Random Sampling and Populations

Populations, Samples, and Generalizing from a Sample

Today, we will...

• learn about collecting data from a sample that is selected from a population

• what can be learned about the population by looking at a sample from that population

​represents every possible person that data can be collected from

​represents a portion of the entire population

Multiple Choice

A ______ is the entire set of objects from which data might be collected

• sample

• population

• numerical summary

• statistic

Multiple Choice

A _______ is a subset of the population.

• population

• numerical value

• statistic

• sample

Collecting Data

• ​Select randomly 5 seventh grade boys and record their shoe size in a table.

• ​Find the 5 boys in the class who has largest shoe size and record in a table.

​Student	​Shoe Size
​John	​10
​Brian	​7
​Henry	​8
​James	​7.5
​Caleb	​8

​Student	​Shoe Size
​John	​10
​Paul	​10
​William	​9
​Mark	​8.5
​Ben	​9

The first method is collected at random. The second method seeks out the largest shoe sizes.

​Which method from the previous slide shows more accurate representation of the population?

​Method 1 is a better representation of the population - chosen at random. Method 2 had a bias in pushing the data in a certain direction.

Bias

Example: Heidi decides to use a random sample to determine her classmates’ favorite color. She asks, “Is green your favorite color?” Is Heidi’s question biased? If so, give an example of an unbiased question that would serve Heidi better.

Statistical bias is a systematic tendency which causes differences between results and facts

​Answer: Heidi’s question is biased as it suggests that people should say their favorite color is green. “What is your favorite color?” is an unbiased question, as it doesn’t suggest a certain answer.

Multiple Choice

True or False: All samples lead to a good prediction about the entire population.

• True

• False

Multiple Choice

A student wants to know which type of of pizza high school students prefer. Which of the following options is a good, representative sample of the population?

• Asking all the 10th graders in the school

• Asking 20 students from each grade level

• Asking the school principal which type of pizza he prefers

• Asking the students who walk to school

Multiple Choice

A beverage company wants to see if people in the United States like their new logo. Which of the following represents the population?

• 2,000 people ages 5-13

• A selection of logo artists

• A selection of shoppers from different states

• all the people in the United States

Multiple Choice

A beverage company wants to see if people in the United States like their new logo. Which of the following represents the best choice for a sample?

• a collection of shoppers from different states

• all the people living in the United States

• a selection of logo artists

• 2,000 children from ages 5-13

Multiple Choice

Which of the following is NOT a reason why random samples are preferred over surveying the entire population.

• A random sample allows you to survey whoever you want.

• Surveying the entire population may cost too much money.

• Surveying the entire population takes too much time.

• Surveying the entire population can be a challenge because not everyone may respond.

Multiple Choice

Which of the following situations would you MOST want to collect a sample rather than surveying the entire population?

• the median price of homes in Ohio

• how many students in the class like mushrooms on their pizza

• how many students in the school have more than one pet

• the typical number of home runs for each player on the baseball team

Multiple Choice

A toy store owner wants to know how much kids spend each month on toys. Which choice is the best representation of the population?

• 220 wealthy kids

• all the kids who buy toys

• 100 boys ages 8-12

• 125 girls ages 10-15

Multiple Choice

Ana wants to know the average student’s opinion of the tardy policy at her school. Which group of students should she survey in order to achieve the most accurate results?

• 30 of her friends

• 30 randomly selected students in the school

• 30 students who are often tardy

• 30 students who are not often tardy

Multiple Choice

A survey company was trying to see if people in a state thought the pollution was too high. Which choice BEST represents the population to be surveyed?

• a selection of people who live in small towns

• a selection of people who live in clean neighborhoods

• a selection of people from each city in the state

• all the people in the state

Multiple Choice

A school principal wants to see which subject the 695 students in his school liked best. Which choice BEST represents a representative sample?

• all the girls in the school

• the students who have an A in math class

• the students who have a D in science class

• 1 classroom for each grade level

Multiple Choice

True or False: You want to see how many students take the bus home from school. You go to the bus stop and ask students how they get home everyday. This is a good, representation of the population.

• True

• False

Census

• when data is collected from an entire population

• The United States conducts a census of its population every 10 years

Open Ended

The United States conducts a census every 10 years. Why do you think the census is important in the United States?

Poll

How do you feel about the difference between population and sample and how a sample represents the population?

• I feel confident and I'm ready to move on

• I almost have it.

• I'm a little confused and have more questions.

• I am lost and need help.