Season 01 • Episode 06 • The consultant task
0The consultant task
Season 01
Episode 06 Time frame 1 period
Prerequisites :
Objectives :
•
Use statististo makea deision.Materials :
•
Slideshow.•
Info sheets in enveloppeswith seleted infosabout the situation.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 :
•
1 headmaster;•
1 deputy headmaster;•
1 shool aountant;•
1 teaher;•
1 representative of the regionalounil;•
1 representative of the parents.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 :
•
the standard deviationsof the twosets of exams (with amistake);•
the dot plots for the two sets of exams (with a mistake);•
the standard deviationsand dot plots of the two sets of exams (orreted);•
the raw data - this one should onlybegiven atthe end.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