Stats – Modified Boxplots Worksheet
Name: _________________________
Enter the data (Average Math Score on the 2006 PISA for OECD Member
Countries as well as Partners) into your calculator and answer the following
questions
Find the:
Max.:
Q3:
Med.:
Q1:
Min.:
_____
_____
_____
_____
_____
Mean: _____
Range: _____
IQR: _____
Calculate the upper fence (Q3 + 1.5IQR):
Are there any values above the upper fence (i.e. outliers)? If so, list them:
Now, list the highest value in the data set that is below the upper fence:
This is where your right whisker will extend to.
Calculate the lower fence (Q1 – 1.5IQR):
Are there any values below the lower fence (i.e. outliers)? If so, list them:
Now, list the lowest value in the data set that is above the lower fence:
This is where your left whisker will extend to.
Draw the modified boxplot of this data below (draw dashed lines to indicate the
fence locations):
360 370 380 390 400 410 420 430 440
450 460 470 480
490 500
Finland
Hong Kong-China
Korea
Netherlands
Switzerland
Canada
Liechtenstein
Macao-China
Japan
New Zealand
Belgium
Australia
Denmark
Czech Republic
Iceland
Austria
Germany
Sweden
Ireland
France
Poland
United Kingdom
Slovak Republic
Hungary
Luxembourg
Norway
Latvia
Spain
Russian Federation
United States
Portugal
Italy
Greece
Uruguay
Turkey
Thailand
Mexico
Indonesia
Brazil
Tunisia
510 520 530
540 550
548
547
547
531
530
527
525
525
523
522
520
520
513
510
506
505
504
502
501
496
495
495
492
491
490
490
486
480
476
474
466
462
459
427
424
417
406
391
370
365
From the boxplot, does it appear that the data is skewed? If so, in what direction?
Construct a histogram of the data and sketch it below:
On your histogram,
mark where the
mean, median, and
quartiles are. Also,
mark where the
USA’s score is.
360 370 380 390 400 410
420 430 440
450 460 470 480
490 500
510 520 530 540
550
According to your histogram, are there any outliers present in the data?
If yes, what are they?
Is your list of outliers the same as your list that you obtained from your lower and upper fence?
Now that you have the boxplot and the histogram, describe the distribution:
Is the mean of this data significantly different than the median? If so, why do you think that is?
Approximately what percent of the total scores are below the United States’ score?
This value would represent the U.S.’s percentile ranking.
Would you consider the U.S.’s score to be representative of the scores on this list? Why or why not?
Background Info: The Organisation for Economic Co-operation and Development, or OECD, comprises 30 member countries sharing a
commitment to democratic government and the market economy. PISA is an acronym taken from the name Programme for
International Student Assessment. Schools in each country are randomly selected by the international contractor for participation in
PISA. At these schools, the test is given to students who are between age 15 years 3 months and age 16 years 2 months at the time of
the test, rather than to students in a specific year of school. The selection of schools and students is kept as inclusive as possible, so
that the sample of students comes from a broad range of backgrounds and abilities.