Mid-Topic Checkpoint
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Remember when a sample can be called representative.
What inference we could draw looking at the given table?
Use proportional reasoning to estimate the number of spectators based on the survey results.
Population: All spectators that attend games at a soccer field where Sunil works.
Example Way of Collecting a Sample: See solution.
Sunil can infer that most spectators attend 1 or 2 games during the soccer season.
About 800, see solution.
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How many games do most spectators attend during the soccer season? |
First let's determine the population for Sunil's survey. Remember that a population is an entire group of people from which data can be collected. In Sunil's study, the population is all spectators that attend games at a soccer field where Sunil works. Now, we want to think how Sunil could collect a representative sample of this population.
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Representative Sample |
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A sample that has the same characteristics as the population. |
There are some ways in which we can determine a representative sample. The most reliable way is to generate a random sample. For example, Sunil could assign each ticket a different integer and then draw some numbers randomly. People with ticket numbers Sunil drew could be then surveyed.
| Soccer Game Attendance | |
|---|---|
| Number of Games | Number of Spectators |
| 1-2 | 57 |
| 3-4 | 43 |
| 5 or more | 50 |
Based on the results from the survey, Sunil can infer that most spectators attend 1 or 2 games during the soccer season.
Now, we want to use the survey data to estimate the number of spectators n who attended 5 or more games this season if 2400 spectators attend at least 1 game this soccer season. Before we do that, let's take a look at the results of Sunil's survey and highlight the number of spectators in a sample that attended at least 5 games.
| Soccer Game Attendance | |
|---|---|
| Number of Games | Number of Spectators |
| 1-2 | 57 |
| 3-4 | 43 |
| 5 or more | 50 |
LHS * 2400=RHS* 2400
a/2400* 2400 = a
a/c* b = a* b/c
Calculate quotient
Rearrange equation