Math Problem Statement

Ali wants to find the average time it takes Lincoln High School students to run a lap around the track. He considers a sample of students to find the average time. (a) Which unit(s) could be used for the unit of measurement? (b) Which of the procedures would be the best way to find the average time?

Solution

Let's go over the two parts of the question in your image:

(a) Units of Measurement:

The question asks which units could be used for measuring the time it takes students to run a lap. The units that could apply for time are:

  • Minutes (plausible for longer times).
  • Seconds (appropriate for short lap times).

Units like centimeters, meters, and hours are not appropriate:

  • Centimeters and meters measure distance, not time.
  • Hours would be far too large for such short activities like running a lap.

Thus, the correct answers for part (a) are:

  • Minutes
  • Seconds

(b) Best Procedure to Find the Average Time:

You are asked to select the best procedure to find the average time. The goal is to get a reliable and unbiased sample that accurately represents the whole student population.

Among the options:

  • Asking students to state their own times is prone to inaccuracies since they may not be precise.
  • Measuring the time of only 4 students may not provide a large enough sample to be representative.

The best option would be:

  • Randomly picking 24 students and measuring their times. This method provides a larger, randomized sample and ensures accuracy by using proper measurements.

Thus, the best choice for part (b) is:

  • Randomly pick 24 students to run a lap around the track and measure their times.

Do you have any questions or would you like more details on these concepts?

Here are 5 related questions you might want to explore:

  1. Why is it important to use random selection in experiments?
  2. What is the benefit of using a larger sample size for calculating averages?
  3. How does the unit of measurement affect the precision of time tracking?
  4. What are some methods to ensure accurate time measurements in running events?
  5. How could we visualize the data collected from the 24 students?

Tip: Random sampling helps avoid bias and makes the results more representative of the entire population.

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Math Problem Analysis

Mathematical Concepts

Time Measurement
Statistics
Random Sampling
Average Calculation

Formulas

Average = (Sum of individual times) / (Number of students)

Theorems

Law of Large Numbers
Sampling Theory

Suitable Grade Level

Grades 6-8