Season 01 • Episode 06 • The consultant task

Season 01 • Episode 06 • The consultant task

The consultant task

Season 01

Episode 06 Time frame 1 period

Prerequisites :

Objectives :

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Materials :

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For this ativity,the lass isdivided in groupsof (ideally) 6 pupils.

1 – The cast 5 mins

The pupils in eahgroup of 6 have toat asadministratorsof a large shool :

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2 – The situation 10 mins

The teaher explains the situationwith aslideshow, emphasizingthe deisionthathas to

bemade.

To improve students' test sores on state assessments, administrators from a

large shool require studentsto take pratie exams. Two outsideonsultants

reate and sore the open-ended questions from these exams. Although both

onsultants use the same general sheme to sore student responses, the ad-

ministrators suspet that the two onsultantsdo not interpretand apply the

sheme inthe same way, resultingin dierenes insores between the exams

sored by the two onsultants.The onsultants'ontrats with the shoolare

up for renewal, and the administrators are trying to deideif they should be

renewed. They deide to use the most reent pratie exam to ompare the

soresassignedfromeahonsultantandtodeidewhetherthereisadierene

inthewaytheexamsaresored.Theadministratorsselet50examssoredby

the rst onsultant and 50 exams sored by the seond onsultant.They nd

that the average sore for the 50 exams sored by the rst onsultant is 9.7

(out of a possible 15 points), while the average sore for the 50 exams sored

by theseondonsultantis10.3(outofapossible15points). Whatshouldthe

the two onsultants. He sends the additional info as a letter in an enveloppe. If a group

doesn'taskforinformationtheteaheranneverthelesssendalettertohelpthedisussion

move forwards.

The omity has to ome toa deisionat the end of the hour.

Additionnal informationare, in the order they should be handed out :

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The consultant task

Season 01

Episode 06

Document Info sheet #1

Standard deviations

While the mean is a statistial measure of entral tendeny, the standard deviation is a

measure ofdispersion.Eventhoughtheomputationitselfisabitompliated,intuitively

it givesan idea of how the values are spread. It shows how muh variation there is from

the mean. A low standard deviation indiates that the data points tend to be very lose

tothe mean,whereashigh standarddeviationindiatesthat thedata isspreadout overa

large range of values. Withsores out of a possible 15 points, astandard deviationlose

to1would beonsideredverysmall, whileastandard deviationequalto5ormorewould

bevery high.

Consultant 1 Consultant 2

First quartile 7 6

Median 11 7.5

Third quartile 12 8

Mean 9.7 10.3

Dot plots

Consultant 1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

Consultant 2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

The consultant task

Season 01

Episode 06

Document Info sheet #3

Corrected standard deviations and dot plots

Consultant 1 Consultant 2

First quartile 7 6

Median 11 7.5

Third quartile 12 8

Mean 9.7 7.6

Standard deviation 3.376 1.726

Consultant 1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

Consultant 2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

Raw data

Consultant 1 Consultant 1

Sore Frequeny Sore Frequeny

0 0 0 0

1 0 1 0

2 1 2 0

3 2 3 0

4 2 4 0

5 0 5 2

6 6 6 13

7 3 7 10

8 5 8 13

9 1 9 8

10 3 10 2

11 8 11 1

12 9 12 0

13 4 13 0

14 5 14 0