mean,median,ormodepencilactivity

8/6/2019 Mean,Median,orModepencilactivity

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Mean, Median, or Mode

Which one is my pencil?


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Made by activity set in classroom


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Rationale

Determination of mean, median, andmode are often presented as roteprocess.

However, in many instances, noconceptual meanings are associatedwith the algorithms or graphicalmethods.


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Introducing the activity

Two factors should be considered beforebeginning this activity

Choice of pencils and class size.

Since one purpose of the activity is to havestudents find the mean and median lengthsof pencils, do not use mechanical pencils.

Use wooden pencils that have beensharpened to different lengths, and hand

those to students for the activity.


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Penciling in the activity

Although the emphasis of the activityis on statistical concepts, it beginswith estimation and measurement.

After students estimate the length oftheir pencil in centimetres, theymeasure the actual length.

They record their values and those ofthe class in the table on activity sheet1.


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Discussion

Discuss with students how much theirestimates differed from the actualmeasurements, followed by probable

reasons for the differences.


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Since pencils cannot be folded or cut,students should next measure twostrips of paper that are equal to the

length of their pencil, then put theirname and measurements on thestrips for record-keeping purposes.

It is important for students to be ableto easily identify their pencil/paper

strips from everyone elses.


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Instruction for students

measure two strips of paper thatare equal to the length of yourpencil, then put your name and

measurements on the strips forrecord-keeping purposes.


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Take one paper pencil from each student,organise them by length, and tape themtogether into one long strip.

Collect the second paper pencil from eachstudent, and keep them in a separate pile.

The taped set should be used when findingthe mean; the other set will be used whenfinding median and mode.


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Physical determination of mean

Use the long taped strip and fold itnumerous times to find the mean.

See Activity sheet 2

The students simply fold the paper into thenumber of pieces equal to the number ofobservations (16 or 32).

At this point, lead an informal discussion ofpowers of 2, since it will take either four orfive folds to get 16 or 32 equal pieces,respectively.


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Once the paper folding is complete,students should be able to see theequal pieces while being able to view

all the original pencils lengths. The length of each equal piece is the

mean.


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Although this method enhancesstudents understanding of mean, wefeel it is important to explore the

concept further. Students should compare their

individual pencil length with the meanand explain why there areobservations both above and below

the mean.


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By using pencils that are sharpened tovarious lengths at the start, we control thevariability of the data set.

If our goal is to look at evenly distributeddata, we will use pencils that do not havelengths at one extreme or the other.

This allows students to see that the numberof pencils above the mean as compared

with those below the mean is roughlyequivalent.


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If our goal is to examine outliers, wewill distribute pencils that are muchshorter or much longer.

Students then see that balance ismore difficult to create; more pencillengths on one side or the other ofthe mean will provide a physical

example of skewed data.


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Mean and mode

Students finish their exploration ofthe mean by using the mathematicalformula, which involves adding all the

data and dividing by the number ofpencils

See activity sheet 3.


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Students should place the other classset of strips alongside each other,ordered from smallest to largest,

resembling a staircase. Unimodal or bimodal?


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With the strips remaining in order, wenow find the median.

Since the data set will be an even

number of observations, finding themedian requires using the middle twoobservations.

Quartiles?


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outliers

Use extremely short or long pencils toillustrate the effect of outliers on themean, and then contrast the effect of

outliers on the median.


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The big payoff

Ask the students, what will happen ifonly one pencil was in the data set?

Student discover that they cannot

make a fold, so a number raised tothe zero power is 1.


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conclusion

Leaning intentions: using hands on physicalmodels for familiar concepts, revisitingestimation and measurement andintroducing power of 2.

KC: Thinking (clarifying concepts),appreciating variability in real world: usinglanguage, symbol and text; cooperation,helping others, working together.

mean,median,ormodepencilactivity

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