Grade 7 Mathematics
We can't always study everyone in a group (the population). Instead, we study a smaller group (a sample) and use it to make predictions about the whole population.
The KEY is making sure our sample is RANDOM - everyone has an equal chance of being chosen!
Population: The ENTIRE group you want to learn about
Example: All 500 students at your school
Sample: A SMALLER group selected from the population
Example: 50 students randomly selected from the school
Inference: A conclusion about the population based on sample data
Example: "About 60% of all students prefer pizza" (based on sample results)
Every member of the population has an EQUAL chance of being selected.
Examples:
Some members are MORE likely to be selected than others.
Examples:
Example: A random sample of 80 students shows 45 prefer chocolate ice cream.
Step 1: Find the percentage: 45/80 = 0.5625 = about 56%
Step 2: If there are 400 students total, predict: 0.56 x 400 = 224 students
Inference: About 224 students in the school prefer chocolate ice cream.
WRONG: "We surveyed 500 people at a health food store, and 90% said they eat healthy. So 90% of all Americans eat healthy!"
RIGHT: People at a health food store are more likely to eat healthy than average people. This sample is BIASED and doesn't represent all Americans. The location of sampling matters!
1. Identify if each sample is RANDOM or BIASED:
a) To survey student opinions on lunch, the principal selects every 5th student from an alphabetical list.
Circle: RANDOM / BIASED
b) A reporter asks people leaving a movie theater what kind of movies they like.
Circle: RANDOM / BIASED Why?
c) A researcher assigns each student a number and uses a computer to randomly select 30 numbers.
Circle: RANDOM / BIASED
2. A random sample of 60 students found that 24 walk to school.
a) What percentage of the sample walks to school? %
b) If there are 450 students at the school, predict how many walk to school: students
3. A company wants to know if customers like their new product. Which sampling method is BEST?
A) Survey customers who call to complain
B) Survey customers who write positive reviews online
C) Randomly select 100 customers from the purchase database
D) Survey employees about what customers say
Best answer: Why?
4. In a random sample of 75 voters, 45 support Candidate A.
a) What fraction of the sample supports Candidate A?
b) If 12,000 people will vote, predict how many will support Candidate A: