Titanic Tragedy-Part I:
A Develop Understanding Task
Part I
Data from http://en.wikipedia.org/wiki/RMS_Titanic
Art by Willy Stower
The RMS Titanic had 2224 people on board ship (including the children), yet there was lifeboat
space for only 1178. Various factors on that fateful day also made it so many lifeboats were not full
when they were launched.
Women
Person
category
1st Class
2nd Class
3rd Class
Crew
Total
Number
aboard
144
93
165
23
425
Number
saved
140
80
76
20
316
Men
Number
lost
4
13
89
3
109
Person
category
1st Class
2nd Class
3rd Class
Crew
Total
Number
aboard
175
168
462
885
1690
Number
saved
57
14
75
192
338
Number
lost
118
154
387
693
1352
Note: in addition to the adults there were 109 children, undifferentiated by gender, of which 56 died and 53 survived.
Create a variety of graphical representations to show relationships between survival and gender.
Historically when populations are in danger, societies protect women. Does the Titanic data
support this priority? In other words, is survival rate independent from gender? Use your graphical
representations and numerical evidence to support your conclusions.
Titanic Tragedy-Part I: – Teacher Notes
A Develop Understanding Task
Purpose: Develop student understanding around the concept of testing the independence of
possibly related variables. In the process, students will also solidify their understanding of 2-way
Tables, Venn Diagrams and conditional probabilities, as they refine
Surfaces ideas such as:
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finding conditional probabilities and using those probabilities to make conjectures about
independence between categories
recognizing the features of a two-way table indicates that a relationship is independent
(proportionality of a category to the total is maintained for conditions within the population)
explaining independence relationship in context of events
understanding that variability and sample sizes from random sampling might impact
probability decisions
giving evidence to support conclusions
Core Standards Focus:
S.CP.2: Understand that two events A and B are independent if the probability of A and B
occurring together is the product of their probabilities, and use this characterization to determine if
they are independent.
S.CP.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret
independence of A and B as saying that the conditional probability of A given B is the same as the
probability of A, and the conditional probability of B given A is the same as the probability of B.
Related Standards:
S.CP.1, S.CP.4, S.CP.5
Launch (Whole Class):
Ask: What do you know about the Titanic tragedy? (Janet: “Well, it sank.”)
Provide additional background about the Titanic tragedy.
Explore (Small Group):
Distribute the task sheets and allow participants to explore the data. Choose some individuals or
groups to share their graphical representations, numerical calculations, and conclusions about
conditional probabilities.
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We can expect to see Venn diagrams and 2-way tables because of the prior tasks.
Participants may also choose to compare data using bar graphs or circle graphs. Point out
that a bar graph does not show the relationship between survival and gender.
Compare and contrast different representations and ask participants to find similarities and
parallels. Look for representations that differ because counts were used rather than
percentages in comparing categories.
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Segmented bar graphs can lead to rich discussions about representing data, what kinds of
information can be obtained by displaying in counts vs. percents, and how the graphs
change.
This task uses categorical data. It is important to define displays of data carefully so that the
diagrams don’t have cases where an individual both dies and survives, or is both male and
female. This quality makes it difficult when thinking about how to construct a Venn
diagram, or how to label columns and rows in 2-way tables.
There are two variables represented in this task. If you are creating a two way table, one
variable represents the rows of data, and one represents the columns.
The idea of showing independence between categories is difficult to grasp and typically
takes exposure to multiple data sets, including both examples and non-examples, to gain a
solid understanding.
Look for evidence of understanding that if survival rate is dependent on gender (not
independent) then the percent of surviving women will be different than surviving men, and in
fact the percent of surviving women or men will be different than the overall survival rate.
Ask participants “What is the probability of survival?” Discuss how you decide how to
determine that probability and record on sticky the different probabilities of survival,
P(Survive), P(Survive|Female), P(Survive|Male) and compare. (If time allows other
probabilities could be compared.)
Discuss (Whole Class):
1. Ask participants to summarize the characteristics of data that would indicate independence
between categories, ie, that proportionality between categories of subgroups will equal each
other, and that of the overall population.
2. What would a segmented bar graph showing proportions look like for this data? (The bars would
be of equal length, and the “survive” portions would be equal at about 30%)
3. Formalize the proportionality relationship of independent events with the probability equation,
P(A)=P(A|B) [i.e., P(Survive) = P(Survive|Female)=P(Survive|Male)]
4. Have participants formalize a definition of independence both in a sentence and using probability
notation. Write these on a poster for display.
5. Relate the equation back to the Titanic data and verify conclusions.
6. Time permitting, you may productively use Titanic Tragedy-Part II together with this task (Part
I).