Populations and Samples

Good Morning!
Today we will be continuing with our study of Samples and Populations.

Do Now You want to conduct a survey of at least 10% of the 500 students at CHCS to determine how many will be coming to the next basketball game. (Write your answer on your own paper.)

How many people will you need to survey? How will you choose your sample so that it is representative?

Samples and Populations

Unit 5, Lessons 22 and 23

Let's Review!

Multiple Choice

A POPULATION is....

• Always the number of people in a city

• A group of people, animals, objects, etc. that you want to study

• All of the people in the school who are popular

Populations

Populations are groups of people,
animals, objects, etc. that you want to study

Populations are usually too large to study directly. For example, if you want to know how people will vote in an election, it is not feasible (reasonable) to ask every single person in a country. So we use a method called "sampling."

Multiple Choice

A statistical SAMPLE is....

• a subset of a population used to represent the whole
• a complete list of all individuals in a group
• a product you receive to test out in the store

A statistical sample is a SUBSET (a selected group that is less than the whole population) chosen to study specific characteristics of a population.

For example, suppose you want
to figure out how many people
in your school have 2 or more
siblings. You could choose 50
people at random and ask
how many siblings they have.

Multiple Select

VERY IMPORTANT!!!

In order to be valid (representative), a SAMPLE must be....
(select all that apply)

• Unbiased (chosen at random)

• Biased toward one characteristic

• Large enough to represent the whole

• Small enough to count on your fingers

Valid Statistical Samples

A sample can be assumed to represent the whole only if it is....

1) Chosen at RANDOM without bias toward a specific characteristic AND
2) LARGE ENOUGH to represent the whole.
(10% of the population is usually a good start)

Let's Practice!

Multiple Choice

A doctor for any adult over 18 years old wants to offer evening appointments and is interested to know how many of her clients would use these appointments. She makes a list of all patients aged 18 to 35 and randomly chooses every fifth person on the list to survey. Is this likely to be a representative sample?

• Yes, the sample method is random

• No, 1 out of 5 is not a large enough sample

• No, it does not include all ages and age may have an impact on preferences

• Yes, the sample is large enough

Multiple Choice

A baseball league has players who are 12 and 13 years old. Dakota considers three plans to select a representative sample.

Which method is LEAST likely to provide a valid sample?

• Plan A: Put the names of the 12 year olds in a box and select 10% without looking. Repeat for 13 year olds.

• Plan B: Select all the players on the team with the most wins this season.

• Plan C: Assign a random number to each player. Spin a spinner repeatedly to select numbers for a sample of 15% of the league.

Let's learn something new...

Making inferences about populations from samples

Making Inferences

An INFERENCE is an informed guess based on available information

Once you have a representative sample, you can use the information about this sample to make guesses about the population. The most common way to apply information to a population is using a PERCENT.

Multiple Choice

There are 406 students at Destiny's school.

She chooses 40 students at random and asks them how they get to school. In the sample...

16 ride the subway
8 walk
8 ride the bus
4 ride a bike

4 ride in a car

What PERCENT of students in her SAMPLE walk to school?

• 8%

• 40%

• 20%

Extrapolating to a Population

Extrapolation is the process of applying a known trend or proportion to a larger population.

Let's use the PERCENT of students in the sample who walk to school (20%) to make a prediction of the number of students in the POPULATION (406) who will walk to school.

(406)(.2) = 81.2
....so approximately 81 students in the whole school will likely walk to school.

Multiple Choice

PUT BOTH STEPS TOGETHER...
There are 406 students in Destiny's school, and 16 out of 40 students in her sample ride the subway. How many students in Destiny's SCHOOL can be expected to ride the subway?

• 16

• 81

• 162

IMPORTANT!
Predictions are not certainties!

Extrapolations made from samples are always LIKELY outcomes for the population, not definite.

Always make sure to check for INCORRECT answers that contain the idea that a specific outcome will DEFINITELY be the case.

Multiple Select

A random sample of 60 students are surveyed about electives they CURRENTLY take.
26 students take dance
10 students take engineering
9 students take music
15 students take computer science
Which statements about the students are true? Choose all that apply.

• There are many excellent dancers in the school.

• About 25% of the students are likely take computer science.

• In every 60 students, 9 will always take music.

• NEXT year, 9 out of every 60 students will take music.

• In a group of 120 students, about 20 are likely taking engineering.

Multiple Choice

Is Alex's estimate reasonable and why?

• Yes, 48 out of 120 people in the sample are seniors who buy tickets in the afternoon (40%).

• Yes, 15 out of 60 people who buy tickets in the evening are seniors according to the sample (25%).

• No, no seniors buy tickets in the evening.

• No, 57 out of 120 people who buy tickets in the evening are adults.

Let's Practice!
Page 490-492
(all problems not in the Quizizz)
Must do: At least three problems
Can do: Up to three more problems