common measures of central tendency and …arkansasgardencorps.com/documents/lessons/The 3ms and...Measures of central tendency such as mean, median and mode allow the comparison of

Frameworks

scienceNS 1.6.3 Compare scientific data using mean, median, mode and range using SI units.NS 1.6.5 Communicate results and conclusions from scientific inquiry.NS 1.7.3 Interpret scientific data using mean, median, mode and range using SI units.NS 1.7.5 Communicate results and conclusions from scientific inquiry.NS 1.8.4 Interpret scientific data using mean, median, mode and range using SI units. NS 1.8.7 Communicate results and conclusions from scientific inquiry following peer review.

maTHDAP.15.6.2 Compare and interpret information provided by measures of central tendencies (mean, median and mode) and measures of spread (range).DAP.15.7.2 Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range).DAP.15.8.2 Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range).

LaNGUaGe arTsW.5.6.10 Write across the curriculum.W.5.7.10 Write across the curriculum.W.5.8.10 Write across the curriculum.

s objecTivesThe students will learn:

objecTive #1 To describe the purpose of measures of central tendency.

objecTive #2 To define and calculate the mean, median, mode and range.

objecTive #3 To convert kilograms to pounds.

objecTive #4 To describe different media to communicate a scientific investigation.

scientific method (part 3 of 4)

the 3m’s and more:common measures of central tendency and communication

CHARACTERISTICS &PROCESSES OF SCIENCE

ACHRI/DGS/KFK/080911/V1 DRAFT COPY • ©2011 Delta Garden Study.


Page 2 CHARACTERISTICS & PROCESSES OF SCIENCE • The 3M’s and More: Teachers’ Guide

Garden cro

ps will be measured and analyzed using measures of central tendency.

overviewMeasures of central tendency such as mean, median and mode allow the comparison of data.

GardeN acTiviTiess Harvesting and weighing produce

s Plant, harvest and work in the garden following the Garden Guide

s Recipes and Taste tests as time permits (refer to Delta Garden Study Recipe Book)


CHARACTERISTICS & PROCESSES OF SCIENCE • The 3M’s and More: Teachers’ Guide Page 3

Tips For TeacHersPre-lesson preparation:

1. Review the “Study Guide for Students” pages to familiarize yourself with the extent of knowledge this lesson is designed to convey to students.

2. Review the “Supporting Information for Teachers” pages to familiarize yourself with additional information to teach as needed. This section is designed for reference purposes, not as lecture material read to the class.

3. Check with the Garden Program Specialist whether records showing prior produce yields are available and which produce is available for harvesting.

LessoN oUTLiNe

activities estimated duration actual duration

in the classroom

s Offer the icebreaker 5 minutes

in the garden s Harvest and weigh available produce and convert weight into pounds

10 minutes

s Explain measures of central tendency 10 minutes

s Plant, harvest and work in the garden following the Garden Guide

10 minutes

s Implement recipes and taste tests as time permits (refer to Delta Garden Recipe book)

5 minutes

back in the classroom

s Hand out Student Learning Workbooks, review and assign “Take it Home Activity” as homework

5 minutes

classroommaterials needed

s Student Learning Workbooks

s List showing weekly produce yields collected over a month or two (available from Garden Program Specialist)

gardenmaterials needed

s Whiteboard, whiteboard pens

s Kitchen scale with kilogram index

s Any appropriate garden tools

s Fresh produce from garden

s List showing weekly produce yields collected over a month or two


Page 4 CHARACTERISTICS & PROCESSES OF SCIENCE • The 3M’s and More: Teachers’ Guide

LessoN pLaN

i. start in the classrooma. icebreaker

Ask the students: “What country produces the most tomatoes annually?”

ANSWER: China (the United States is second).

ii. take class to the gardens Follow the instructions on the next page. The students will harvest

and weigh produce, convert the weight from kilograms to pounds and calculate range, mean, median and mode. The “Supporting Information for Teachers” page describes how the Delta Garden Study is structured according to the scientific method.

meeTs objecTives #1–3

s Discuss how to prepare a written report about this activity. List all required components on whiteboard.

meeTs objecTive #4

Work in the garden under the direction of the Garden Program Specialist:

s Instruct students in planting, raised bed preparation or other garden related tasks that need to be performed. If applicable, point out how the analysis of today’s produce yield prompted this activity. Example: Today’s tomato yield was much lower than expected. The season is drawing to a close. Let’s take up the remaining plants and prepare the ground for cold-season crops, or, today we got a lot of tomatoes because tomatoes are in peak season right now.

s Instruct students to pick and taste available vegetables. Ask for feedback. Ask students to describe which ones they recognize and which ones they eat at home.

meeTs objecTive #1

iii. take class back to classrooms Hand out the Student Learning Workbook as reference material

and class assignment. Review take it home activities and encourage students to do them.


CHARACTERISTICS & PROCESSES OF SCIENCE • The 3M’s and More: Teachers’ Guide Page 5

sUpporTiNG iNFormaTioN For TeacHersWeighing and recording weekly produce yields helps students understand the measures of central tendency as well as some metric units, especially grams and kilograms.

