Statistics connects concepts

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

Starter – Odd One OutSample Problem PlanData Analysis Answer

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

IntroductionThe language of statistics is very important to learn. Not only the meaning of words but the way they are used as well. Some words such as “is” and “are” are avoided. A general rule is the language of statistics is floppy and vague. We almost never know things for certain in statistics so words like “tends”, “suggests” and “typical” are used to convey meaning. Despite this difficulty of uncertainty, mathematics helps people make sense of data. The concept random plays a big part and that is how statistics is connected to probability.

All learning in statistics is done with the PPDAC investigative data detective cycle in mind. Here is a link to the Data Detective poster. The stages of the cycle are firstly the problem or Question being asked. The second is the Plan to try and answer that question. The third is the data all collected and listed. The fourth is the analysis using tables and graphs to create sense. Finally the report or conclusion answers the question asked and comments about the limitations and features. This quite rigid PPDAC strategy or writing frame is a powerful way to create meaning from data. Use it!

TASK 1 – PPD (AC) and a Summative QuestionThe 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

440 0.77 32.7 J Rainbow F460 1.337 49.6 DT Rainbow F505 1.476 41.4 DT Rainbow M505 1.155 32.4 DT Rainbow F495 1.328 39.6 ST Rainbow F460 1.036 38.5 ST Rainbow M470 1.158 40.3 ST Rainbow M460 1.138 42.2 J Rainbow F450 0.89 35.3 DT Rainbow F495 1.059 31.5 DT Rainbow F445 1.11 45.5 ST Rainbow F480 0.92 30.1 J Rainbow F460 1.16 43.1 J Rainbow F455 1.197 45.9 DT Rainbow F475 1.162 39.2 DT Rainbow F430 0.979 44.5 ST Rainbow F500 1.965 56.8 FF Rainbow F475 1.354 45.6 J Rainbow F515 1.533 40.5 J Rainbow F445 0.885 36.3 ST Rainbow M500 2.18 63.0 FF Rainbow F525 1.513 37.8 DT Rainbow M480 1.088 35.5 ST Rainbow F620 2.16 32.7 ST Rainbow F480 1.203 39.3 J Rainbow F445 1.101 45.1 ST Rainbow F480 1.087 35.5 ST Rainbow F430 1.506 68.4 FF Rainbow F470 0.923 32.1 ST Rainbow F470 1.19 41.4 J Rainbow F420 0.763 37.2 ST Rainbow M510 1.45 39.5 ST Rainbow F500 1.311 37.9 J Rainbow F

TASK 1 - Write your own Problem (question) and Plan using this context and Data selected for you. The (AC) is next!TASK 2 – (AC) Analysis and Concluding or Answering

Statistics is the world of data and sense making

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 - Problem or Question. I wonder what a typical trout caught in the 2011 LTTFC weighs? This question is answerable from this data and a reasonable question to ask. There are others.

P – PlanThe data shows a sample of 33 trout selected randomly from the population of about 1000 trout that were caught that year. I will plot these as a dot plot and draw a box and whisker graph. I will then consider the data and make some deductions to try and answer my question about the typical weight.

D - DataThis is shown elsewhere on this page.

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

Statistics connects concepts

The Dot Plot. A dot plot lets you quickly see the Shape and Spread of your data. A Box and Whisker graph lets you easily position the Middle 50% or typical part of the data.

In the diagram the data has been plotted. The LQ data is #9 dot from the left and I have made a slight error there. It should be just over 1kg. The Shape of the graph is a single bump shown in pink as an arc and is between about 0.5 and 2.0 kg. The spread or variation in the data is UQ – LQ = 1.4 – 1.1 or about 0.3kg. The Middle 50% is the typical size a trout would be or between 1.0kg and 1.4kg. There are no odd data but there are three quite heavy good sized fish.

This sample suggests an estimate of teh weight of a typical fish in the 2011 Fishing Competition is between 1.0kg and 1.4kg. This is a random and reprepresentative sample of the population and I would expect to see this pattern in the population of all fish caught in the competition in 2011. There is also no reason why I can not extend this conclusion to all catchable (over 400mm) fish in the whole lake. Trout less than 400mm must be released released and not weighed in. [Interestly, a study around this time by DOC suggested the population of catchable trout to be about 1.5 million trout in Lake Taupo.]

The Summary Data records the value of the Min, LQ, Med, UQ, and Max. Choosing a sample size of 33 is a bit sneaky because there is an exact number for each these data.

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

TASK 3 – Catch a trout in Lake Taupo. You do need a license (on line). Tmost likely way to catch a trout is by boat, jigging, with someone who knows about trout fishing. Trout do get quite large but they are fun to catch.

11lb or 5kg Trophy Trout caught by the author in 1982. The second one I caught like this the next night was released!

TASK 4 – How many cubic kilometres of water are there in Lake Taupo?

(a) 1 (b) 10 (c) 100 (d) 1000

Statistics is the world of data and sense making

Statistics connects concepts

A Language Puzzle

JournallingToday I learned ________________________________________________________________

And I would like to know about ___________________________________________________

CommentsMake 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.

Statistics is the world of data and sense making

Statistics connects concepts

Answers and CommentsStarter – Odd One Out

Sample Problem Plan

Data Analysis Answer

The idea here is to select the odd one .

I choose ____question_____ because _____drives statistical thinking.

TASK 1 - Write your own Problem (question) and Plan using this context and Data selected for you.Compare you answer to the one described in the learning above. • Make sure the question is answerable using this data, specifies a typical numerical value to be estimated and states the population from which the data is being sampled. • Make sure the plan has enough detail for someone else to follow. You can test this by giving the instructions too someone. • The data needs to be randomly sampled and listed in full. A way to randomly sample data is to number the data and use a random number generator to select 33 data from the population. • What is a good sample size? This is a really good question. At the moment choose 25, 29. 33, 37, 41, 45 or 49 and so on if you want an exact LQ, Med and UQ. I wonder why these numbers? Look for a pattern!

TASK 2 – Do the Analysis and Conclusion or answer for your own question from TASK 1. You analysis should be similar to teh analysis above. Give yourself a good comment.

TASK 3 – Catch a trout in Lake Taupo.Good luck and have fun.

TASK 4 – How many cubic kilometres of water are there in Lake Taupo?The answer can be found on the lake front in Taupo along with a lot of other data such as area, depth and coastline length. There is a lookout opposite the Fire Station with all the answers! You could always use teh average depth of 186m and calculate the area. You could also ask Siri! I can say there is enough water in Lake Taupo for every perosn on Earth to have a 200ml glass of water and it is drinkable!

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 Nzwith a special resource called e-AKO https://nzmaths.co.nz/information-about-e-ako-pld-360 . s

Statistics is the world of data and sense making