Venn Diagrams
What is a venn diagram used for?
To show the relationships between different sets of data
What is the "median" of these numbers?
3, 8, 6, 2, 9
6
(Put in order: 2, 3, 6, 8, 9 → middle value is 6)
What is a sample in a survey?
A smaller group selected from a larger population to represent the whole.
In a Venn diagram, what does the overlapping part of two circles represent?
Elements that are common to both sets
A class survey showed that 12 students have a pet and 8 do not. Out of the 12 with pets, 5 are boys. How many girls have a pet? A table shows the number of students who prefer juice or water, split by gender:
7 girls
(12 students have pets – 5 boys = 7 girls)
How many possible outcomes are there when you flip a coin and roll a 6 sided die?
2*6 = 12
What is an outlier in a data set?
A value that is much higher or lower than the rest of the data — it doesn’t fit with the pattern.
Why is it important to use a random sample in a survey?
To avoid bias and make the results more representative of the population.
Set A = {2, 4, 6, 8},
Set B = {6, 8, 10}.
Draw the Venn diagram
Show the correct answer
Out of 30 students, 18 like science and 15 like maths. If 10 like both, how many students like only science?
8 students
(18 total like science – 10 who like both = 8 only science)
You pick a red or blue sweet from a bag, then spin a spinner with 3 colors. How many branches will the full tree diagram have at the second level?
6 branches
(2 choices for sweet × 3 spinner outcomes = 6 total outcomes)
A student got these marks: 7, 9, 8, 10, 2, 7, 8, 7, 9
What is the outlier, and how does it affect the mean?
The outlier is 2, and it lowers the mean.
A school has 600 students. Only 60 are surveyed about lunch options. What percentage of the whole school is this?
10%
(60 ÷ 600 × 100 = 10%)
In a class of 30 students, 18 like maths, 12 like science, and 5 like both. How many students like only maths?
13 students
(18 total like maths – 5 who like both = 13 only maths)
In a school, 20 students are in the drama club, 25 are in the music club, and 10 are in both. How many students are in either drama or music, but not both?
25 students
(Drama only: 20 – 10 = 10; Music only: 25 – 10 = 15; Total = 10 + 15 = 25)
There are 2 red balls and 1 green ball in a bag. You pick one ball, do not put it back, and pick another. What is the probability of picking two red balls?
1/3
(First red: 2/3; second red after red: 1/2 → 2/3 × 1/2 = 1/3)
You are given this data: 5, 6, 8, 8, 9, 12, 14, 9
A new number is added, and now the mode is no longer 8. What number might have been added?
9
A survey asks: "Don’t you agree that our school cafeteria is the best?" What’s wrong with this question?
It’s a leading question — it encourages people to agree, which makes it biased.
In a survey, 25 students like pizza, 20 like burgers, and 10 like both. How many students like only pizza or only burgers?
25 students
(Only pizza: 25 – 10 = 15, Only burgers: 20 – 10 = 10. Total = 15 + 10 = 25)
In a survey of 50 students, 28 said they walk to school, and 18 of them are girls. If 12 boys also walk to school, how many boys were surveyed in total?
20 boys
(18 girls + 12 boys = 30 walkers; 50 total – 30 = 20 non-walkers; all non-walkers must be boys: 12 walkers + 8 non-walkers = 20 boys)
You spin a spinner with equal sections labeled A, B, and C, twice. What is the probability of getting A then B?
1/9
(Each spin: 1/3 chance → 1/3 × 1/3 = 1/9)
A student has test scores of 80, 85, 90, and 95. What score must they get on the 5th test to have a mean of 90?
100
(Sum of current scores: 80 + 85 + 90 + 95 = 350; total needed for mean of 90 over 5 tests = 90 × 5 = 450; 450 – 350 = 100)
You want to know how students in your school feel about homework. Which is the best sampling method?
A. Ask only your friends
B. Ask all students in your year
C. Randomly select students from all year levels
C. Randomly select students from all year levels