Grams and kilograms are units of measurement from the metric scale, based on the number 10. For example, 1 kg = 1,000 grams. 1 kg = 2.2 lbs. Kilograms are part of the International System of Units, commonly abbreviated as SI. The system is founded on seven SI base units for seven base quantities, which are assumed to be mutually independent. Kilogram is the unit for measuring mass, meters measure length and seconds measure time. There are four more base units, which the students will learn about in other classes. Most countries today have adopted the SI for everyday use, except the United States and some others.

instructions

1. Check with the Garden Program Specialist about records of daily or weekly produce yields. They should be available.

2. On the day of the lesson, take students to the garden and harvest some available crops. Instruct students to weigh them and record weight. Explain grams and kilograms.

3. Provide the conversion formula and instruct students to convert the kilogram weight into pounds.

4. Point out that knowing today’s produce yield doesn’t really tell us much. But by comparing this figure to other information can we assess its significance. Explain that measures of central tendency allow us to compare data.

5. Display or write out list of past produce yields. Use these data to explain and demonstrate how to calculate the mean, median and mode. Define range.

6. Then compare the results to today’s yield. Is it more, less, the same? Describe how the comparison might influence our garden activities. Example: If today’s yield is below average, what are some reasons? Are our plants suffering from drought or disease? Is the season drawing to a close?

7. Discuss how these records might be even more useful for next year’s growing season and for other schools that intend to establish vegetable gardens.

8. Describe how to prepare a written summary and conclusion of this data analysis. Compare and contrast backboards, posters, slide presentations and papers. List all required components on the whiteboard.

soUrces

independent science research project, pre-ap 8th Grade science studentscompiled by Susanne Hughes, Pulaski Heights Middle School, Little Rock, Ark.

science, Level GreenNational Geographic, The McGraw-Hill Companies, 2005

National institute of standards and Technologyhttp://physics.nist.gov/cuu/Units/units.html

www.tomato.org

study guide for studentswhether you are conducting some research or experiments for a class, or simply doing a project outside of school, you will most likely start by gathering some figures or numbers. Maybe you are measuring daily temperatures or keeping track of the scores of your favorite football team. Perhaps you are running a little lawn care business over the summer and want to record your earnings. Pretty soon, these figures will be able to tell you something besides their actual value. You will notice a central tendency. This is a statistical term to describe how numbers are distributed.

Remember the last time you took a pop quiz? When the teacher handed back the grades, you didn’t just look at your score, but mentally compared it to other exams you’ve taken. You probably also wanted to know how the class did. Only if you can compare your score to some other information will you be able to put your grade in some sort of perspective. Did your grade improve? Did you do better or worse than the class average?

The three most common measures of central tendency are the mean, median and mode. Let’s check what they mean in this example of a group of 52 6th grade students receiving the following scores on an exam:

63, 63, 65, 65, 66, 68, 69, 69,

70, 70, 70, 70, 71, 71, 71, 71, 74, 74, 75, 75, 76, 76, 77,

80, 81, 81, 81, 82, 83, 83, 83, 83, 84, 85, 85, 86, 87, 87, 87, 87, 87, 88, 88, 89,

92, 92, 93, 94, 95, 97, 97, 98

Mean is the average. You calculate the mean by adding all numbers in a group and then dividing them by the total of these numbers. Here, the sum of all scores is 4,088, divided by 52 (total number of students taking the exam) is 80.157, or rounded down to 80. If you scored more than 80, you did better than the average; if you scored 79 or less, you were below average.

Median is the middle number of a group of numbers. Half the numbers have values greater than the median; half the numbers have values less than the median. The median in this example is 81.

Mode is the most frequently occurring number in a group. Here, it is 87; it occurs 5 times.

Continued next page

scientific method (part 3 of 4)

the 3m’s and more:common measures of central tendency and communication

CHARACTERISTICS &PROCESSES OF SCIENCE



CHARACTERISTICS & PROCESSES OF SCIENCE • The 3M’s and More: Study Guide Page 2

Remember the three measures as the 3M’s and each individual one like this:

The mean requires a “mean” calculation; you have to add the numbers and then divide them.

The median sounds similar to “middle”; it splits a group into two halves.

The mode sounds almost like “most,” as in most frequently occurring number.

In addition to mean, median and mode, you need to be able to calculate range. Range is the difference between the lowest and highest value. It tells you how spread out the numbers are. In this example, the range is 98-63 = 35. Typically, the larger the data, the larger the range.

You see why measures of central tendency are much more useful than individual scores for comparing different data. Your teacher can compare the average score of an exam to that of past exams to determine whether or not the class as a whole improved its academic performance. The principal can ask her to calculate the mean of all those average exam scores taken during the school year to compare the result to that of last year’s 6th grade students or those at other schools. And so forth.

