a very good idea.

Answers and Comments

Starter – Odd One Out

question

summative

sample

comparative

bivariate

relationship

The idea here is to select the odd one .

I choose ____sample______ because ____in all statistics we take samples_____

Task 1 and Task 2

Your answers will vary but be very similar to what is written above. Send any final reports to me for checking if needed.

For interest I took all 122 trout from the 2011 Trout database and made a dot plot for both F and M. You can draw the box and whisker and convince yourself that the sample above was valid. Notice also the huge numbers of female trout compared to the number of male trout caught. Male trout could be more wary of being caught but that is very unlikely. More likely is that more female trout mean more breeding and prolonging the trout species. A male trout can fertilize many millions of trout eggs from many females.

A Random Sample

It is possible that the right and largest fish only are selected in a sample. This is a very unlikely event and is even more unlikely if the sample size is kept up around 30 to 50. More on sample size here.

No crossword puzzle .

Feedback

Students and teachers are welcome to email [email protected] with comments. This was a lesson that could be given to a NZC Level 2, 3, 4, 5 student for some placevalue learning and revision. Students should select a set time each day and perhaps using the timer on a cell phone set 45 minutes or so to learn and practice mathematics. Keep trying on problems and expect to struggle. Persevering and struggling are great competencies to develop. You can learn more about these from https://www.youcubed.org/resource/growth-mindset/. We have a great math website in NZ with a special resource called e-AKO https://nzmaths.co.nz/information-about-e-ako-pld-360 .

In Statistics “the eyes have it!”