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Distinguish between a population parameter and a sample statistic.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Data Analysis and Probability
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Data
- Population (in data analysis)
- Random sampling
- Statistical question
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grades 6 and 7, students examined creating statistical questions to formulate data, and they looked into different calculations that can be produced from data. In Mathematics for College Statistics, students explore the differences in populations/samples and parameters/statistics.
- Instruction defines a population to be all of a particular group, while a sample is a subset
of the population.
- For example, a population could be all students who attend Sunset High School, while a sample could be 100 randomly sampled students.
- Instruction emphasizes that calculations from data from an entire population produce
parameters. Calculations from data derived from a sample produce statistics.
- If 29.6% of all students at Sunset High School are freshman, 29.6% would be a parameter. If 32% of our random sample are freshman, then 32% would be a statistic.
- Instruction includes the idea that parameters and statistics can include percentages and modes (for categorical data) and means, medians, standard deviations, interquartile ranges, quartiles and ranges (for numerical data).
- Instruction includes examples where students identify populations, samples, parameters,
and statistics.
- For example, suppose that recent election results show that 49% of all eligible Leon County residents actually voted in the most recent election. A random sample of 200 randomly sample eligible Leon County residents is taken, and 53% say they intend to vote in the next election. The population would be all eligible Leon County residents, with a population parameter of 49%. The sample would be the 200 eligible Leon county residents, with 53% as the sample statistic.
- Instruction notes the difficulty in collecting data from every individual in a population, which therefore, makes actually calculating a true population parameter very difficult. Since samples are easier to obtain, statistics can be calculated more easily and then used to estimate a population parameter. Statistics are often referred to as estimators because of this.
- Instruction includes a discussion about the natural variation that occurs when comparing statistics to parameters and when comparing the statistics of one sample to the statistics of a different sample.
Common Misconceptions or Errors
- Students often have difficulty grasping that statistics and parameters are actual calculations. Students will sometimes confuse the parameter with the actual population or confuse the statistic with the actual sample. Other times they will misinterpret statistics and parameters as data instead of the calculations that result from the data.
Instructional Tasks
Instructional Task 1 (MTR.4.1)- Part A. Suppose we want to know the mean commute time of all employees who live in Florida. Identify the population of interest. Do you think it is possible to collect data from all employees who live in Florida? Explain your reasoning.
- Part B. Using the scenario above, what is the population parameter of interest? Do you think it is possible to actually calculate this particular value? Explain why or why not.
- Part C. Suppose we randomly sample 2000 employees from all over the state of Florida, and we calculate the mean commute time of these 2000 residents to be 26.8 minutes. Identify the sample and the statistic.
- Part D. Do you think the statistic from Part C would be an exact match for the population parameter we are interested in? Explain your reasoning.
Instructional Items
Instructional Item 1- An elementary school principal wants to know the typical amount of time that the parents of
students at her school spend reading to their children each week. She sends home a parent
survey with each child, and of the 173 surveys returned, she calculates the median to be 50
minutes of reading each week.
- Part A. Identify the population and parameter of interest.
- Part B. Identify the sample and statistic of interest.
Related Courses
This benchmark is part of these courses.
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond (current))
1210305: Mathematics for College Statistics (Specifically in versions: 2022 and beyond (current))
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
Related Resources
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Lesson Plan
Problem-Solving Task
Text Resource
Student Resources
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Parent Resources
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