However, simply compiling a set of numbers and calculating central tendency is often not enough. You will be asked to not only provide figures, but also a written communication of some sort. This is particularly important for any scientific inquiries. Each must include the following components:sQuestion or ProblemsExisting InformationsHypothesissProcedures (materials, experiments, etc.)sAnalysis of ResultssConclusion

You might have several options to communicate your project:

A tri-fold backboard: You prepare summaries, often as bullet points, of each component on clearly labeled index cards or sheets of paper. These should be arranged and attached in logical order, except for the main question or problem. This should be displayed at the top of the middle section. The backboard should look visually appealing, color-coordinated and with something eye-catching. Charts, maps, graphs, etc., should be interesting and convincing to the viewer. All

parts should come together as a whole. Your presentation is restricted to the physical

dimensions of the board, which limits your ability to elaborate on

certain points.

A poster: This is very similar to the backboard, except that it is a smaller, one-dimensional format.

A PowerPoint® presentation: This is an electronic way

of sharing information. It requires a computer and a large

projection screen if you are trying to share the presentation with lots

of people. Just as with backboards, you prepare brief summaries of each component, often as bullet points or short phrases. You can be more detailed since your presentation is not limited to the physical dimensions of a paper medium. But you might be given a time limit, e.g., 10 minutes. When you show your PowerPoint presentation, you play a slide show. However, instead of simply reading your slides out loud, you add more oral explanations and descriptions as necessary. A good PowerPoint presentation provides enough data for a viewer to understand the main points even without listening to your talk, but does not require you to read from the slides. Full sentences should not be put in power point slides unless you are directly quoting from a reference.

A written report: In a written paper, you describe your project in detail. Individual chapters or sections explain the various components of your project. Your paper must be free of grammatical and punctuation errors and follow the overall English composition rules and guidelines. You may include pictures, graphs, photographs, charts, maps, etc. Your paper might have to meet minimum or maximum word/


Page 3 CHARACTERISTICS & PROCESSES OF SCIENCE • The 3M’s and More: Study Guide

page requirements (e.g., at least 1,000 word or no more than 10 pages) and be formatted in a particular style, such as double line spacing. Many students spend more time and effort preparing a written paper than a backboard or PowerPoint presentation.

A written report and poster: Here, you combine two media. In your written report, you provide a detailed description of your project, but you don’t include any images. Instead, you attach the images to a poster, clearly labeled. Then you read your paper to your audience and point to the images on the poster as relevant.

scientific inquiry has two functions, first, to provide a descriptive account of how scientific inquiry is carried out and second, to provide an explanatory account of why scientific inquiry succeeds

mean the mean is obtained by adding several quantities together and dividing the sum by the number of quantities: the mean of 1, 5, 2, and 8 is 4.

median The midpoint of the numbers that are arranged in order of value.

mode A term referring to the most frequently occurring term in a set of numbers.

range The difference between the highest and lowest value in a set of numbers.

central tendency the tendency of samples of a given measurement to cluster around some central value.


the 3m’s and moreCHARACTERISTICS & PROCESSES OF SCIENCE

Aclass

assignment

NS 1.6.3 Compare scientific data using mean, median, mode and range using SI units.NS 1.6.5 Communicate results and conclusions from scientific inquiry.

1. make up a set of data that shows daily temperatures for the months of july and august. Then calculate the mean and the median.

Take it HomeKeep a walking log for 3 days.

Then calculate the mean number of minutes you walked each day, and the mean for the 3 days combined.



Aclass

assignment

answer key

1. make up a set of data that shows daily temperatures for the months of july and august. Then calculate the mean and the median. Answers may vary.



Bclass

assignment

NS 1.7.3 Interpret scientific data using mean, median, mode and range using SI units.NS 1.7.5 Communicate results and conclusions from scientific inquiry.


2. You’ve discovered that your lawn care business nets you a mode of $10. make up a set of data that supports that calculation.





Bclass

assignment

answer key


2. You’ve discovered that your lawn care business nets you a mode of $10. make up a set of data that supports that calculation. Answers may vary.



Cclass

assignment

NS 1.8.3 Interpret scientific data using mean, median, mode and range using SI units. NS 1.8.7 Communicate results and conclusions from scientific inquiry following peer review.


2. You’ve discovered that your lawn care business nets you a mode of $10. make up a set of data that supports that calculation.

3. List 3 advantages and 3 disadvantages of bulletin board or tri-fold presentations:

advantages

1. _______________________

2. _______________________

3. _______________________

disadvantages

1. _______________________

2. _______________________

3. _______________________





Cclass

assignment

answer key


2. You’ve discovered that your lawn care business nets you a mode of $10. make up a set of data that supports that calculation. Answers may vary.

3. List 3 advantages and 3 disadvantages of bulletin board or tri fold presentations:

advantages1. visually appealing

2. easy to carry around

3. can be left alone for viewing

disadvantages1. not very high tech

2. limited to the space on the board

3. must make the best use possible of your space

Documents

common measures of central tendency and …arkansasgardencorps.com/documents/lessons/The 3ms and...Measures of central tendency such as mean, median and mode allow the comparison of