Let’s explore ways to get representative samples.
A survey was taken at a movie theater to estimate the average age of moviegoers.
Here is a dot plot showing the ages of the first 20 people surveyed.
Take turns with your partner reading each option aloud. For each situation, discuss:
Lin is running in an election to be president of the seventh grade. She wants to predict her chances of winning. She has the following ideas for surveying a sample of the students who will be voting:
Ask everyone on her basketball team who they are voting for.
Ask every third girl waiting in the lunch line who they are voting for.
Ask the first 15 students to arrive at school one morning who they are voting for.
A nutritionist wants to collect data on how much caffeine the average American drinks per day. She has the following ideas for how she could obtain a sample:
Ask the first 20 adults who arrive at a grocery store after 10:00 a.m. about the average amount of caffeine they consume each day.
Every 30 minutes, ask the first adult who comes into a coffee shop about the average amount of caffeine they consume each day.
Your teacher will have some students draw straws from a bag.
| straw 1 | straw 2 | straw 3 | straw 4 | straw 5 | |
|---|---|---|---|---|---|
| sample 1 | |||||
| sample 2 |
Estimate the mean length of all the straws in the bag based on:
There were a total of 35 straws in the bag. Suppose we put the straws in order from shortest to longest and then assigned each straw a number from 1 to 35. For each of these methods, decide whether it would be fair way to select a sample of 5 straws. Explain your reasoning.
Computers accept inputs, follow instructions, and produce outputs, so they cannot produce truly random numbers. If you knew the input, you could predict the output by following the same instructions the computer is following. When truly random numbers are needed, scientists measure natural phenomena such as radioactive decay or temperature variations. Before such measurements were possible, statisticians used random number tables, like this:
Use this table to select a sample of 5 straws. Pick a starting point at random in the table. If the number is between 01 and 35, include that number straw in your sample. If the number has already been selected, or is not between 01 and 35, ignore it, and move on to the next number.
A sample is selected at random from a population if it has an equal chance of being selected as every other sample of the same size. For example, if there are 25 students in a class, then we can write each of the students' names on a slip of paper and select 5 papers from a bag to get a sample of 5 students selected at random from the class.
Other methods of selecting a sample from a population are likely to be biased. This means that it is less likely that the sample will be representative of the population as a whole. For example, if we select the first 5 students who walk in the door, that will not give us a random sample because students who typically come late are not likely to be selected. A sample that is selected at random may not always be a representative sample, but it is more likely to be representative than using other methods.
It is not always possible to select a sample at random. For example, if we want to know the average length of wild salmon, it is not possible to identify each one individually, select a few at random from the list, and then capture and measure those exact fish. When a sample cannot be selected at random, it is important to try to reduce bias as much as possible when selecting the sample.
