# Four bean mix stats and prob investigation ```Name
Semester 2
Major Assessment Task: Four Bean Mix Investigation
Subject
Mathematics: Statistics and Probability
Year Level
8
Due Date
Conditions
Students will get 2 hours of class time and will be given approximately a week after this to finish this
Curriculum
Statistics and Probability
Data representation and interpretation




Distinguish between a population and a sample and investigate techniques for collecting
data, including census, sampling and observation (VCMSP297)
Explore the practicalities and implications of obtaining data through sampling using a variety
of investigative processes (VCMSP298)
Explore the variation of means and proportions of random samples drawn from the same
population (VCMSP299)
Investigate the effect of individual data values including outliers, on the range, mean and
median (VCMSP300)
Chance



Purpose




Identify complementary events and use the sum of probabilities to solve problems
(VCMSP294)
Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or'
(A or B or both) and 'and' (VCMSP295)
Represent events in two-way tables and Venn diagrams and solve related problems
(VCMSP296)
Students will increase their confidence in mathematical modelling of real life scenarios.
Students will become more familiar with the measures of centre and spread
Students will calculate expected values of probabilities
Students will develop their mathematics communication skills.
Your class has been contracted by Woolworths investigate the percentages of each bean in
their cans of “Woolworths Four Bean Mix”
Note: ingredients are usually listed from highest percentage of total weight to lowest
percentage.
Marking Rubric
Extended
Abstract
Explains how to
create a Venn
diagram and
two-way table
Synthesises all
information
(survey, tables,
cost) to create an
evidence backed
report to
Woolworths
Relational
Creates Venn
diagram and
two-way table
Multistructural
Creates column
graphs with
appropriate
features
Explains claims
using evidence
(mean, median,
mode)
Refers to
evidence in
report
Unistructural
Uses tables
Makes claims
Prestructural
Indicative
behaviors
Insufficient
evidence
Represents data
Insufficient
evidence
Interprets data
Capabilities
Assessment
Subject
Marks: _______ / 20
Comment:
Explains how to
create two way
tables and Venn
diagrams using
union and
intersection
symbols or
terminology
Uses probability
notation such as
Pr(C)
Discusses
measures of
centre in relation
to can label
information
Demonstrates an
algebraic
understanding of
expected value
Shows
working/evidenc
e for calculations
Calculates
expected number
of chickpeas
Presents
probabilities in
appropriate
format
(simplified
fractions or % or
decimal with
number of
decimal places
rounded to
communicated)
Includes units, %
signs, etc in
appropriate
places
Insufficient
evidence
Uses correct
notation and
terminology
Finds mean,
median and
mode for bean
number and
weight
Calculates
probabilities
from two-way
table or Venn
diagram
Communication
Finds mean,
Calculates
median or mode
probability of
for bean number chickpea from
or weight
data
Insufficient
Insufficient
evidence
evidence
Calculates
Calculates
measures of
probabilities
centre
Problem solving
Four Bean Mix
Year 8 Mathematics
calculated from the above rubric, one mark per criteria
You are to create a report (by hand or on iPad) that has the following information. Each part
must be clearly indicated with an appropriate title.
Part 1:


A photo/sketch of all the beans from one can organised by type – this needs to be
well labelled so the reader knows what they are looking at
A table which summarises the following information for at least 10 cans of beans.
You will need to collect data from your classmates.










Total number of beans, total number of each bean, for example:
Can
Number of Number of Number of Number of Total
chickpeas
Red
Green
Borlotti
number of
Kidney
Baby Lima beans
all beans
beans
beans
1
2
3
…
10
Total
The mean, median, mode and range for frequency of each type of bean and the total
number of beans (show working)
The percent of number of beans for each type of bean (show working)
A column graph which communicates the mean number of each type of bean in each.
Appropriate scale, title, axis labels are required
Same as above, but for weight of beans
Can
Weight of
Weight of
chickpeas
Red Kidney
beans
1
2
3
…
10
Total
Weight of
Green Baby
Lima beans
Weight of
Borlotti
beans
Total
weight of
beans
The mean, median, mode and range for total weight of each type of bean (show
working)
The percent (of total) in weight of beans for each type (show working)
A column graph which communicates the mean weight of each type of bean
Research the cost of each type of bean (on its own). Compare the costs using evidence
Survey at least 10 people, what is their favourite and least favourite type of bean out
of these four? Summarise the data in an appropriate format.


Write a short paragraph summarising the data collected, your findings on cost and
consumer preferences to report back to Woolworths.
Discuss: does the number and weight order data you have match the listed order of
ingredients on the can label?
Part 2:
One customer likes only chickpeas out of these four beans. They accidentally bought
hundreds of cans of “Woolworths Four Bean Mix” and now need some help figuring out how
many chickpeas they actually have.
Answer the following questions using the class data, show working:





On average, what is the probability of any one bean selected being a chickpea?
On average, what is the probability of any one bean selected NOT being a chickpea?
If they have 100 cans, how many individual chickpeas would they expect to have?
If they have 1070 cans, how many individual chickpeas would they expect to have?
If they have x cans, how many individual chickpeas would they expect to have? Write
Part 3:
Do a survey on your at least 20 people to find out if they:


Like (or dislike) chickpeas
Like (or dislike) red kidney beans
Represent this information visually:







Create a Venn diagram to represent this information
Create a two way table to represent this information
How many people did you survey in total?
How many people liked neither chickpeas nor red kidney beans?
How many people surveyed like chickpeas?
How many people like both red kidney beans and chickpeas?
How many people like chickpeas or red kidney beans (or both)?
For a randomly selected person, calculate the probability that they:




liked neither chickpeas nor red kidney beans?
like chickpeas?
like both red kidney beans and chickpeas?
like chickpeas or red kidney beans (or both)?
Write a brief paragraph explaining how to create a Venn diagram and two-way table step-bystep, as if you were teaching someone else to do it.
```