Statistics is about relationships

Mathematics Lessons for Remote Learning Strand: Probability and Statistics Target: Y7, 8, 9, 10 –NZC Level 3/4Topic: PS Comparative Statistisical Investigations and Language

Starter – Odd One Out

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e samplecomparativ

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The idea here is to select the odd one .

I choose __________ because _____________________LearningTHE DEEP UNDERSTANDING OF STATISTICSBeing enabled to collect and use data to make sense of the world around us and to solve problems

Asking Better QuestionsThere 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 F415 0.787 39.8 DT Rainbow F580 2.06 38.1 FF Rainbow F405 0.746 40.6 DT Rainbow F500 1.965 56.8 FF Rainbow F435 1.016 44.6 DT Rainbow M430 0.897 40.8 DT Rainbow F495 1.52 45.3 ST Rainbow F425 0.986 46.4 J Rainbow F480 1.088 35.5 ST Rainbow F490 1.218 37.4 ST Rainbow F460 1.036 38.5 ST Rainbow M420 0.842 41.1 ST Rainbow F480 1.089 35.6 ST Rainbow M420 0.763 37.2 ST Rainbow M505 1.261 35.4 DT Rainbow F520 1.56 40.1 J Rainbow F430 0.958 43.5 DT Rainbow M555 2.316 48.9 FF Rainbow M475 1.32 44.5 J Rainbow F495 1.172 34.9 J Rainbow F540 2.176 49.9 FF Rainbow F520 1.976 50.8 DT Rainbow M480 1.203 39.3 J Rainbow F445 1.072 43.9 ST Rainbow F495 1.059 31.5 DT Rainbow F425 1.684 79.3 ST Rainbow F430 0.979 44.5 ST Rainbow F470 0.975 33.9 DT Rainbow F590 2.155 37.9 FF Rainbow F510 1.594 43.4 DT Rainbow F440 1.025 43.5 DT Rainbow F440 0.957 40.6 J Rainbow M425 0.823 38.7 DT Rainbow F450 0.89 35.3 DT Rainbow F415 0.824 41.7 ST Rainbow F480 0.92 30.1 J Rainbow F415 0.715 36.1 DT Rainbow F435 1.053 46.2 J Rainbow F515 1.533 40.5 J Rainbow F480 1.355 44.3 J Rainbow F470 1.097 38.2 DT Rainbow F430 0.806 36.6 DT Rainbow F460 1.16 43.1 J Rainbow F430 0.961 43.7 J Rainbow F455 1.197 45.9 DT Rainbow F625 2.688 39.8 FF Rainbow F505 1.561 43.8 DT Rainbow M475 1.018 34.3 DT Rainbow F

TASK 1 – PPD (AC) and a Comparative QuestionYour 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.

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.

P – PlanI 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 - DataShown elsewhere on this page. All randomly selected.

Condition Factor Calculator.http://superfly.co.nz/pro_reports/condition_factor.htm

Statistics is about relationships

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.]

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

JournallingToday I learned ________________________________________________________________

And I would like to know about ___________________________________________________

CommentsMake any comment you feel like making here.

In Statistics “the eyes have it!”

C - ConclusionThe 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.

Statistics is about relationships

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 CommentsStarter – 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 2Your 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 SampleIt 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 .

FeedbackStudents and teachers are welcome to email jimhogan2@icloud.com 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!”