schools.reap.org.nz maths lessons... · web view430 0.897 40.8 dt rainbow f 495 1.52 45.3 st...
TRANSCRIPT
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!”